From 3a026f3ff6f371025aa14d71e44cc91998aa0579 Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Wed, 15 Apr 2026 17:16:19 +0200 Subject: [PATCH 01/25] add parsing of ECC group from ECC parameters --- doc/api_ref/pubkey.rst | 21 +- readme.rst | 2 +- src/build-data/oids.txt | 21 + src/cli/perf_pk_sig.cpp | 68 +++ src/lib/asn1/static_oids.cpp | 74 ++- src/lib/ffi/ffi.h | 16 + src/lib/ffi/ffi_pkey_algs.cpp | 59 ++ .../dilithium/dilithium_common/dilithium.cpp | 107 +++- .../dilithium_symmetric_primitives.cpp | 6 +- .../dilithium_symmetric_primitives.h | 10 +- src/lib/pubkey/dilithium/ml_dsa/ml_dsa_impl.h | 5 +- src/lib/pubkey/ecc_key/ecc_key.cpp | 27 +- src/lib/pubkey/mldsa-composite/info.txt | 22 + src/lib/pubkey/mldsa-composite/mldsa_comp.cpp | 435 ++++++++++++++ src/lib/pubkey/mldsa-composite/mldsa_comp.h | 157 +++++ .../mldsa-composite/mldsa_comp_parameters.cpp | 444 ++++++++++++++ .../mldsa-composite/mldsa_comp_parameters.h | 136 +++++ src/lib/pubkey/pk_algs.cpp | 36 ++ src/tests/data/pubkey/api_sign.vec | 5 + src/tests/data/pubkey/mldsa_composite.vec | 171 ++++++ src/tests/test_dilithium.cpp | 64 ++ src/tests/test_ffi.cpp | 36 +- src/tests/test_mldsa_composite.cpp | 546 ++++++++++++++++++ 23 files changed, 2438 insertions(+), 30 deletions(-) create mode 100644 src/lib/pubkey/mldsa-composite/info.txt create mode 100644 src/lib/pubkey/mldsa-composite/mldsa_comp.cpp create mode 100644 src/lib/pubkey/mldsa-composite/mldsa_comp.h create mode 100644 src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp create mode 100644 src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h create mode 100644 src/tests/data/pubkey/mldsa_composite.vec create mode 100644 src/tests/test_mldsa_composite.cpp diff --git a/doc/api_ref/pubkey.rst b/doc/api_ref/pubkey.rst index cce2414d6d7..eb072fbf8ef 100644 --- a/doc/api_ref/pubkey.rst +++ b/doc/api_ref/pubkey.rst @@ -168,6 +168,15 @@ Currently two flavors of Dilithium are implemented in separate Botan modules: * ``dilithium_aes``, that uses AES instead of Keccak-based primitives. This mode is deprecated and will be removed in a future release. +ML-DSA (draft-ietf-lamps-pq-composite-sigs-15) +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +Composite signature algorithms combining ML-DSA with a traditional signature algorithm. All +variants defined in draft-ietf-lamps-pq-composite-sigs-15 are supported. Each is modelled as a +distinct algorithm in Botan. The module for the composite algorithms is given by `mldsa-composite`, but note that +naturally only those algorithm combinations are available for which the respective module +support is compiled. + + ML-KEM (FIPS 203) ~~~~~~~~~~~~~~~~~ @@ -1039,7 +1048,17 @@ Botan implements the following signature algorithms: - ``,`` #. ML-DSA (Dilithium). - Takes the optional parameter ``Deterministic`` (default) or ``Randomized``. + Takes and optional parameter string formed by comma-separated list of the following format ``[(Deterministic|Randomized),][Pure,][ctx_hex=]``, where the ordering of the comma-separated elements is arbitrary. The specification of ``Pure`` is redundant since currently only the pure variant of ML-DSA is implemented. The defaults of the other values are ``Randomized`` and an empty context parameter (`ctx_hex`). Non-empty context parameters are only supported by ML-DSA, but not by Dilithium. ``Deterministic`` or ``Randomized`` may also be specified in a verification operation thought it has no effect there. + +#. ML-DSA-composite (draft-ietf-lamps-pq-composite-sigs-15). + Takes no parameters. The following algorithms are defined and are accessed by the respective + string value: MLDSA44-RSA2048-PKCS15-SHA256, MLDSA65-RSA3072-PKCS15-SHA512, + MLDSA65-RSA4096-PKCS15-SHA512, MLDSA44-RSA2048-PSS-SHA256, MLDSA65-RSA3072-PSS-SHA512, + MLDSA65-RSA4096-PSS-SHA512, MLDSA87-RSA3072-PSS-SHA512, MLDSA87-RSA4096-PSS-SHA512, + MLDSA44-ECDSA-P256-SHA256, MLDSA65-ECDSA-P256-SHA512, MLDSA65-ECDSA-P384-SHA512, + MLDSA65-ECDSA-brainpoolP256r1-SHA512, MLDSA87-ECDSA-P384-SHA512, + MLDSA87-ECDSA-brainpoolP384r1-SHA512, MLDSA87-ECDSA-P521-SHA512, MLDSA44-Ed25519-SHA512, + MLDSA65-Ed25519-SHA512, MLDSA87-Ed448-SHAKE256 #. SLH-DSA. Takes the optional parameter ``Deterministic`` (default) or ``Randomized``. #. XMSS. Takes no parameter. diff --git a/readme.rst b/readme.rst index 78a77e5c83b..7ad1fbea70d 100644 --- a/readme.rst +++ b/readme.rst @@ -116,7 +116,7 @@ Public Key Cryptography * RSA signatures and encryption * DH, ECDH, X25519 and X448 key agreement * Elliptic curve signature schemes ECDSA, Ed25519, Ed448, ECGDSA, ECKCDSA, SM2 -* Post-quantum signature schemes ML-DSA (Dilithium), SLH-DSA (SPHINCS+), HSS/LMS, XMSS +* Post-quantum signature schemes ML-DSA (Dilithium), ML-DSA-composite, SLH-DSA (SPHINCS+), HSS/LMS, XMSS * Post-quantum key encapsulation schemes ML-KEM (Kyber), FrodoKEM, Classic McEliece Ciphers, hashes, MACs, and checksums diff --git a/src/build-data/oids.txt b/src/build-data/oids.txt index 1ab9e883541..64c4dd164ef 100644 --- a/src/build-data/oids.txt +++ b/src/build-data/oids.txt @@ -493,3 +493,24 @@ 1.3.6.1.4.1.25258.4.1 = numsp256d1 1.3.6.1.4.1.25258.4.2 = numsp384d1 1.3.6.1.4.1.25258.4.3 = numsp512d1 + +# ML-DSA composite from draft-ietf-lamps-pq-composite-sigs +1.3.6.1.5.5.7.6.37 = MLDSA44-RSA2048-PSS-SHA256 +1.3.6.1.5.5.7.6.38 = MLDSA44-RSA2048-PKCS15-SHA256 +1.3.6.1.5.5.7.6.39 = MLDSA44-Ed25519-SHA512 +1.3.6.1.5.5.7.6.40 = MLDSA44-ECDSA-P256-SHA256 +1.3.6.1.5.5.7.6.41 = MLDSA65-RSA3072-PSS-SHA512 +1.3.6.1.5.5.7.6.42 = MLDSA65-RSA3072-PKCS15-SHA512 +1.3.6.1.5.5.7.6.43 = MLDSA65-RSA4096-PSS-SHA512 +1.3.6.1.5.5.7.6.44 = MLDSA65-RSA4096-PKCS15-SHA512 +1.3.6.1.5.5.7.6.45 = MLDSA65-ECDSA-P256-SHA512 +1.3.6.1.5.5.7.6.46 = MLDSA65-ECDSA-P384-SHA512 +1.3.6.1.5.5.7.6.47 = MLDSA65-ECDSA-brainpoolP256r1-SHA512 +1.3.6.1.5.5.7.6.48 = MLDSA65-Ed25519-SHA512 +1.3.6.1.5.5.7.6.49 = MLDSA87-ECDSA-P384-SHA512 +1.3.6.1.5.5.7.6.50 = MLDSA87-ECDSA-brainpoolP384r1-SHA512 +1.3.6.1.5.5.7.6.51 = MLDSA87-Ed448-SHAKE256 +1.3.6.1.5.5.7.6.52 = MLDSA87-RSA3072-PSS-SHA512 +1.3.6.1.5.5.7.6.53 = MLDSA87-RSA4096-PSS-SHA512 +1.3.6.1.5.5.7.6.54 = MLDSA87-ECDSA-P521-SHA512 + diff --git a/src/cli/perf_pk_sig.cpp b/src/cli/perf_pk_sig.cpp index bf5fd0d59fd..67e9f62aaa6 100644 --- a/src/cli/perf_pk_sig.cpp +++ b/src/cli/perf_pk_sig.cpp @@ -13,6 +13,11 @@ #include #endif +#if defined(BOTAN_HAS_MLDSA_COMPOSITE) + #include + #include +#endif + namespace Botan_CLI { namespace { @@ -405,4 +410,67 @@ BOTAN_REGISTER_PERF_TEST("ML-DSA", PerfTest_ML_DSA); } // namespace +#if defined(BOTAN_HAS_MLDSA_COMPOSITE) + +template +class PerfTest_MLDSA_Composite final : public PerfTest_PKSig { + public: + std::string algo() const override { return Botan::MLDSA_Composite_Param::from_id_supported_or_throw(A).id_str(); } + + std::string hash() const override { return ""; } + + std::vector keygen_params(const PerfConfig& /*config*/) const override { + return {Botan::MLDSA_Composite_Param::from_id_supported_or_throw(A).id_str()}; + } +}; + +// NOLINTNEXTLINE(cppcoreguidelines-macro-usag) + #define BOTAN_REGISTER_PERF_TEST_TMPL(name, Perf_Class) \ + /* NOLINTNEXTLINE(cert-err58-cpp) */ \ + const Botan_CLI::PerfTest::Registration reg_perf_##Perf_Class##_##name( \ + #name, []() -> std::unique_ptr { \ + /* NOLINTNEXTLINE(bugprone-macro-parentheses) */ \ + return std::make_unique>(); \ + }) + + #if defined(BOTAN_HAS_RSA) +BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA44_RSA2048_PKCS15_SHA256, PerfTest_MLDSA_Composite); +BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA65_RSA3072_PKCS15_SHA512, PerfTest_MLDSA_Composite); +BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA65_RSA4096_PKCS15_SHA512, PerfTest_MLDSA_Composite); + #endif + #if defined(BOTAN_HAS_PSS) +BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA44_RSA2048_PSS_SHA256, PerfTest_MLDSA_Composite); +BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA65_RSA3072_PSS_SHA512, PerfTest_MLDSA_Composite); +BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA65_RSA4096_PSS_SHA512, PerfTest_MLDSA_Composite); +BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA87_RSA3072_PSS_SHA512, PerfTest_MLDSA_Composite); +BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA87_RSA4096_PSS_SHA512, PerfTest_MLDSA_Composite); + #endif + #if defined(BOTAN_HAS_ECDSA) + #if BOTAN_HAS_PCURVES_SECP256R1 +BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA44_ECDSA_P256_SHA256, PerfTest_MLDSA_Composite); +BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA65_ECDSA_P256_SHA512, PerfTest_MLDSA_Composite); + #endif + #if BOTAN_HAS_PCURVES_SECP384R1 +BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA65_ECDSA_P384_SHA512, PerfTest_MLDSA_Composite); +BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA87_ECDSA_P384_SHA512, PerfTest_MLDSA_Composite); + #endif + #if BOTAN_HAS_PCURVES_BRAINPOOL256R1 +BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA65_ECDSA_brainpoolP256r1_SHA512, PerfTest_MLDSA_Composite); + #endif + #if BOTAN_HAS_PCURVES_BRAINPOOL384R1 +BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA87_ECDSA_brainpoolP384r1_SHA512, PerfTest_MLDSA_Composite); + #endif + #if BOTAN_HAS_PCURVES_SECP521R1 +BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA87_ECDSA_P521_SHA512, PerfTest_MLDSA_Composite); + #endif + #endif + #if defined(BOTAN_HAS_ED25519) +BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA44_Ed25519_SHA512, PerfTest_MLDSA_Composite); +BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA65_Ed25519_SHA512, PerfTest_MLDSA_Composite); + #endif + #if defined(BOTAN_HAS_ED448) && defined(BOTAN_HAS_SHAKE) +BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA87_Ed448_SHAKE256, PerfTest_MLDSA_Composite); + #endif +#endif + } // namespace Botan_CLI diff --git a/src/lib/asn1/static_oids.cpp b/src/lib/asn1/static_oids.cpp index f6c7fc77473..659e23941a0 100644 --- a/src/lib/asn1/static_oids.cpp +++ b/src/lib/asn1/static_oids.cpp @@ -1,5 +1,5 @@ /* -* This file was automatically generated by ./src/scripts/dev_tools/gen_oids.py on 2026-05-13 +* This file was automatically generated by ./src/scripts/dev_tools/gen_oids.py on 2026-05-28 * All manual changes will be lost. Edit the script instead. * * Botan is released under the Simplified BSD License (see license.txt) @@ -583,6 +583,42 @@ std::optional OID_Map::lookup_static_oid(const OID& oid) { return if_match(oid, {1, 3, 6, 1, 5, 5, 7, 3, 8}, "PKIX.TimeStamping"); case 0x94929: return if_match(oid, {1, 3, 6, 1, 5, 5, 7, 3, 9}, "PKIX.OCSPSigning"); + case 0x94B88: + return if_match(oid, {1, 3, 6, 1, 5, 5, 7, 6, 37}, "MLDSA44-RSA2048-PSS-SHA256"); + case 0x94B89: + return if_match(oid, {1, 3, 6, 1, 5, 5, 7, 6, 38}, "MLDSA44-RSA2048-PKCS15-SHA256"); + case 0x94B8A: + return if_match(oid, {1, 3, 6, 1, 5, 5, 7, 6, 39}, "MLDSA44-Ed25519-SHA512"); + case 0x94B8B: + return if_match(oid, {1, 3, 6, 1, 5, 5, 7, 6, 40}, "MLDSA44-ECDSA-P256-SHA256"); + case 0x94B8C: + return if_match(oid, {1, 3, 6, 1, 5, 5, 7, 6, 41}, "MLDSA65-RSA3072-PSS-SHA512"); + case 0x94B8D: + return if_match(oid, {1, 3, 6, 1, 5, 5, 7, 6, 42}, "MLDSA65-RSA3072-PKCS15-SHA512"); + case 0x94B8E: + return if_match(oid, {1, 3, 6, 1, 5, 5, 7, 6, 43}, "MLDSA65-RSA4096-PSS-SHA512"); + case 0x94B8F: + return if_match(oid, {1, 3, 6, 1, 5, 5, 7, 6, 44}, "MLDSA65-RSA4096-PKCS15-SHA512"); + case 0x94B90: + return if_match(oid, {1, 3, 6, 1, 5, 5, 7, 6, 45}, "MLDSA65-ECDSA-P256-SHA512"); + case 0x94B91: + return if_match(oid, {1, 3, 6, 1, 5, 5, 7, 6, 46}, "MLDSA65-ECDSA-P384-SHA512"); + case 0x94B92: + return if_match(oid, {1, 3, 6, 1, 5, 5, 7, 6, 47}, "MLDSA65-ECDSA-brainpoolP256r1-SHA512"); + case 0x94B93: + return if_match(oid, {1, 3, 6, 1, 5, 5, 7, 6, 48}, "MLDSA65-Ed25519-SHA512"); + case 0x94B94: + return if_match(oid, {1, 3, 6, 1, 5, 5, 7, 6, 49}, "MLDSA87-ECDSA-P384-SHA512"); + case 0x94B95: + return if_match(oid, {1, 3, 6, 1, 5, 5, 7, 6, 50}, "MLDSA87-ECDSA-brainpoolP384r1-SHA512"); + case 0x94B96: + return if_match(oid, {1, 3, 6, 1, 5, 5, 7, 6, 51}, "MLDSA87-Ed448-SHAKE256"); + case 0x94B97: + return if_match(oid, {1, 3, 6, 1, 5, 5, 7, 6, 52}, "MLDSA87-RSA3072-PSS-SHA512"); + case 0x94B98: + return if_match(oid, {1, 3, 6, 1, 5, 5, 7, 6, 53}, "MLDSA87-RSA4096-PSS-SHA512"); + case 0x94B99: + return if_match(oid, {1, 3, 6, 1, 5, 5, 7, 6, 54}, "MLDSA87-ECDSA-P521-SHA512"); case 0x94CEA: return if_match(oid, {1, 3, 6, 1, 5, 5, 7, 8, 5}, "PKIX.XMPPAddr"); case 0x94CEE: @@ -747,6 +783,8 @@ std::optional OID_Map::lookup_static_oid_name(std::string_view req) { return if_match(req, "Twofish/GCM", {1, 3, 6, 1, 4, 1, 25258, 3, 102}); case 0x00CF3: return if_match(req, "SphincsPlus-sha2-192f-r3.1", {1, 3, 6, 1, 4, 1, 25258, 1, 12, 2, 4}); + case 0x00F60: + return if_match(req, "MLDSA44-RSA2048-PKCS15-SHA256", {1, 3, 6, 1, 5, 5, 7, 6, 38}); case 0x015FE: return if_match(req, "FrodoKEM-640-SHAKE", {1, 3, 6, 1, 4, 1, 25258, 1, 14, 1}); case 0x01F9E: @@ -893,6 +931,8 @@ std::optional OID_Map::lookup_static_oid_name(std::string_view req) { return if_match(req, "secp384r1", {1, 3, 132, 0, 34}); case 0x32899: return if_match(req, "TripleDES/CBC", {1, 2, 840, 113549, 3, 7}); + case 0x330E9: + return if_match(req, "MLDSA65-ECDSA-brainpoolP256r1-SHA512", {1, 3, 6, 1, 5, 5, 7, 6, 47}); case 0x33C9C: return if_match(req, "PKIX.SmtpUTF8Mailbox", {1, 3, 6, 1, 5, 5, 7, 8, 9}); case 0x33D04: @@ -905,10 +945,14 @@ std::optional OID_Map::lookup_static_oid_name(std::string_view req) { return if_match(req, "SHAKE-128", {2, 16, 840, 1, 101, 3, 4, 2, 11}); case 0x36693: return if_match(req, "ClassicMcEliece_348864", {1, 3, 6, 1, 4, 1, 22554, 5, 1, 1}); + case 0x37294: + return if_match(req, "MLDSA65-ECDSA-P256-SHA512", {1, 3, 6, 1, 5, 5, 7, 6, 45}); case 0x373C7: return if_match(req, "ML-DSA-4x4", {2, 16, 840, 1, 101, 3, 4, 3, 17}); case 0x3750B: return if_match(req, "ClassicMcEliece_8192128", {1, 3, 6, 1, 4, 1, 22554, 5, 1, 9}); + case 0x38CEB: + return if_match(req, "MLDSA65-RSA4096-PKCS15-SHA512", {1, 3, 6, 1, 5, 5, 7, 6, 44}); case 0x39890: return if_match(req, "Ed448", {1, 3, 101, 113}); case 0x3A438: @@ -965,6 +1009,8 @@ std::optional OID_Map::lookup_static_oid_name(std::string_view req) { return if_match(req, "SHAKE-256", {2, 16, 840, 1, 101, 3, 4, 2, 12}); case 0x4663C: return if_match(req, "X509v3.PolicyConstraints", {2, 5, 29, 36}); + case 0x4793E: + return if_match(req, "MLDSA65-Ed25519-SHA512", {1, 3, 6, 1, 5, 5, 7, 6, 48}); case 0x480F7: return if_match(req, "Serpent/OCB", {1, 3, 6, 1, 4, 1, 25258, 3, 2, 4}); case 0x48627: @@ -981,6 +1027,8 @@ std::optional OID_Map::lookup_static_oid_name(std::string_view req) { return if_match(req, "eFrodoKEM-976-AES", {1, 3, 6, 1, 4, 1, 25258, 1, 17, 2}); case 0x4C513: return if_match(req, "DSA/SHA-224", {2, 16, 840, 1, 101, 3, 4, 3, 1}); + case 0x4C6A2: + return if_match(req, "MLDSA44-Ed25519-SHA512", {1, 3, 6, 1, 5, 5, 7, 6, 39}); case 0x4C806: return if_match(req, "DSA/SHA-256", {2, 16, 840, 1, 101, 3, 4, 3, 2}); case 0x4D740: @@ -989,6 +1037,8 @@ std::optional OID_Map::lookup_static_oid_name(std::string_view req) { return if_match(req, "RSA/PKCS1v15(SHA-512)", {1, 2, 840, 113549, 1, 1, 13}); case 0x4ED5D: return if_match(req, "CAST-128/CBC", {1, 2, 840, 113533, 7, 66, 10}); + case 0x4F7FD: + return if_match(req, "MLDSA87-Ed448-SHAKE256", {1, 3, 6, 1, 5, 5, 7, 6, 51}); case 0x4FCDC: return if_match(req, "RSA", {1, 2, 840, 113549, 1, 1, 1}); case 0x501CB: @@ -1027,6 +1077,8 @@ std::optional OID_Map::lookup_static_oid_name(std::string_view req) { return if_match(req, "brainpool320r1", {1, 3, 36, 3, 3, 2, 8, 1, 1, 9}); case 0x56D0D: return if_match(req, "SphincsPlus-shake-128f-r3.1", {1, 3, 6, 1, 4, 1, 25258, 1, 12, 1, 2}); + case 0x56E32: + return if_match(req, "MLDSA65-RSA4096-PSS-SHA512", {1, 3, 6, 1, 5, 5, 7, 6, 43}); case 0x57077: return if_match(req, "XMSS-draft6", {1, 3, 6, 1, 4, 1, 25258, 1, 5}); case 0x5818B: @@ -1083,6 +1135,8 @@ std::optional OID_Map::lookup_static_oid_name(std::string_view req) { return if_match(req, "AES-192/CBC", {2, 16, 840, 1, 101, 3, 4, 1, 22}); case 0x61F7E: return if_match(req, "AES-192/CCM", {2, 16, 840, 1, 101, 3, 4, 1, 27}); + case 0x6334D: + return if_match(req, "MLDSA65-ECDSA-P384-SHA512", {1, 3, 6, 1, 5, 5, 7, 6, 46}); case 0x64947: return if_match(req, "OpenPGP.Ed25519", {1, 3, 6, 1, 4, 1, 11591, 15, 1}); case 0x652E7: @@ -1121,6 +1175,8 @@ std::optional OID_Map::lookup_static_oid_name(std::string_view req) { return if_match(req, "PKCS12.SafeContentsBag", {1, 2, 840, 113549, 1, 12, 10, 1, 6}); case 0x6FB26: return if_match(req, "PKIX.AuthorityInformationAccess", {1, 3, 6, 1, 5, 5, 7, 1, 1}); + case 0x6FDF8: + return if_match(req, "MLDSA87-ECDSA-P384-SHA512", {1, 3, 6, 1, 5, 5, 7, 6, 49}); case 0x70BB6: return if_match(req, "brainpool384r1", {1, 3, 36, 3, 3, 2, 8, 1, 1, 11}); case 0x70EA6: @@ -1129,6 +1185,8 @@ std::optional OID_Map::lookup_static_oid_name(std::string_view req) { return if_match(req, "SphincsPlus-haraka-128f-r3.1", {1, 3, 6, 1, 4, 1, 25258, 1, 12, 3, 2}); case 0x7382C: return if_match(req, "ML-KEM-1024", {2, 16, 840, 1, 101, 3, 4, 4, 3}); + case 0x7406D: + return if_match(req, "MLDSA44-ECDSA-P256-SHA256", {1, 3, 6, 1, 5, 5, 7, 6, 40}); case 0x743BD: return if_match(req, "AES-256/OCB", {1, 3, 6, 1, 4, 1, 25258, 3, 2, 3}); case 0x7498E: @@ -1209,6 +1267,8 @@ std::optional OID_Map::lookup_static_oid_name(std::string_view req) { return if_match(req, "ClassicMcEliece_6960119pcf", {1, 3, 6, 1, 4, 1, 25258, 1, 18, 4}); case 0x84CA4: return if_match(req, "secp256k1", {1, 3, 132, 0, 10}); + case 0x85097: + return if_match(req, "MLDSA87-ECDSA-P521-SHA512", {1, 3, 6, 1, 5, 5, 7, 6, 54}); case 0x85381: return if_match(req, "secp256r1", {1, 2, 840, 10045, 3, 1, 7}); case 0x854FC: @@ -1217,6 +1277,8 @@ std::optional OID_Map::lookup_static_oid_name(std::string_view req) { return if_match(req, "Serpent/SIV", {1, 3, 6, 1, 4, 1, 25258, 3, 4, 4}); case 0x862D9: return if_match(req, "ECGDSA/SHA-512", {1, 3, 36, 3, 3, 2, 5, 4, 6}); + case 0x86448: + return if_match(req, "MLDSA44-RSA2048-PSS-SHA256", {1, 3, 6, 1, 5, 5, 7, 6, 37}); case 0x87585: return if_match(req, "Twofish/CBC", {1, 3, 6, 1, 4, 1, 25258, 3, 3}); case 0x877D1: @@ -1231,6 +1293,8 @@ std::optional OID_Map::lookup_static_oid_name(std::string_view req) { return if_match(req, "PBE-PKCS5v20", {1, 2, 840, 113549, 1, 5, 13}); case 0x8976D: return if_match(req, "PKCS9.MessageDigest", {1, 2, 840, 113549, 1, 9, 4}); + case 0x8AA2B: + return if_match(req, "MLDSA87-RSA3072-PSS-SHA512", {1, 3, 6, 1, 5, 5, 7, 6, 52}); case 0x8B002: return if_match(req, "Camellia-256/OCB", {1, 3, 6, 1, 4, 1, 25258, 3, 2, 8}); case 0x8B935: @@ -1345,6 +1409,8 @@ std::optional OID_Map::lookup_static_oid_name(std::string_view req) { return if_match(req, "Camellia-192/SIV", {1, 3, 6, 1, 4, 1, 25258, 3, 4, 7}); case 0xAAE2B: return if_match(req, "Dilithium-8x7-AES-r3", {1, 3, 6, 1, 4, 1, 25258, 1, 10, 3}); + case 0xAB866: + return if_match(req, "MLDSA65-RSA3072-PKCS15-SHA512", {1, 3, 6, 1, 5, 5, 7, 6, 42}); case 0xABCED: return if_match(req, "GOST.IssuerSigningTool", {1, 2, 643, 100, 112}); case 0xABD24: @@ -1371,6 +1437,8 @@ std::optional OID_Map::lookup_static_oid_name(std::string_view req) { return if_match(req, "X520.Locality", {2, 5, 4, 7}); case 0xB2FBD: return if_match(req, "ECKCDSA/SHA-224", {1, 2, 410, 200004, 1, 100, 4, 4}); + case 0xB31C6: + return if_match(req, "MLDSA65-RSA3072-PSS-SHA512", {1, 3, 6, 1, 5, 5, 7, 6, 41}); case 0xB32B0: return if_match(req, "ECKCDSA/SHA-256", {1, 2, 410, 200004, 1, 100, 4, 5}); case 0xB360E: @@ -1425,6 +1493,10 @@ std::optional OID_Map::lookup_static_oid_name(std::string_view req) { return if_match(req, "SHA-1", {1, 3, 14, 3, 2, 26}); case 0xC28D1: return if_match(req, "PKIX.OCSPSigning", {1, 3, 6, 1, 5, 5, 7, 3, 9}); + case 0xC2EB3: + return if_match(req, "MLDSA87-RSA4096-PSS-SHA512", {1, 3, 6, 1, 5, 5, 7, 6, 53}); + case 0xC38CA: + return if_match(req, "MLDSA87-ECDSA-brainpoolP384r1-SHA512", {1, 3, 6, 1, 5, 5, 7, 6, 50}); case 0xC42CA: return if_match(req, "brainpool256r1", {1, 3, 36, 3, 3, 2, 8, 1, 1, 7}); default: diff --git a/src/lib/ffi/ffi.h b/src/lib/ffi/ffi.h index 79ad43a37da..326997afd6c 100644 --- a/src/lib/ffi/ffi.h +++ b/src/lib/ffi/ffi.h @@ -2053,6 +2053,22 @@ int botan_privkey_load_ml_dsa(botan_privkey_t* key, const uint8_t privkey[], siz BOTAN_FFI_EXPORT(3, 6) int botan_pubkey_load_ml_dsa(botan_pubkey_t* key, const uint8_t pubkey[], size_t key_len, const char* mldsa_mode); +/* +* Algorithm specific key operations: MLDSA-Composite +*/ + +BOTAN_FFI_EXPORT(3, 12) +int botan_privkey_load_mldsa_composite(botan_privkey_t* key, + const uint8_t privkey[], + size_t key_len, + const char* mldsa_composite_algo); + +BOTAN_FFI_EXPORT(3, 12) +int botan_pubkey_load_mldsa_composite(botan_pubkey_t* key, + const uint8_t pubkey[], + size_t key_len, + const char* mldsa_composite_algo); + /* * Algorithm specific key operations: Kyber R3 * diff --git a/src/lib/ffi/ffi_pkey_algs.cpp b/src/lib/ffi/ffi_pkey_algs.cpp index a8f43251621..0e7ee1a7a27 100644 --- a/src/lib/ffi/ffi_pkey_algs.cpp +++ b/src/lib/ffi/ffi_pkey_algs.cpp @@ -7,6 +7,8 @@ */ #include +#include +#include #include #include @@ -1398,6 +1400,63 @@ int botan_pubkey_load_ml_dsa(botan_pubkey_t* key, const uint8_t pubkey[], size_t #endif } +/* +* Algorithm specific key operations: MLDSA-Composite +*/ + +int botan_privkey_load_mldsa_composite(botan_privkey_t* key, + const uint8_t privkey[], + size_t key_len, + const char* mldsa_composite_algo) { +#if defined(BOTAN_HAS_MLDSA_COMPOSITE) + if(key == nullptr || privkey == nullptr || mldsa_composite_algo == nullptr) { + return BOTAN_FFI_ERROR_NULL_POINTER; + } + *key = nullptr; + + return ffi_guard_thunk(__func__, [=]() -> int { + auto param = Botan::MLDSA_Composite_Param::from_id_str(mldsa_composite_algo); + if(!param.has_value()) { + return BOTAN_FFI_ERROR_BAD_PARAMETER; + } + + auto mldsa_composite_key = + std::make_unique(param.value().id(), std::span{privkey, key_len}); + return ffi_new_object(key, std::move(mldsa_composite_key)); + }); +#else + BOTAN_UNUSED(key, key_len, privkey, mldsa_mode); + return BOTAN_FFI_ERROR_NOT_IMPLEMENTED; +#endif +} + +int botan_pubkey_load_mldsa_composite(botan_pubkey_t* key, + const uint8_t pubkey[], + size_t key_len, + const char* mldsa_composite_algo) { +#if defined(BOTAN_HAS_ML_DSA) + if(key == nullptr || pubkey == nullptr || mldsa_composite_algo == nullptr) { + return BOTAN_FFI_ERROR_NULL_POINTER; + } + + *key = nullptr; + + return ffi_guard_thunk(__func__, [=]() -> int { + auto param = Botan::MLDSA_Composite_Param::from_id_str(mldsa_composite_algo); + if(!param.has_value()) { + return BOTAN_FFI_ERROR_BAD_PARAMETER; + } + + auto mldsa_composite_key = + std::make_unique(param.value().id(), std::span{pubkey, key_len}); + return ffi_new_object(key, std::move(mldsa_composite_key)); + }); +#else + BOTAN_UNUSED(key, key_len, pubkey, mldsa_mode); + return BOTAN_FFI_ERROR_NOT_IMPLEMENTED; +#endif +} + /* * Algorithm specific key operations: SLH-DSA */ diff --git a/src/lib/pubkey/dilithium/dilithium_common/dilithium.cpp b/src/lib/pubkey/dilithium/dilithium_common/dilithium.cpp index ae071d7bacc..7693c5d85c6 100644 --- a/src/lib/pubkey/dilithium/dilithium_common/dilithium.cpp +++ b/src/lib/pubkey/dilithium/dilithium_common/dilithium.cpp @@ -8,6 +8,7 @@ * (C) 2021-2022 Manuel Glaser - Rohde & Schwarz Cybersecurity * (C) 2021-2023 Michael Boric, René Meusel - Rohde & Schwarz Cybersecurity * (C) 2024 René Meusel - Rohde & Schwarz Cybersecurity +* (C) 2026 Falko Strenzke – MTG AG * * Botan is released under the Simplified BSD License (see license.txt) */ @@ -15,17 +16,20 @@ #include #include +#include #include - #include #include #include #include #include #include +#include #include #include +#include + namespace Botan { namespace { @@ -69,6 +73,84 @@ DilithiumMode::Mode dilithium_mode_from_oid(const OID& oid) { throw Invalid_Argument(fmt("OID '{}' is not registered as a Dilithium/ML-DSA mode", oid)); } +class MLDSA_Signing_Parameters { + public: + template + class Once_Settable { + public: + explicit Once_Settable(const T& default_value) : m_is_set(false), m_value(default_value) {} + + void set_value(const T& value) { + if(m_is_set) { + throw Invalid_Argument( + "signature/verification parameter contains value for same key (at least) twice"); + } + m_is_set = true; + m_value = value; + } + + const T& value() const { return m_value; } + + private: + bool m_is_set; + T m_value; + }; + + explicit MLDSA_Signing_Parameters(std::string_view param_str) : m_rndmzd(true), m_ctx({}) { + const char* error_tmpl = "Parameter string '{}' is not a valid ML-DSA or Dilithium parameter specification"; + if(param_str.empty()) { + // return the defaults + return; + } + const auto v = split_on(param_str, ','); + for(const auto& y : v) { + if(y == "Pure") { + continue; + } + if(y == "Deterministic") { + m_rndmzd.set_value(false); + continue; + } + if(y == "Randomized") { + m_rndmzd.set_value(true); + continue; + } + const char* ctx_key = "ctx_hex"; + const size_t prefix_len = std::char_traits::length(ctx_key); + if(y.starts_with(ctx_key)) { + if((y.size() > prefix_len && y[prefix_len] != '=')) { + throw Invalid_Argument(fmt(error_tmpl), param_str); + } + std::string z; + // check only whether a non-empty context parameter string was specified + if(y.size() > prefix_len + 1) { + // no whitespace allowed + if(y.find(' ') != std::string::npos) { + throw Invalid_Argument(fmt(error_tmpl), param_str); + } + // get the value of the hex-encoded context string + z = y.substr(prefix_len + 1); + } + m_ctx.set_value(hex_decode(z)); + continue; + } + throw Invalid_Argument(Botan::fmt("invalid token parameter string for ML-DSA/Dilithium: ", y)); + } + } + + bool is_pure_signing() const { return m_pure_sign; } + + bool is_randomized_signing() const { return m_rndmzd.value(); } + + const std::vector& user_context() const { return m_ctx.value(); } + + private: + Once_Settable m_rndmzd; + Once_Settable> m_ctx; + + const bool m_pure_sign = true; +}; + } // namespace DilithiumMode::DilithiumMode(const OID& oid) : m_mode(dilithium_mode_from_oid(oid)) {} @@ -137,10 +219,12 @@ bool DilithiumMode::is_available() const { class Dilithium_Signature_Operation final : public PK_Ops::Signature { public: - Dilithium_Signature_Operation(DilithiumInternalKeypair keypair, bool randomized) : + Dilithium_Signature_Operation(DilithiumInternalKeypair keypair, + bool randomized, + std::span user_context = {}) : m_keypair(std::move(keypair)), m_randomized(randomized), - m_h(m_keypair.second->mode().symmetric_primitives().get_message_hash(m_keypair.first->tr())), + m_h(m_keypair.second->mode().symmetric_primitives().get_message_hash(m_keypair.first->tr(), user_context)), m_s1(ntt(m_keypair.second->s1().clone())), m_s2(ntt(m_keypair.second->s2().clone())), m_t0(ntt(m_keypair.second->t0().clone())), @@ -257,11 +341,12 @@ class Dilithium_Signature_Operation final : public PK_Ops::Signature { class Dilithium_Verification_Operation final : public PK_Ops::Verification { public: - explicit Dilithium_Verification_Operation(std::shared_ptr pubkey) : + explicit Dilithium_Verification_Operation(std::shared_ptr pubkey, + std::span user_context = {}) : m_pub_key(std::move(pubkey)), m_A(Dilithium_Algos::expand_A(m_pub_key->rho(), m_pub_key->mode())), m_t1_ntt_shifted(ntt(m_pub_key->t1() << DilithiumConstants::D)), - m_h(m_pub_key->mode().symmetric_primitives().get_message_hash(m_pub_key->tr())) {} + m_h(m_pub_key->mode().symmetric_primitives().get_message_hash(m_pub_key->tr(), user_context)) {} void update(std::span input) override { m_h->update(input); } @@ -395,9 +480,9 @@ std::unique_ptr Dilithium_PublicKey::generate_another(RandomNumberG std::unique_ptr Dilithium_PublicKey::create_verification_op(std::string_view params, std::string_view provider) const { - BOTAN_ARG_CHECK(params.empty() || params == "Pure", "Unexpected parameters for verifying with Dilithium"); + const MLDSA_Signing_Parameters sig_par(params); if(provider.empty() || provider == "base") { - return std::make_unique(m_public); + return std::make_unique(m_public, sig_par.user_context()); } throw Provider_Not_Found(algo_name(), provider); } @@ -456,17 +541,15 @@ std::unique_ptr Dilithium_PrivateKey::create_signature_op(Ran std::string_view params, std::string_view provider) const { BOTAN_UNUSED(rng); - - BOTAN_ARG_CHECK(params.empty() || params == "Deterministic" || params == "Randomized", - "Unexpected parameters for signing with ML-DSA/Dilithium"); + const MLDSA_Signing_Parameters sig_par(params); // FIPS 204, Section 3.4 // By default, this standard specifies the signing algorithm to use both // types of randomness [fresh from the RNG and a value in the private key]. // This is referred to as the “hedged” variant of the signing procedure. - const bool randomized = (params.empty() || params == "Randomized"); if(provider.empty() || provider == "base") { - return std::make_unique(DilithiumInternalKeypair{m_public, m_private}, randomized); + return std::make_unique( + DilithiumInternalKeypair{m_public, m_private}, sig_par.is_randomized_signing(), sig_par.user_context()); } throw Provider_Not_Found(algo_name(), provider); } diff --git a/src/lib/pubkey/dilithium/dilithium_common/dilithium_symmetric_primitives.cpp b/src/lib/pubkey/dilithium/dilithium_common/dilithium_symmetric_primitives.cpp index 3a2aec6e798..1b5aaa9fe1b 100644 --- a/src/lib/pubkey/dilithium/dilithium_common/dilithium_symmetric_primitives.cpp +++ b/src/lib/pubkey/dilithium/dilithium_common/dilithium_symmetric_primitives.cpp @@ -27,8 +27,10 @@ namespace Botan { -DilithiumMessageHash::DilithiumMessageHash(DilithiumHashedPublicKey tr) : - m_tr(std::move(tr)), m_shake(XOF::create_or_throw("SHAKE-256")) {} +DilithiumMessageHash::DilithiumMessageHash(DilithiumHashedPublicKey tr, std::span user_context) : + m_tr(std::move(tr)), + m_user_context(user_context.begin(), user_context.end()), + m_shake(XOF::create_or_throw("SHAKE-256")) {} DilithiumMessageHash::~DilithiumMessageHash() = default; diff --git a/src/lib/pubkey/dilithium/dilithium_common/dilithium_symmetric_primitives.h b/src/lib/pubkey/dilithium/dilithium_common/dilithium_symmetric_primitives.h index d3a1c5533eb..8fb891bdd39 100644 --- a/src/lib/pubkey/dilithium/dilithium_common/dilithium_symmetric_primitives.h +++ b/src/lib/pubkey/dilithium/dilithium_common/dilithium_symmetric_primitives.h @@ -27,7 +27,7 @@ class RandomNumberGenerator; */ class DilithiumMessageHash /* NOLINT(*-special-member-functions) */ { public: - explicit DilithiumMessageHash(DilithiumHashedPublicKey tr); + explicit DilithiumMessageHash(DilithiumHashedPublicKey tr, std::span user_context = {}); virtual ~DilithiumMessageHash(); @@ -65,12 +65,13 @@ class DilithiumMessageHash /* NOLINT(*-special-member-functions) */ { void ensure_started() { if(!m_was_started) { // FIPS 204, page 17, footnote 4: By default, the context is the empty string [...] - start({}); + start(m_user_context); } } private: DilithiumHashedPublicKey m_tr; + std::vector m_user_context; bool m_was_started = false; std::unique_ptr m_shake; }; @@ -106,8 +107,9 @@ class Dilithium_Symmetric_Primitives_Base { Dilithium_Symmetric_Primitives_Base(Dilithium_Symmetric_Primitives_Base&&) = delete; Dilithium_Symmetric_Primitives_Base& operator=(Dilithium_Symmetric_Primitives_Base&&) = delete; - virtual std::unique_ptr get_message_hash(DilithiumHashedPublicKey tr) const { - return std::make_unique(std::move(tr)); + virtual std::unique_ptr get_message_hash(DilithiumHashedPublicKey tr, + std::span user_context) const { + return std::make_unique(std::move(tr), user_context); } /// Computes the private random seed rho prime used for signing diff --git a/src/lib/pubkey/dilithium/ml_dsa/ml_dsa_impl.h b/src/lib/pubkey/dilithium/ml_dsa/ml_dsa_impl.h index 7dee2e8146f..ac87e38f48d 100644 --- a/src/lib/pubkey/dilithium/ml_dsa/ml_dsa_impl.h +++ b/src/lib/pubkey/dilithium/ml_dsa/ml_dsa_impl.h @@ -85,8 +85,9 @@ class ML_DSA_Symmetric_Primitives final : public Dilithium_Symmetric_Primitives_ return seed; } - std::unique_ptr get_message_hash(DilithiumHashedPublicKey tr) const override { - return std::make_unique(std::move(tr)); + std::unique_ptr get_message_hash(DilithiumHashedPublicKey tr, + std::span user_context) const override { + return std::make_unique(std::move(tr), user_context); } std::optional> seed_expansion_domain_separator() const override { diff --git a/src/lib/pubkey/ecc_key/ecc_key.cpp b/src/lib/pubkey/ecc_key/ecc_key.cpp index 9258e968642..97645d40ff9 100644 --- a/src/lib/pubkey/ecc_key/ecc_key.cpp +++ b/src/lib/pubkey/ecc_key/ecc_key.cpp @@ -17,6 +17,8 @@ #include #include +#include + #if defined(BOTAN_HAS_LEGACY_EC_POINT) #include #endif @@ -177,8 +179,6 @@ EC_PrivateKey::EC_PrivateKey(const AlgorithmIdentifier& alg_id, std::span key_bits, bool with_modular_inverse) : m_with_modular_inverse(with_modular_inverse) { - const EC_Group group(alg_id.parameters()); - OID key_parameters; secure_vector private_key_bits; secure_vector public_key_bits; @@ -192,12 +192,31 @@ EC_PrivateKey::EC_PrivateKey(const AlgorithmIdentifier& alg_id, .end_cons() .verify_end(); - m_private_key = std::make_shared(group, private_key_bits); + std::unique_ptr group; + + if(!alg_id.parameters_are_empty()) { + group = std::make_unique(alg_id.parameters()); + } + if(!key_parameters.empty()) { + if(group) { + if(EC_Group(key_parameters) != *group) { + throw Invalid_Argument( + "Domain parameters supplied AlgorithmIdentifier does not match the ECC private key's domain parameters in EC_PrivateKey construction"); + } + } else { + group = std::make_unique(key_parameters); + } + } + if(!group) { + throw Invalid_Argument("Domain parameters are not supplied in EC_PrivateKey construction"); + } + + m_private_key = std::make_shared(*group, private_key_bits); if(public_key_bits.empty()) { m_public_key = m_private_key->public_key(with_modular_inverse); } else { - m_public_key = std::make_shared(group, public_key_bits); + m_public_key = std::make_shared(*group, public_key_bits); } m_domain_encoding = default_encoding_for(domain()); diff --git a/src/lib/pubkey/mldsa-composite/info.txt b/src/lib/pubkey/mldsa-composite/info.txt new file mode 100644 index 00000000000..200782fe27e --- /dev/null +++ b/src/lib/pubkey/mldsa-composite/info.txt @@ -0,0 +1,22 @@ + +MLDSA_COMPOSITE -> 20260315 + + + +name -> "ML-DSA-composite" + + + +mldsa_comp.h +mldsa_comp_parameters.h + + + + + + +dilithium +rng +hash +asn1 + diff --git a/src/lib/pubkey/mldsa-composite/mldsa_comp.cpp b/src/lib/pubkey/mldsa-composite/mldsa_comp.cpp new file mode 100644 index 00000000000..a887369e93a --- /dev/null +++ b/src/lib/pubkey/mldsa-composite/mldsa_comp.cpp @@ -0,0 +1,435 @@ +#include + +#include +#include +#include +#include +#if defined BOTAN_HAS_ECDSA + #include +#endif +#if defined BOTAN_HAS_ED25519 + #include +#endif +#if defined BOTAN_HAS_ED448 + #include +#endif +#include +#include +#include +#include +#include +#include +#include +#include + +#include +#include +#include +#include + +namespace Botan { + +namespace { +std::span mldsa_pubkey_subspan(const MLDSA_Composite_Param& param, std::span key_bits) { + const OID oid(param.mldsa_oid_str()); + const AlgorithmIdentifier aid(oid, AlgorithmIdentifier::Encoding_Option::USE_EMPTY_PARAM); + if(key_bits.size() <= param.mldsa_pubkey_size()) { + throw Invalid_Argument(fmt("encoded MLDSA component public key is too short (len = {})", key_bits.size())); + } + return std::span(key_bits.begin(), param.mldsa_pubkey_size()); +} + +std::span mldsa_privkey_subspan(const MLDSA_Composite_Param& param, std::span key_bits) { + const OID oid(param.mldsa_oid_str()); + const AlgorithmIdentifier aid(oid, AlgorithmIdentifier::Encoding_Option::USE_EMPTY_PARAM); + if(key_bits.size() <= param.mldsa_privkey_size()) { + throw Invalid_Argument("encoded MLDSA component private key is too short"); + } + return std::span(key_bits.begin(), param.mldsa_privkey_size()); +} + +std::span traditional_pubkey_subspan(const MLDSA_Composite_Param& param, + std::span key_bits) { + const size_t offset = param.mldsa_pubkey_size(); + if(key_bits.size() <= 1 + offset) { + throw Invalid_Argument(fmt("encoded traditional component public key is too short (len = {})", key_bits.size())); + } + return std::span(key_bits.begin() + offset, key_bits.end()); +} + +std::span traditional_privkey_subspan(const MLDSA_Composite_Param& param, + std::span key_bits) { + const size_t offset = param.mldsa_privkey_size(); + if(key_bits.size() <= 1 + offset) { + throw Invalid_Argument("encoded traditional component private key is too short"); + } + return std::span(key_bits.begin() + offset, key_bits.end()); +} +} // namespace + +class MLDSA_Composite_Verification_Operation final : public PK_Ops::Verification_with_Hash { + public: + explicit MLDSA_Composite_Verification_Operation(const MLDSA_Composite_Param& param, + const ML_DSA_PublicKey& mldsa_pubkey, + const Public_Key* trad_pubkey) : + PK_Ops::Verification_with_Hash(param.prehash_func()), + m_parameters(param), + m_mldsa_ver_op(mldsa_pubkey.create_verification_op(param.mldsa_param_str(), "")), + m_traditional_ver_op(trad_pubkey->create_verification_op(param.traditional_padding(), "")) {} + + bool verify(std::span ph, std::span sig) override { + const size_t mldsa_sig_size = m_parameters.mldsa_signature_size(); + + if(sig.size() <= mldsa_sig_size) { + // return early before the state of the component verification OPs is affected + return false; + } + // M' = Prefix || Label || len(ctx) || ctx || PH( M ) + std::string msg_str = "CompositeAlgorithmSignatures2025"; + msg_str += m_parameters.label(); + std::vector msg(msg_str.begin(), msg_str.end()); + msg.push_back(0); // ctx = empty + msg.insert(msg.end(), ph.begin(), ph.end()); + + const std::span mldsa_sig(sig.begin(), sig.begin() + mldsa_sig_size); + std::span trad_sig(sig.begin() + mldsa_sig_size, sig.end()); + std::vector trad_sig_buf; + +#if defined(BOTAN_HAS_ECDSA) + if(m_parameters.traditional_algorithm() == "ECDSA") { + BER_Decoder dec(trad_sig); + BigInt ri; + BigInt si; + dec.start_sequence().decode(ri).decode(si).end_cons(); + const auto group = Botan::EC_Group::from_name(m_parameters.curve()); + const EC_Scalar r = EC_Scalar::from_bigint(group, ri); + const EC_Scalar s = EC_Scalar::from_bigint(group, si); + + trad_sig_buf = EC_Scalar::serialize_pair(r, s); + trad_sig = trad_sig_buf; + } +#endif + // We do the update of the internal OPs directly before invoking their verifications, + // because any early returns of this function otherwise leave them in the state with + // a pending message. + m_mldsa_ver_op->update(msg); + m_traditional_ver_op->update(msg); + // must invoke both signature verifications to ensure the correct hasher state + bool result = m_mldsa_ver_op->is_valid_signature(mldsa_sig); + result &= m_traditional_ver_op->is_valid_signature(trad_sig); + return result; + } + + private: + MLDSA_Composite_Param m_parameters; + + std::unique_ptr m_mldsa_ver_op; + std::unique_ptr m_traditional_ver_op; +}; + +class MLDSA_Composite_Signature_Operation final : public PK_Ops::Signature_with_Hash { + public: + MLDSA_Composite_Signature_Operation(const MLDSA_Composite_Param& param, + const ML_DSA_PrivateKey& mldsa_privkey, + const Private_Key* trad_privkey, + RandomNumberGenerator& rng) : + + PK_Ops::Signature_with_Hash(param.prehash_func()), + m_parameters(param), + m_mldsa_sig_op(mldsa_privkey.create_signature_op(rng, param.mldsa_param_str(), "")), + m_traditional_sig_op(trad_privkey->create_signature_op(rng, param.traditional_padding(), "")) {} + + std::vector raw_sign(std::span ph, RandomNumberGenerator& rng) override { + // PROBLEM: when called repeatedly, the computed pre-hash ph differs and leads to failed verifications. + // M' = Prefix || Label || len(ctx) || ctx || PH( M ) + std::string msg_str = "CompositeAlgorithmSignatures2025"; + msg_str += m_parameters.label(); + std::vector msg(msg_str.begin(), msg_str.end()); + msg.push_back(0); // ctx = empty + msg.insert(msg.end(), ph.begin(), ph.end()); + m_mldsa_sig_op->update(msg); + m_traditional_sig_op->update(msg); + auto sig = m_mldsa_sig_op->sign(rng); + auto trad_sig = m_traditional_sig_op->sign(rng); + + if(m_parameters.traditional_algorithm() == "ECDSA") { + BOTAN_ASSERT(trad_sig.size() % 2 == 0, "ECDSA signature size is not divisible by 2"); + std::vector enc_sig; + const std::span rs(trad_sig.begin(), trad_sig.begin() + trad_sig.size() / 2); + const std::span ss(trad_sig.begin() + trad_sig.size() / 2, trad_sig.end()); + const BigInt r(rs); + const BigInt s(ss); + DER_Encoder enc(enc_sig); + enc.start_sequence().encode(r).encode(s).end_cons(); + std::swap(trad_sig, enc_sig); + } + sig.insert(sig.end(), trad_sig.begin(), trad_sig.end()); + return sig; + } + + size_t signature_length() const override { + size_t encoding_len = 0; + if(m_parameters.traditional_algorithm() == "ECDSA") { + encoding_len = + 3 /* SEQ */ + 2 * 2 /* 2x INTEGER T+L */ + 2 * 1 /* 2x potential leading sign octet in INTEGER */; + } + return m_mldsa_sig_op->signature_length() + m_traditional_sig_op->signature_length() + encoding_len; + } + + AlgorithmIdentifier algorithm_identifier() const override { return m_parameters.get_composite_algorithm_id(); } + + private: + + private: + MLDSA_Composite_Param m_parameters; + std::unique_ptr m_mldsa_sig_op; + std::unique_ptr m_traditional_sig_op; +}; + +// static +std::shared_ptr MLDSA_Composite_PublicKey::load_traditional_public_key(const MLDSA_Composite_Param& param, + std::span key_bits) { +#if defined(BOTAN_HAS_ECDSA) + if(param.traditional_algorithm() == "ECDSA") { + const auto group = Botan::EC_Group::from_name(param.curve()); + return std::make_shared(group, EC_AffinePoint(group, key_bits)); + } +#endif + return load_public_key(param.get_traditional_algorithm_id(), key_bits); +} + +MLDSA_Composite_PublicKey::MLDSA_Composite_PublicKey(const MLDSA_Composite_PublicKey& other) : + m_parameters(std::make_shared(*other.m_parameters)), + m_mldsa_pubkey(std::make_shared(*other.m_mldsa_pubkey)), + // m_traditional_pubkey(std::make_shared(*other.m_traditional_pubkey)) {} + m_traditional_pubkey(load_traditional_public_key(*m_parameters, other.m_traditional_pubkey->public_key_bits())) {} + +MLDSA_Composite_PublicKey::MLDSA_Composite_PublicKey(const AlgorithmIdentifier& algo_id, + std::span key_bits) : + m_parameters(std::make_shared(MLDSA_Composite_Param::from_algo_id_or_throw(algo_id))), + m_mldsa_pubkey(std::make_shared(m_parameters->get_mldsa_algorithm_id(), + mldsa_pubkey_subspan(*m_parameters, key_bits))), + m_traditional_pubkey( + load_traditional_public_key(*m_parameters, traditional_pubkey_subspan(*m_parameters, key_bits))) {} + +MLDSA_Composite_PublicKey::MLDSA_Composite_PublicKey(MLDSA_Composite_Param::id_t id, + std::span key_bits) : + m_parameters(std::make_shared(MLDSA_Composite_Param::from_id_supported_or_throw(id))), + m_mldsa_pubkey(std::make_shared(m_parameters->get_mldsa_algorithm_id(), + mldsa_pubkey_subspan(*m_parameters, key_bits))), + m_traditional_pubkey( + load_traditional_public_key(*m_parameters, traditional_pubkey_subspan(*m_parameters, key_bits))) {} + +MLDSA_Composite_PublicKey& MLDSA_Composite_PublicKey::operator=(const MLDSA_Composite_PublicKey& rhs) { + if(this == &rhs) { + return *this; + } + m_parameters = std::make_shared(*rhs.m_parameters); + m_mldsa_pubkey = std::make_shared(*rhs.m_mldsa_pubkey); + // m_traditional_pubkey = std::make_shared(*rhs.m_traditional_pubkey); + m_traditional_pubkey = load_traditional_public_key(*m_parameters, rhs.m_traditional_pubkey->public_key_bits()); + return *this; +} + +std::vector MLDSA_Composite_PublicKey::raw_public_key_bits() const { + return public_key_bits(); +} + +OID MLDSA_Composite_PublicKey::object_identifier() const { + return m_parameters->object_identifier(); +} + +std::vector MLDSA_Composite_PublicKey::public_key_bits() const { + std::vector result(this->m_mldsa_pubkey->public_key_bits()); + std::vector trad_bytes = this->m_traditional_pubkey->public_key_bits(); + result.insert(result.end(), trad_bytes.begin(), trad_bytes.end()); + return result; +} + +std::unique_ptr MLDSA_Composite_PublicKey::generate_another(RandomNumberGenerator& rng) const { + return std::make_unique(rng, *m_parameters); +} + +// ALLOW NON-EMPTY CTX VIA PARAMS? +std::unique_ptr MLDSA_Composite_PublicKey::create_verification_op( + std::string_view params_for_ctx, std::string_view provider) const { + if(!params_for_ctx.empty()) { + throw Botan::Invalid_Argument("signature parameters not supported for MLDSA composite signatures"); + } + if(provider.empty() || provider == "base") { + return std::make_unique( + *this->m_parameters, *this->m_mldsa_pubkey, this->m_traditional_pubkey.get()); + } + throw Provider_Not_Found(algo_name(), provider); +} + +std::unique_ptr MLDSA_Composite_PublicKey::create_x509_verification_op( + const AlgorithmIdentifier& alg_id, std::string_view provider) const { + if(provider.empty() || provider == "base") { + if(alg_id != this->algorithm_identifier()) { + throw Decoding_Error("Unexpected AlgorithmIdentifier for MLDSA-Composite X.509 signature"); + } + return std::make_unique( + *this->m_parameters, *this->m_mldsa_pubkey, this->m_traditional_pubkey.get()); + } + throw Provider_Not_Found(algo_name(), provider); +} + +std::shared_ptr MLDSA_Composite_PrivateKey::load_traditional_private_key( + const MLDSA_Composite_Param& param, std::span trad_key_bits) { +#if defined(BOTAN_HAS_ED25519) + if(param.traditional_algorithm() == "Ed25519") { + return std::shared_ptr(new Ed25519_PrivateKey(Ed25519_PrivateKey::from_seed(trad_key_bits))); + } +#endif + +#if defined(BOTAN_HAS_ED448) + if(param.traditional_algorithm() == "Ed448") { + return std::make_shared(trad_key_bits); + } +#endif + +#if defined(BOTAN_HAS_ECDSA) + if(param.traditional_algorithm() == "ECDSA") { + return std::make_shared(param.get_traditional_algorithm_id(), trad_key_bits); + } +#endif + return load_private_key(param.get_traditional_algorithm_id(), trad_key_bits); +} + +MLDSA_Composite_PrivateKey::MLDSA_Composite_PrivateKey(MLDSA_Composite_Param::id_t id, std::span sk) : + m_parameters(std::make_shared(MLDSA_Composite_Param::from_id_supported_or_throw(id))), + m_mldsa_privkey(std::make_shared(m_parameters->get_mldsa_algorithm_id(), + mldsa_privkey_subspan(*m_parameters, sk))), + m_traditional_privkey( + load_traditional_private_key(*m_parameters, traditional_privkey_subspan(*m_parameters, sk))) { + init_pubkey_members(); +} + +secure_vector MLDSA_Composite_PrivateKey::encode_traditional_private_key() const { + secure_vector trad_bytes; + + if(m_parameters->traditional_algorithm() == "ECDSA") { + /* For ML-DSA hybrid, we MUST encode this private key format: + * SEQUENCE { + * INTEGER 1 + * OCTET STRING + * B9 4E 76 09 A7 17 6A BA FB D4 A3 4F AB AE 42 B0 + * 91 E4 4D 9E 46 E6 7F CA 56 6C 2A 18 8A 63 C6 5F + * [0] { + * OBJECT IDENTIFIER prime256v1 (1 2 840 10045 3 1 7) + * } + * } */ + const OID oid = OIDS::str2oid_or_empty(m_parameters->curve()); + BOTAN_ASSERT(!oid.empty(), "lookup of MLDSA-composite curve OID"); + trad_bytes = DER_Encoder() + .start_sequence() + .encode(static_cast(1)) + .encode(m_traditional_privkey->raw_private_key_bits(), ASN1_Type::OctetString) + .start_explicit_context_specific(0) + .encode(oid) + .end_cons() + .end_cons() + .get_contents(); + } else { + trad_bytes = m_traditional_privkey->private_key_bits(); + } + if(m_parameters->traditional_algorithm() == "Ed25519" || m_parameters->traditional_algorithm() == "Ed448") { + secure_vector key_bits; + BER_Decoder(trad_bytes).decode(key_bits, ASN1_Type::OctetString).discard_remaining(); + std::swap(trad_bytes, key_bits); + } + return trad_bytes; +} + +secure_vector MLDSA_Composite_PrivateKey::private_key_bits() const { + secure_vector result = + m_mldsa_privkey + ->raw_private_key_bits(); // "raw_...()" should still return the raw seed even after fixing the PKCS#8 encoding format for ML-DSA + secure_vector trad_bytes = encode_traditional_private_key(); + result.insert(result.end(), trad_bytes.begin(), trad_bytes.end()); + return result; +} + +secure_vector MLDSA_Composite_PrivateKey::raw_private_key_bits() const { + return private_key_bits(); +} + +std::unique_ptr MLDSA_Composite_PrivateKey::public_key() const { + return std::make_unique(*this); +} + +/** + * Create a signature operation that produces a MLDSA_Composite signature. + */ +std::unique_ptr MLDSA_Composite_PrivateKey::create_signature_op(RandomNumberGenerator& rng, + std::string_view params_for_ctx, + std::string_view provider) const { + if(!params_for_ctx.empty()) { + throw Botan::Invalid_Argument("signature parameters not supported for MLDSA composite signatures"); + } + if(provider.empty() || provider == "base") { + return std::make_unique( + *this->m_parameters, *this->m_mldsa_privkey, this->m_traditional_privkey.get(), rng); + } + throw Provider_Not_Found(algo_name(), provider); +} + +MLDSA_Composite_PrivateKey::MLDSA_Composite_PrivateKey(const AlgorithmIdentifier& algo_id, + std::span sk) : + + m_parameters(std::make_shared(MLDSA_Composite_Param::from_algo_id_or_throw(algo_id))), + m_mldsa_privkey(std::make_shared(m_parameters->get_mldsa_algorithm_id(), + mldsa_privkey_subspan(*m_parameters, sk))), + m_traditional_privkey(load_traditional_private_key(*m_parameters, traditional_privkey_subspan(*m_parameters, sk))) + +{ + init_pubkey_members(); +} + +// static +std::unique_ptr MLDSA_Composite_PrivateKey::create_traditional_private_key(RandomNumberGenerator& rng, + MLDSA_Composite_Param param) { +#if defined(BOTAN_HAS_ECDSA) + if(param.traditional_algorithm() == "ECDSA") { + const auto group = Botan::EC_Group::from_name(param.curve()); + return std::make_unique(rng, group); + } +#endif + return create_private_key(param.traditional_algorithm(), rng, param.get_traditional_algo_param_str()); +} + +MLDSA_Composite_PrivateKey::MLDSA_Composite_PrivateKey(RandomNumberGenerator& rng, MLDSA_Composite_Param param) : + m_parameters(std::make_shared(param)), + m_mldsa_privkey(std::make_shared(rng, m_parameters->get_mldsa_mode())), + m_traditional_privkey(create_traditional_private_key(rng, param)) { + init_pubkey_members(); +} + +void MLDSA_Composite_PrivateKey::init_pubkey_members() { + MLDSA_Composite_PublicKey::m_parameters = m_parameters; + MLDSA_Composite_PublicKey::m_mldsa_pubkey = m_mldsa_privkey; + MLDSA_Composite_PublicKey::m_traditional_pubkey = m_traditional_privkey; +} + +MLDSA_Composite_PrivateKey::MLDSA_Composite_PrivateKey(const MLDSA_Composite_PrivateKey& other) : + MLDSA_Composite_PublicKey(other), // this assigns private-key independent members in the public key! + m_parameters(std::make_shared(*other.m_parameters)), + m_mldsa_privkey(std::make_shared(*other.m_mldsa_privkey)), + m_traditional_privkey(load_traditional_private_key( + *m_parameters, traditional_privkey_subspan(*m_parameters, other.private_key_bits()))) { + init_pubkey_members(); // set them as shared, otherwise inconsistency may result +} + +MLDSA_Composite_PrivateKey& MLDSA_Composite_PrivateKey::operator=(const MLDSA_Composite_PrivateKey& rhs) { + if(this == &rhs) { + return *this; + } + m_parameters = std::make_shared(*rhs.m_parameters); + m_mldsa_privkey = std::make_shared(*rhs.m_mldsa_privkey); + m_traditional_privkey = + load_traditional_private_key(*m_parameters, traditional_privkey_subspan(*m_parameters, rhs.private_key_bits())); + init_pubkey_members(); + return *this; +} +} // namespace Botan diff --git a/src/lib/pubkey/mldsa-composite/mldsa_comp.h b/src/lib/pubkey/mldsa-composite/mldsa_comp.h new file mode 100644 index 00000000000..e1ea7556b24 --- /dev/null +++ b/src/lib/pubkey/mldsa-composite/mldsa_comp.h @@ -0,0 +1,157 @@ +/* + * ML-DSA Composite Signature Schemes + * (C) 2026 Falko Strenzke, MTG AG + * + * Botan is released under the Simplified BSD License (see license.txt) + **/ + +#ifndef BOTAN_MLDSA_COMP_H_ +#define BOTAN_MLDSA_COMP_H_ + +#include +#include +#include +#include +#include +#include + +namespace Botan { + +class BOTAN_PUBLIC_API(3, 0) MLDSA_Composite_PublicKey : public virtual Public_Key { + public: + /** + * Loads a public key. + * + * @param key_bits DER encoded public key bits + */ + BOTAN_FUTURE_EXPLICIT MLDSA_Composite_PublicKey(MLDSA_Composite_Param::id_t id, + std::span key_bits); + + BOTAN_FUTURE_EXPLICIT MLDSA_Composite_PublicKey(const AlgorithmIdentifier& algo_id, + std::span key_bits); + + std::string algo_name() const override { return "MLDSA_Composite"; } + + AlgorithmIdentifier algorithm_identifier() const override { + return AlgorithmIdentifier(object_identifier(), AlgorithmIdentifier::USE_EMPTY_PARAM); + } + + bool check_key(RandomNumberGenerator& rng, bool strong) const override { + return this->m_mldsa_pubkey->check_key(rng, strong) && this->m_traditional_pubkey->check_key(rng, strong); + } + + OID object_identifier() const override; + + /** + * Return the pessimistic estimated key strength, i.e., the smaller strength of the component keys. + * This is justified by the assumption that composite algorithms are used in the assumption that + * one of the component algorithms might be broken. + * + * @return the mimium of the components' estimated strengths. + */ + size_t estimated_strength() const override { + return std::max(this->m_mldsa_pubkey->estimated_strength(), this->m_traditional_pubkey->estimated_strength()); + } + + /** + * + * @return The sum of the component key lengths. + */ + size_t key_length() const override { return m_mldsa_pubkey->key_length() + m_traditional_pubkey->key_length(); } + + std::vector raw_public_key_bits() const override; + + std::vector public_key_bits() const override; + + BOTAN_DEPRECATED("Use raw_public_key_bits()") std::vector raw_public_key() const; + + std::unique_ptr generate_another(RandomNumberGenerator& rng) const final; + + bool supports_operation(PublicKeyOperation op) const override { return (op == PublicKeyOperation::Signature); } + + std::unique_ptr create_verification_op(std::string_view params, + std::string_view provider) const override; + + std::unique_ptr create_x509_verification_op(const AlgorithmIdentifier& alg_id, + std::string_view provider) const override; + + MLDSA_Composite_PublicKey(const MLDSA_Composite_PublicKey& other); + + MLDSA_Composite_PublicKey& operator=(const MLDSA_Composite_PublicKey& rhs); + + ~MLDSA_Composite_PublicKey() override = default; + + MLDSA_Composite_PublicKey(const MLDSA_Composite_PublicKey&& other) = delete; + MLDSA_Composite_PublicKey& operator=(const MLDSA_Composite_PublicKey&& rhs) = delete; + + protected: + static std::shared_ptr load_traditional_public_key(const MLDSA_Composite_Param& param, + std::span key_bits); + MLDSA_Composite_PublicKey() = default; + + std::shared_ptr m_parameters; // NOLINT(*non-private-member-variable*) + std::shared_ptr m_mldsa_pubkey; // NOLINT(*non-private-member-variable*) + std::shared_ptr m_traditional_pubkey; // NOLINT(*non-private-member-variable*) +}; + +BOTAN_DIAGNOSTIC_PUSH +BOTAN_DIAGNOSTIC_IGNORE_INHERITED_VIA_DOMINANCE + +class BOTAN_PUBLIC_API(3, 0) MLDSA_Composite_PrivateKey final : public virtual MLDSA_Composite_PublicKey, + public virtual Botan::Private_Key { + public: + std::unique_ptr public_key() const override; + + /** + * Generates a new key pair + */ + MLDSA_Composite_PrivateKey(RandomNumberGenerator& rng, MLDSA_Composite_Param param); + + /** + * Read an encoded private key. + */ + MLDSA_Composite_PrivateKey(const AlgorithmIdentifier& alg_id, std::span sk); + + MLDSA_Composite_PrivateKey(MLDSA_Composite_Param::id_t id, std::span sk); + + /** + * Read an encoded private key given the composite @p param. + */ + //MLDSA_Composite_PrivateKey(std::span sk, MLDSA_Composite_Param param); + + secure_vector private_key_bits() const override; + + secure_vector raw_private_key_bits() const override; + + /** + * Create a signature operation that produces a MLDSA_Composite signature. + */ + std::unique_ptr create_signature_op(RandomNumberGenerator& rng, + std::string_view params, + std::string_view provider) const override; + + MLDSA_Composite_PrivateKey(const MLDSA_Composite_PrivateKey& other); + + MLDSA_Composite_PrivateKey& operator=(const MLDSA_Composite_PrivateKey& rhs); + + ~MLDSA_Composite_PrivateKey() override = default; + + MLDSA_Composite_PrivateKey(const MLDSA_Composite_PrivateKey&& other) = delete; + MLDSA_Composite_PrivateKey& operator=(const MLDSA_Composite_PrivateKey&& rhs) = delete; + + private: + static std::shared_ptr load_traditional_private_key(const MLDSA_Composite_Param& param, + std::span key_bits); + static std::unique_ptr create_traditional_private_key(RandomNumberGenerator& rng, + MLDSA_Composite_Param param); + void init_pubkey_members(); + + secure_vector encode_traditional_private_key() const; + friend class MLDSA_Composite_Signature_Operation; + std::shared_ptr m_parameters; + std::shared_ptr m_mldsa_privkey; + std::shared_ptr m_traditional_privkey; +}; + +} // namespace Botan +#endif /* BOTAN_MLDSA_COMP_H_ */ diff --git a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp new file mode 100644 index 00000000000..75673e468f5 --- /dev/null +++ b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp @@ -0,0 +1,444 @@ +/* + * ML-DSA Composite Signature Schemes + * (C) 2026 Falko Strenzke, MTG AG + * + * Botan is released under the Simplified BSD License (see license.txt) + **/ + +#include + +#include +#include +#include +#include +#include +#include +#include +#include + +namespace Botan { + +const MLDSA_Composite_Param MLDSA_Composite_Param::mldsa_composite_registry[] = { + + MLDSA_Composite_Param(MLDSA_Composite_Param::id_t::MLDSA44_RSA2048_PKCS15_SHA256, + "MLDSA44-RSA2048-PKCS15-SHA256", + "COMPSIG-MLDSA44-RSA2048-PKCS15-SHA256", + "SHA-256", + DilithiumMode::ML_DSA_4x4, + "RSA", + "PKCS1v15(SHA-256)", + "", + 2048), + MLDSA_Composite_Param(MLDSA_Composite_Param::id_t::MLDSA65_RSA3072_PKCS15_SHA512, + "MLDSA65-RSA3072-PKCS15-SHA512", + "COMPSIG-MLDSA65-RSA3072-PKCS15-SHA512", + "SHA-512", + DilithiumMode::ML_DSA_6x5, + "RSA", + "PKCS1v15(SHA-256)", + "", + 3072), + MLDSA_Composite_Param(MLDSA_Composite_Param::id_t::MLDSA65_RSA4096_PKCS15_SHA512, + "MLDSA65-RSA4096-PKCS15-SHA512", + "COMPSIG-MLDSA65-RSA4096-PKCS15-SHA512", + "SHA-512", + DilithiumMode::ML_DSA_6x5, + "RSA", + "PKCS1v15(SHA-384)", + "", + 4096), + MLDSA_Composite_Param(MLDSA_Composite_Param::id_t::MLDSA44_RSA2048_PSS_SHA256, + "MLDSA44-RSA2048-PSS-SHA256", + "COMPSIG-MLDSA44-RSA2048-PSS-SHA256", + "SHA-256", + DilithiumMode::ML_DSA_4x4, + "RSA", + "PSS(SHA-256,MGF1,32)", + "", + 2048), + MLDSA_Composite_Param(MLDSA_Composite_Param::id_t::MLDSA65_RSA3072_PSS_SHA512, + "MLDSA65-RSA3072-PSS-SHA512", + "COMPSIG-MLDSA65-RSA3072-PSS-SHA512", + "SHA-512", + DilithiumMode::ML_DSA_6x5, + "RSA", + "PSS(SHA-256,MGF1,32)", + "", + 3072), + MLDSA_Composite_Param(MLDSA_Composite_Param::id_t::MLDSA65_RSA4096_PSS_SHA512, + "MLDSA65-RSA4096-PSS-SHA512", + "COMPSIG-MLDSA65-RSA4096-PSS-SHA512", + "SHA-512", + DilithiumMode::ML_DSA_6x5, + "RSA", + "PSS(SHA-384,MGF1,48)", + "", + 4096), + MLDSA_Composite_Param(MLDSA_Composite_Param::id_t::MLDSA87_RSA3072_PSS_SHA512, + "MLDSA87-RSA3072-PSS-SHA512", + "COMPSIG-MLDSA87-RSA3072-PSS-SHA512", + "SHA-512", + DilithiumMode::ML_DSA_8x7, + "RSA", + "PSS(SHA-256,MGF1,32)", + "", + 3072), + MLDSA_Composite_Param(MLDSA_Composite_Param::id_t::MLDSA87_RSA4096_PSS_SHA512, + "MLDSA87-RSA4096-PSS-SHA512", + "COMPSIG-MLDSA87-RSA4096-PSS-SHA512", + "SHA-512", + DilithiumMode::ML_DSA_8x7, + "RSA", + "PSS(SHA-384,MGF1,48)", + "", + 4096), + MLDSA_Composite_Param(MLDSA_Composite_Param::id_t::MLDSA44_ECDSA_P256_SHA256, + "MLDSA44-ECDSA-P256-SHA256", + "COMPSIG-MLDSA44-ECDSA-P256-SHA256", + "SHA-256", + DilithiumMode::ML_DSA_4x4, + "ECDSA", + "SHA-256", + "secp256r1", + 0), + MLDSA_Composite_Param(MLDSA_Composite_Param::id_t::MLDSA65_ECDSA_P256_SHA512, + "MLDSA65-ECDSA-P256-SHA512", + "COMPSIG-MLDSA65-ECDSA-P256-SHA512", + "SHA-512", + DilithiumMode::ML_DSA_6x5, + "ECDSA", + "SHA-256", + "secp256r1", + 0), + MLDSA_Composite_Param(MLDSA_Composite_Param::id_t::MLDSA65_ECDSA_P384_SHA512, + "MLDSA65-ECDSA-P384-SHA512", + "COMPSIG-MLDSA65-ECDSA-P384-SHA512", + "SHA-512", + DilithiumMode::ML_DSA_6x5, + "ECDSA", + "SHA-384", + "secp384r1", + 0), + MLDSA_Composite_Param(MLDSA_Composite_Param::id_t::MLDSA65_ECDSA_brainpoolP256r1_SHA512, + "MLDSA65-ECDSA-brainpoolP256r1-SHA512", + "COMPSIG-MLDSA65-ECDSA-BP256-SHA512", + "SHA-512", + DilithiumMode::ML_DSA_6x5, + "ECDSA", + "SHA-256", + "brainpool256r1", + 0), + MLDSA_Composite_Param(MLDSA_Composite_Param::id_t::MLDSA87_ECDSA_P384_SHA512, + "MLDSA87-ECDSA-P384-SHA512", + "COMPSIG-MLDSA87-ECDSA-P384-SHA512", + "SHA-512", + DilithiumMode::ML_DSA_8x7, + "ECDSA", + "SHA-384", + "secp384r1", + 0), + MLDSA_Composite_Param(MLDSA_Composite_Param::id_t::MLDSA87_ECDSA_brainpoolP384r1_SHA512, + "MLDSA87-ECDSA-brainpoolP384r1-SHA512", + "COMPSIG-MLDSA87-ECDSA-BP384-SHA512", + "SHA-512", + DilithiumMode::ML_DSA_8x7, + "ECDSA", + "SHA-384", + "brainpool384r1", + 0), + MLDSA_Composite_Param(MLDSA_Composite_Param::id_t::MLDSA87_ECDSA_P521_SHA512, + "MLDSA87-ECDSA-P521-SHA512", + "COMPSIG-MLDSA87-ECDSA-P521-SHA512", + "SHA-512", + DilithiumMode::ML_DSA_8x7, + "ECDSA", + "SHA-512", + "secp521r1", + 0), + MLDSA_Composite_Param(MLDSA_Composite_Param::id_t::MLDSA44_Ed25519_SHA512, + "MLDSA44-Ed25519-SHA512", + "COMPSIG-MLDSA44-Ed25519-SHA512", + "SHA-512", + DilithiumMode::ML_DSA_4x4, + "Ed25519", + "", + "", + 0), + MLDSA_Composite_Param(MLDSA_Composite_Param::id_t::MLDSA65_Ed25519_SHA512, + "MLDSA65-Ed25519-SHA512", + "COMPSIG-MLDSA65-Ed25519-SHA512", + "SHA-512", + DilithiumMode::ML_DSA_6x5, + "Ed25519", + "", + "", + 0), + MLDSA_Composite_Param(MLDSA_Composite_Param::id_t::MLDSA87_Ed448_SHAKE256, + "MLDSA87-Ed448-SHAKE256", + "COMPSIG-MLDSA87-Ed448-SHAKE256", + "SHAKE-256(512)", + DilithiumMode::ML_DSA_8x7, + "Ed448", + "", + "", + 0), + +}; + +// static +std::vector MLDSA_Composite_Param::all_param_sets() { + std::vector result; + for(const auto& param : mldsa_composite_registry) { + result.push_back(param); + } + return result; +} + +// static +std::vector MLDSA_Composite_Param::all_supported_param_sets() { + std::vector result; + for(const auto& param : mldsa_composite_registry) { + if(param.is_supported()) { + result.push_back(param); + } + } + return result; +} + +// static +std::optional MLDSA_Composite_Param::from_id_str(std::string_view id_str) { + for(const auto& param : mldsa_composite_registry) { + if(param.m_id_str == id_str) { + return std::optional(param); + } + } + return std::optional(); +} + +//static +std::optional MLDSA_Composite_Param::from_algo_id(const AlgorithmIdentifier& algo_id) { + for(const auto& param : mldsa_composite_registry) { + if(param.get_composite_algorithm_id() == algo_id) { + return std::optional(param); + } + } + return std::optional(); +} + +//static +MLDSA_Composite_Param MLDSA_Composite_Param::from_algo_id_or_throw(const AlgorithmIdentifier& algo_id) { + const auto result = from_algo_id(algo_id); + if(!result.has_value()) { + throw Botan::Invalid_Argument("no parameter found for provided MLDSA composite algo id"); + } + return result.value(); +} + +// static +MLDSA_Composite_Param MLDSA_Composite_Param::from_id_str_or_throw(std::string_view id_str) { + const auto result = from_id_str(id_str); + if(!result.has_value()) { + throw Botan::Invalid_Argument("no parameter found for provided MLDSA composite id " + std::string(id_str)); + } + return result.value(); +} + +// static +std::optional MLDSA_Composite_Param::from_id(MLDSA_Composite_Param::id_t id) { + for(const auto& param : mldsa_composite_registry) { + if(param.m_id == id) { + return std::optional(param); + } + } + return std::optional(); +} + +// static +MLDSA_Composite_Param MLDSA_Composite_Param::from_id_supported_or_throw(MLDSA_Composite_Param::id_t id) { + const auto result = from_id(id); + if(!result.has_value()) { + throw Botan::Invalid_Argument("no parameter found for provided MLDSA composite id (enum)"); + } + if(!result.value().is_supported()) { + throw Not_Implemented("Parameter set " + result.value().id_str() + + " is not supported by Botan's build configuration"); + } + return result.value(); +} + +MLDSA_Composite_Param::MLDSA_Composite_Param(id_t the_id, + const char* the_id_str, + const char* the_label, + const char* the_prehash_func, + DilithiumMode::Mode the_mldsa_variant, + const char* the_traditional_algorithm, + const char* the_traditional_padding, + const char* the_curve, + uint32_t the_traditional_key_size) noexcept : + m_id_str(the_id_str), + m_label(the_label), + m_prehash_func(the_prehash_func), + m_traditional_algorithm(the_traditional_algorithm), + m_traditional_padding(the_traditional_padding), + m_curve(the_curve), + m_id(the_id), + m_traditional_key_size(the_traditional_key_size), + m_mldsa_variant(the_mldsa_variant) {} + +const char* MLDSA_Composite_Param::mldsa_oid_str() const { + if(m_mldsa_variant == DilithiumMode::ML_DSA_4x4) { + return "2.16.840.1.101.3.4.3.17"; + } else if(m_mldsa_variant == DilithiumMode::ML_DSA_6x5) { + return "2.16.840.1.101.3.4.3.18"; + } else if(m_mldsa_variant == DilithiumMode::ML_DSA_8x7) { + return "2.16.840.1.101.3.4.3.19"; + } + throw Internal_Error("invalid MLDSA mode in MLDSA composite parameters"); +} + +size_t MLDSA_Composite_Param::mldsa_pubkey_size() const { + if(m_mldsa_variant == DilithiumMode::ML_DSA_4x4) { + return 1312; + } else if(m_mldsa_variant == DilithiumMode::ML_DSA_6x5) { + return 1952; + } + return 2592; // must be ML-DSA-87 +} + +std::string MLDSA_Composite_Param::mldsa_param_str() const { + std::string label_str(m_label); + std::vector label_vec(label_str.begin(), label_str.end()); + return std::string("Pure,Randomized,ctx_hex=") + hex_encode(label_vec); +} + +size_t MLDSA_Composite_Param::mldsa_signature_size() const { + if(this->m_mldsa_variant == DilithiumMode::ML_DSA_4x4) { + return 2420; + } else if(this->m_mldsa_variant == DilithiumMode::ML_DSA_6x5) { + return 3309; + } else if(this->m_mldsa_variant == DilithiumMode::ML_DSA_8x7) { + return 4627; + } + throw Botan::Internal_Error("MLDSA_Composite_Param::mldsa_signature_size() encountered unknown ML-DSA variant "); +} + +AlgorithmIdentifier MLDSA_Composite_Param::get_composite_algorithm_id() const { + std::optional oid; + oid = OID::from_name(m_id_str); + if(!oid.has_value()) { + throw Botan::Internal_Error(fmt("could not look up own MLDSA Composite ID '{}' for OID", m_id_str)); + } + return AlgorithmIdentifier(oid.value(), AlgorithmIdentifier::Encoding_Option::USE_EMPTY_PARAM); +} + +AlgorithmIdentifier MLDSA_Composite_Param::get_mldsa_algorithm_id() const { + const OID oid(this->mldsa_oid_str()); + return AlgorithmIdentifier(oid, AlgorithmIdentifier::Encoding_Option::USE_EMPTY_PARAM); +} + +AlgorithmIdentifier MLDSA_Composite_Param::get_traditional_algorithm_id() const { + std::optional oid; + if(0 == std::strcmp(this->m_traditional_algorithm, "ECDSA")) { + oid = OID::from_name(std::string("ECDSA/") + m_prehash_func); + } else { + oid = OID::from_name(this->m_traditional_algorithm); + } + if(!oid.has_value()) { + throw Botan::Internal_Error( + "MLDSA_Composite_Param::get_traditional_algorithm_id_by_id(): could not lookup algorithm OID of traditional algorithm as expected"); + } + return AlgorithmIdentifier(oid.value(), AlgorithmIdentifier::Encoding_Option::USE_EMPTY_PARAM); +} + +std::string MLDSA_Composite_Param::get_traditional_algo_param_str() const { + if(0 == strcmp(this->m_traditional_algorithm, "RSA")) { + return std::to_string(m_traditional_key_size); + } + return ""; +} + +bool MLDSA_Composite_Param::is_supported() const { + switch(m_id) { + case MLDSA44_RSA2048_PKCS15_SHA256: + [[fallthrough]]; + case MLDSA65_RSA3072_PKCS15_SHA512: + [[fallthrough]]; + case MLDSA65_RSA4096_PKCS15_SHA512: +#if defined BOTAN_HAS_RSA + return true; +#else + return false; +#endif + case MLDSA44_RSA2048_PSS_SHA256: + [[fallthrough]]; + case MLDSA65_RSA3072_PSS_SHA512: + [[fallthrough]]; + case MLDSA65_RSA4096_PSS_SHA512: + [[fallthrough]]; + case MLDSA87_RSA3072_PSS_SHA512: + [[fallthrough]]; + case MLDSA87_RSA4096_PSS_SHA512: + +#if defined BOTAN_HAS_RSA && defined BOTAN_HAS_PSS + return true; +#else + return false; +#endif + case MLDSA44_ECDSA_P256_SHA256: + [[fallthrough]]; + /* NOLINTNEXTLINE(bugprone-branch-clone) */ + case MLDSA65_ECDSA_P256_SHA512: +#if defined BOTAN_HAS_ECDSA && defined BOTAN_HAS_PCURVES_SECP256R1 + return true; +#else + return false; +#endif + case MLDSA65_ECDSA_P384_SHA512: + [[fallthrough]]; + /* NOLINTNEXTLINE(bugprone-branch-clone) */ + case MLDSA87_ECDSA_P384_SHA512: +#if defined BOTAN_HAS_ECDSA && defined BOTAN_HAS_PCURVES_SECP384R1 + return true; +#else + return false; +#endif + case MLDSA65_ECDSA_brainpoolP256r1_SHA512: +#if defined BOTAN_HAS_ECDSA && defined BOTAN_HAS_PCURVES_BRAINPOOL256R1 + return true; +#else + return false; +#endif + case MLDSA87_ECDSA_brainpoolP384r1_SHA512: +#if defined BOTAN_HAS_ECDSA && defined BOTAN_HAS_PCURVES_BRAINPOOL384R1 + return true; +#else + return false; +#endif + case MLDSA87_ECDSA_P521_SHA512: +#if defined BOTAN_HAS_ECDSA && defined BOTAN_HAS_PCURVES_BRAINPOOL512R1 + return true; +#else + return false; +#endif + case MLDSA_Composite_Param::id_t::MLDSA44_Ed25519_SHA512: + [[fallthrough]]; + /* NOLINTNEXTLINE(bugprone-branch-clone) */ + case MLDSA_Composite_Param::id_t::MLDSA65_Ed25519_SHA512: +#if defined BOTAN_HAS_ED25519 + return true; +#else + return false; +#endif + /* NOLINTNEXTLINE(bugprone-branch-clone) */ + case MLDSA_Composite_Param::id_t::MLDSA87_Ed448_SHAKE256: +#if defined BOTAN_HAS_ED448 && defined BOTAN_HAS_SHAKE + return true; +#else + return false; +#endif + } + // should be dead code, needed for compiler (why?) + return false; +} + +} // namespace Botan diff --git a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h new file mode 100644 index 00000000000..de701ba0946 --- /dev/null +++ b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h @@ -0,0 +1,136 @@ +/* + * ML-DSA Composite Signature Schemes + * (C) 2026 Falko Strenzke, MTG AG + * + * Botan is released under the Simplified BSD License (see license.txt) + **/ + +#ifndef BOTAN_MLDSA_COMP_PARAMETERS_H_ +#define BOTAN_MLDSA_COMP_PARAMETERS_H_ + +#include +#include +#include +#include + +namespace Botan { + +class BOTAN_PUBLIC_API(3, 0) MLDSA_Composite_Param { + public: + enum id_t : uint32_t /* NOLINT(*-enum-size,*-use-enum-class) */ { + MLDSA44_RSA2048_PKCS15_SHA256, + MLDSA65_RSA3072_PKCS15_SHA512, + MLDSA65_RSA4096_PKCS15_SHA512, + MLDSA44_RSA2048_PSS_SHA256, + MLDSA65_RSA3072_PSS_SHA512, + MLDSA65_RSA4096_PSS_SHA512, + MLDSA87_RSA3072_PSS_SHA512, + MLDSA87_RSA4096_PSS_SHA512, + MLDSA44_ECDSA_P256_SHA256, + MLDSA65_ECDSA_P256_SHA512, + MLDSA65_ECDSA_P384_SHA512, + MLDSA65_ECDSA_brainpoolP256r1_SHA512, + MLDSA87_ECDSA_P384_SHA512, + MLDSA87_ECDSA_brainpoolP384r1_SHA512, + MLDSA87_ECDSA_P521_SHA512, + MLDSA44_Ed25519_SHA512, + MLDSA65_Ed25519_SHA512, + MLDSA87_Ed448_SHAKE256, + }; + + static std::vector all_param_sets(); + + static std::vector all_supported_param_sets(); + + /** + * @brief Create a paramters object from the provided id. If the parameters are not supported by the build configuration of the library, throw a Not_Implemented exception. + * + * @param id The id of the parameter set to create. + * + * @return The parameter object. + */ + static MLDSA_Composite_Param from_id_supported_or_throw(MLDSA_Composite_Param::id_t id); + + static std::optional from_id(MLDSA_Composite_Param::id_t id); + + static MLDSA_Composite_Param from_id_str_or_throw(std::string_view id_str); + + static std::optional from_id_str(std::string_view id_str); + + static std::optional from_algo_id(const AlgorithmIdentifier& algo_id); + + static MLDSA_Composite_Param from_algo_id_or_throw(const AlgorithmIdentifier& algo_id); + + MLDSA_Composite_Param clone() const { return MLDSA_Composite_Param::from_id_supported_or_throw(m_id); } + + /** + * @brief + * Find out whether the library build supports this parameter. + * + * @return true if the parameter is supported, false otherwhise + */ + bool is_supported() const; + + AlgorithmIdentifier get_composite_algorithm_id() const; + + AlgorithmIdentifier get_mldsa_algorithm_id() const; + + AlgorithmIdentifier get_traditional_algorithm_id() const; + + OID object_identifier() const { return OID_Map::global_registry().str2oid(this->m_id_str); } + + std::string mldsa_param_str() const; + + DilithiumMode get_mldsa_mode() const { return m_mldsa_variant; } + + size_t mldsa_signature_size() const; + + size_t mldsa_pubkey_size() const; + + const char* mldsa_oid_str() const; + + MLDSA_Composite_Param::id_t id() const { return m_id; } + + std::string id_str() const { return std::string(this->m_id_str); } + + std::string label() const { return std::string(this->m_label); } + + std::string prehash_func() const { return std::string(this->m_prehash_func); } + + std::string traditional_algorithm() const { return std::string(this->m_traditional_algorithm); } + + std::string traditional_padding() const { return std::string(this->m_traditional_padding); } + + std::string curve() const { return std::string(this->m_curve); } + + std::string get_traditional_algo_param_str() const; + size_t traditional_pubkey_encoded_size() const; + + size_t mldsa_privkey_size() const { return 32; } + + private: + MLDSA_Composite_Param(id_t id, + const char* id_str, + const char* label, + const char* prehash_func, + DilithiumMode::Mode mldsa_variant, + const char* traditional_algorithm, + const char* traditional_padding, + const char* curve, + uint32_t traditional_key_size) noexcept; + + const char* m_id_str; + const char* m_label; + const char* m_prehash_func; + const char* m_traditional_algorithm; + const char* m_traditional_padding; + const char* m_curve; + id_t m_id; + uint32_t m_traditional_key_size; + DilithiumMode::Mode m_mldsa_variant; + + static const MLDSA_Composite_Param mldsa_composite_registry[]; +}; + +} // namespace Botan +#endif /* BOTAN_MLDSA_COMP_PARAMETERS_H_ */ diff --git a/src/lib/pubkey/pk_algs.cpp b/src/lib/pubkey/pk_algs.cpp index 4e8a4e13a3a..ca1b6a29244 100644 --- a/src/lib/pubkey/pk_algs.cpp +++ b/src/lib/pubkey/pk_algs.cpp @@ -12,6 +12,7 @@ #include #include #include +#include #if defined(BOTAN_HAS_RSA) #include @@ -117,6 +118,10 @@ #include #endif +#if defined(BOTAN_HAS_MLDSA_COMPOSITE) + #include +#endif + #if defined(BOTAN_HAS_SPHINCS_PLUS_WITH_SHA2) || defined(BOTAN_HAS_SPHINCS_PLUS_WITH_SHAKE) #include #endif @@ -267,6 +272,16 @@ std::unique_ptr load_public_key(const AlgorithmIdentifier& alg_id, } #endif +#if defined(BOTAN_HAS_MLDSA_COMPOSITE) + if(alg_name.starts_with("MLDSA")) { + auto comp_parm = MLDSA_Composite_Param::from_id_str(alg_name); + if(comp_parm.has_value()) { + return std::make_unique(comp_parm->id(), key_bits); + } + // we continue the search as there might be other algorithms defined with leading "MLDSA" + } +#endif + #if defined(BOTAN_HAS_HSS_LMS) if(alg_name == "HSS-LMS") { return std::make_unique(alg_id, key_bits); @@ -434,6 +449,16 @@ std::unique_ptr load_private_key(const AlgorithmIdentifier& alg_id, } #endif +#if defined(BOTAN_HAS_MLDSA_COMPOSITE) + if(alg_name.starts_with("MLDSA")) { + auto comp_parm = MLDSA_Composite_Param::from_id_str(alg_name); + if(comp_parm.has_value()) { + return std::make_unique(comp_parm->id(), key_bits); + } + // we continue the search as there might be other algorithms defined with leading "MLDSA" + } +#endif + #if defined(BOTAN_HAS_HSS_LMS) if(alg_name == "HSS-LMS-Private-Key") { return std::make_unique(alg_id, key_bits); @@ -621,6 +646,17 @@ std::unique_ptr create_private_key(std::string_view alg_name, } #endif +#if defined(BOTAN_HAS_MLDSA_COMPOSITE) + + if(alg_name.starts_with("MLDSA")) { + auto comp_parm = MLDSA_Composite_Param::from_id_str(alg_name); + if(comp_parm.has_value()) { + return std::make_unique(rng, comp_parm.value()); + } + // we continue, there might be other algorithms defined with leading "MLDSA" + } +#endif + #if defined(BOTAN_HAS_HSS_LMS) if(alg_name == "HSS-LMS") { const auto hss_params = [&]() -> std::string { diff --git a/src/tests/data/pubkey/api_sign.vec b/src/tests/data/pubkey/api_sign.vec index 43d55ae7d49..dbbcd279438 100644 --- a/src/tests/data/pubkey/api_sign.vec +++ b/src/tests/data/pubkey/api_sign.vec @@ -63,3 +63,8 @@ SigParams = AlgoParams = XMSS-SHA2_10_256 SigParams = SHA2_10_256 + +[MLDSA44_RSA2048_PKCS15_SHA256] + +AlgoParams = +SigParams = diff --git a/src/tests/data/pubkey/mldsa_composite.vec b/src/tests/data/pubkey/mldsa_composite.vec new file mode 100644 index 00000000000..e218d7f40dc --- /dev/null +++ b/src/tests/data/pubkey/mldsa_composite.vec @@ -0,0 +1,171 @@ +[RFC-KAT-pubkey-invalid] +tcId = id-MLDSA44-RSA2048-PSS-SHA256 +pk = YXNsZGpmbGFkc2ZqYWRzbGZqYQo= +x5c = 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 +sk = NPkBm9FU2TX1CaijKEhnsJ9yRbP+Ov+1E+fjPqvkix0wggSjAgEAAoIBAQDUWGUOzXqpodxWXYo/WpR+jN36PtPJ5WGEUOT1HLT1Oa9jPBjP/Z1aYCX9BDxV30+6vTfPSeb5ncVT7bwcXoDIL0kxZphaB+0lhapYUYICBxLkL/UEgy5fxlWfMznw+m9Fu416CJd5WVJ0nqxQT0pv+5rHCNL9xvepuEozIqpee0z9Yxbo2AdaUQ0h+N9KKJITr9otnTgJ3c5AoNsaygapr9rFAmGRbI/JxvgSceIGAmftYHFLqGi6scO05PuNLK9pQMZx8cr1uE9TYSj9OwhOLY937CpwXuEzeziPUpLSoo3jUDhY/bGAYrAtnySszxEn1AYp6qVkC46lXKmryw+XAgMBAAECggEAWF+Nd3Km6TA27i6x2ZoOEPj5bSt2oyD2y8WK9EQFP8XJK4iYXv+S3EkFpl576dUtbm9PadK88QfrVvmq/zeJa0batFeZcma4GJSfh3AspkFhaFxZIY6i3zNA8Se1pofjhWcAA1jOCa/V9DkRR78oIKDbEpimjv2elyDeqJd1xinSdY8p6ub3r+MdwhoBrRJqb2p2Vr46Rv++ZnSYvF5bOiA+2pS4Hx4WxyW/Zx/3almN/Qz149vzpkVNaRLrtNRQbQaZkhSqsDP5KlBWp6zshrAzP8VM9n5OcS/J/l8k1LwsVMYFsn1r98+RMrnCAVgwbQJCBeDWMWOZfZmPaN7AMQKBgQDyB3Qpnf0nbj4atEUx3yihn7peoOE5HCSoxvH+a4t5r8xokmqpqMBMP4L7b8EoN4FuXGaR2EhEBsvHp6m0LzygeGiO4dyx+cay+Eq8WVbZUsylUMfzu0cPmjAEf40rdckHElNOI8VeSw4qqzDl+JIn34wG7RM4tez/It/0bFnKjwKBgQDgmksGsKL3gqAdMEYBZIqaAEwxFIiNNQSpVfN2MOZryHoK9FveDf08oT8l4NcXGXDkx8CoNQIB73FgmWDj3DJKypjM55W0hNSpRwjcsFJ8Cy/dV2hsZYbASV7r4fUSoMjihFbpZVmHKpjZxfGX8a98pfSQyu0kjpDkI+7qVJGOeQKBgHnwjXMmWVSTc5DKwI4G7Ba6PhDNJ4w5hLLQQT44+vWdP/RzyG+gSPphiWGbBYt4o6pxvW+/s3Eqp2L5M0RIBFipMazDWQkGWjjzZdwNevdVgyvLTmKbOYs/2O97QCnkVxtL/VLCLP97+zA+Pg2vthuGwqr+qQ+KgVRuQr2IFZk7AoGBAMY6Rvc7lElgh1Hblh2Kj+1FT/mNRsthvKB7VGm+1M7R3Cyo6B++Nv94zNPwccVYVdQFHFsYlZIBsw3vsJzKbbSmxF8sEWuGRG62W/Lyx4nlEbSHfYkVve0dlGIZRgPP1hxdcpuBMJfkF400b3qL+zbG/WeBQfUewnAn6qf0RZb5AoGAa0WhETbIjDyrcWmtfHKQI9KeO3+fmdrZws4FCgQDURR8RNxznDfUE4JpFP0FyqMe8jlJYPgd5qMoWzMVxuLb3mnYV1gmlNctW6tg9EXNnWiSUyNKkiGxz6YEAiBXTPOU3SeW7Z+2AtshEoRrWA+DvLeiSJ+Kxi/Y9OIu+Dtrz1s= +sk_pkcs8 = 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 + +[RFC-KAT-MLDSA44-ECDSA-P256-SHA256] +tcId = id-MLDSA44-ECDSA-P256-SHA256 +pk = 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 + + +[RFC-KAT-MLDSA65-RSA3072-PSS-SHA512] +tcId = id-MLDSA65-RSA3072-PSS-SHA512 +pk = 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 + +[RFC-KAT-MLDSA65-RSA3072-PKCS15-SHA512] +tcId = id-MLDSA65-RSA3072-PKCS15-SHA512 +pk = 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 + +[RFC-KAT-MLDSA65-RSA4096-PSS-SHA512] +tcId = id-MLDSA65-RSA4096-PSS-SHA512 +pk = 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oUSQw/9nErjocjvW8vx4V6KfZKQHPZ0ROzcCkMcTZNQWKOWFbe0ExdJl+uLWv/F9Plv3AEhtQeCMBm4wonnYdzDHDbeQyvQ= + +[RFC-KAT-MLDSA65-RSA4096-PKCS15-SHA512] +tcId = id-MLDSA65-RSA4096-PKCS15-SHA512 +pk = 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jKhpsSZrxsBL516vmjua46F+DxX0sDCzqVVSCipsa+99FqxtYmlQdFzSYDMa22D9DFUhld2RxS5cb3Ehh0Fk4fr380CyuDI= + +[RFC-KAT-MLDSA65-ECDSA-P256-SHA512] +tcId = id-MLDSA65-ECDSA-P256-SHA512 +pk = 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+ +[RFC-KAT-MLDSA65-ECDSA-P384-SHA512] +tcId = id-MLDSA65-ECDSA-P384-SHA512 +pk = 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AKQJEKdrDu1G9LiA9Fh8kJUWaH0sFV7fU+u4X6lXou95UiU8FTOOPvc/bsby9jmAb0xqt8hy6NU21D3YnjKYbpUwmixntoLmuZEF2o0CSP+SCkGmXKrwfT5azrO7+oWuWJJUXpq+uCCmxpsruLZhlolgi0ePys8A7co7Jf/ZFT8hwgG+H4rrJ/O/6bxVxW/MDHq0ypoRTbpnkx5q6fYdBOsgrOHFqEz+Zcx05ruFCkZlv33MBe+Ls10dlMsv3X6y2tanqKSZKwdUTw9eqpINZ4E5p4e4lTodETSu8o1GNeGjc7dZZNbvmoy7uCizXhSDD8635xZOqwZqNo0UD1JcTuiQPxRh1Q2tMadnYhe7lTwAAhDoS4XeQ7sA8DCQL1hBc+5fX1wD4p8yZAAW40LIE55kzYw/OKo9EKfJ0VccWvt9aPA/eE82RJmxUPP4HctrCZ4uFHJh19Mb7sa0tF+mK4rzWlgj8uvGyrlu2OF/LJhepcF7d8Qta7RCy4MAMsCv/IoKMZncIuaJd7QUWoaR7M9Gy7bWyaNoxQWauBbtIbdNLUHmol1fWSvCNqo0e7nyKPjWIkyvR1dslm5yCNWOGZQzIxrPSP1cJhgQl1etxIkssFprWoltvBKcKKXAQZfabmA68rdlZD3tQIZRIzKxsz8ZV/mXxruN9XjwJXeZjU6gsP5Kksg/r3xc6KfTuFRGE2awD4w4QoI4olvaPxtqp7Uoe6hHBh/HAQlt8yO/ZlZQDhaM8F0ApVxif3vtOgh8dKravnIx9Mj8Lo+mzNunwPQVMiWHtp8FLrnQumJ8REPkyNYdO0V7oE95i+r96i3AxR3yPqGJqIAq2NzoX8einc17SWnN32B8j6FBx5ITMh33z7I34zQPtRlQk1H2OSGMsy0yOZPtVVfaHLxLTHWvoCPIzSB9Nhz2UvttCtngjMVcFW9PQcu/WIbMl87agKV9eKE8UJrXy64Wawv+mRinxMvqb2cqSEcwPgt4YEU/oSt0RGLgw7u8TkdlT7aNj9R2tyw6wqRiGG/vao/9sXwxEwZPlY8+YElif5kRXMa9JBQ+RDF3taQExWviNIgAFjSwnCrtItn2X95ivabzleV2BZixXpv36gROjHPJcC9P9irBOXuda72lhjNg+Ox4uQshSv2RIybeUM3rXiDDS4E/6zZkY5uCzENQ9rkg34xi+0kmas5ojmzPnEcjVn1dZdT1GoY5dgpb4ZeA5OC2uhlAURcNo3ykWkfP6i+byVxENBW7X3DD/ipA7RTlOLQrzkGABHnmEATVpNMZyCbhpyzQ/f1f8Iz8JgckpsR9H9VxC8A4/rDxqkkLRPxCfRZUPgYRj+YExWECgJqjrZnQAFBvRim9wkP7tTzQ1vhuwH0UGIrOOAfJ2ItO+jJVEWNMxyxtUAV+cqhMxQxxrMbJqXUDUDaV4TZMm03VTAJGG5kRHnfDmkpQwOd3CwQP9HwadwDRvLRiMC7MPny6uOpdDBFDxmXbHpkDbRrqNWwuqqiugme9ESwvA607tX0cCFJp/o/JXvlcpW4aTwmQrSBOdoqME9WSp0RUmas/eyA3iA2hTTrGXZVCqBuPZ5NSyZ0TC7vNkUe8ZeibN9G7Fc0Y7SEQRKn8VWCz4Bds4YwiyDJ4VieJSG7To5z4admNE31IjO5fu2bBzXIuvuB97E6xZXFtW23Y4v4fY8XlZw814gjeeOpBqCxG7Db0liBERjMXwB1oZOv/Nd2FI+kj/DrYOZnd4DaO6taj8P/zJIZKapPre9UMlAn8xAK4zXo01rKC2IREIHJn/dU3BboPEg6dr34MdHXEgK/k20PXwD3sh9dT5q79Vw8vyNiC7AW7cFwkOnPIs37towDiLUfr++hccyi3+VVghWDgYOXrZwx011Oh2eInFalApUohcseuH1J/nMTMiOAbKAXG7hERjns+eLuCWqALYA9zxibLbml8U+n+NzIbtMlUap91FRbYbh9R3JraK+TidcAHAn4k4KRDQrazPEFqXi0u/Owuuew03faWj1bFLlZZw74t6eiFbxlRyZgRbv2SonsMZroYoRJ3cH5jowq97CP610aFjCNFuMkV3pEGtioBKNTuDVu7EJOPNbZ7Fx7IcOhuCD3qpbQWXNUVrr0xkhmbH/6MCZz7iL+CSs0eSA87vV4pZOzUhIPFbcNuLL8urn+JEdO1UA/FKqPcqr3XRqzibiYOkBnVZBm/fe+WqooLF39KxSc0jwsYJXXeGA9O7aIpXFChT+dgcnsMMKYPHAkbLwUCqRFfb6qKgu3fYYs6oriVNX/8iaBIYgWY8OEpo+rH7rRxoREMpU9aEmXqlOroMqhz5s3q0cd2F471N0N5t0CTABqTab9EqLnauwx5+cl1K4ZFW8bAxRKZDWOFE6LYr6Ekme33zE0h4unquDeo0YDXxvzHyjmL+Bp+stEVJH6Cenbxcx/4/PnXSrqugvS5K7Y/hRPdRzwJGiwGrwnMJkN4kqvYWlpG8uErx6KrRomYWGKwX+TUO0pG005pMUplUtWhSlhPUBvB2MCiw3YuZcBzJo0NrVMG45Fkr/IU1wzk6ls2SpEsjRzle5dALADqLF7PbQ7Z0bgv9wTpNhODIGa8//2cEXaY2BJJ/ZIv9gonh9g1hm3H/tJs2kmXHUGJfcFtmsUhE0yJkyeqM2IrxvNHsM2xIgzF0CN3WSuSDHB+ybdDYG/hegO459V/ut1PT+4BF1LkwJ6nXEDW2dyv3cSzY/PfUPBmdH8K3IzMOsJV28d4LR3PSeptP40UAsNdFBu0XaJeu2NKjISGMscfz91o3FpPc9bxpWCfOKfUfbv5iJST4ldAkcM1RLPYl+8JEjoGw8A5wUkTE6t0t2tAWDd6riES0fNaga8R9g4x3CrmSDLDJCkTmJyySVj1mQglGWg8tXulj2tMClXPs3Nd1zPn7VcCsYQDQj/PBvfSngMQnJn6M0ke4IZOwKLT48oIEX6G2EAwV9/E5IYrLI9KMgbpCPR2IjJCENnmbZiP1LzCsJlh11R161TFxGSaEZb3IEgqd/jCRfisKfXLVW0331xAQo7uwFwEFfFtIdkQ5XzqR5FNNaZFLZWPuX/Xo2lg29otfwiigpckPwTK2rgDAVUOMTchkeUV08OVZBYEH/DZKCQ8+fGeYk5hNyjkLngaPR/RDY5/Ou08OzImo5lkHxl4Z5X3ZQsjoVup8UD+16Ybv+BNcspLcgUcyoiBWCNXm3O5IO/f1AYr3hhS9JIZ9K5i95k/uM/4zSptGB5N4Nrnfuli2nvJksH8H/lY6I2uA8INGZIF4Xhc4i6ybpSsqhEipv4zvfGHtEVRROMteEV1raxh8rduLyfBbEsp9VG8eKec/dnkAzx3ZoINn/Sh+4oOBf8pi1D0y2SwmvIQ1Qkz2CB/S8Nvmmp4//qC4kOauF4OLchv9dpDTtdJ1F3yJU1xC1bEuzaTOPu2MsvBxi/qVfWV8E9GjJl2d+pldX1oVeYwMUB54gAMkH4rrpQaDJ9+NG8V1eTurBns1e8ghy39CrhxTWmwKe1SvzGo0M09ldNpi3kOXJzMe/blUTPn0PcvDhFtdEaedTTM9jHWUKVHz2yxSW1YH5/8htzzMh/P3+DLF7mPLOGZ4edZkscMZT+dxP2YVQid9227xlteItZJIy5aABCYl4a0FQ7mt5f25F/yFZq7ZnY52AzcQ6kh8q42LXSkHKCdDMR5buTm7BiPd2gj5OZNfjVOSrTQIbC1B1TF/K9QV3NIXCzWtJaJ3P10iskF9JWmaIxvaOBcgDV2s6mGfBSkb9VGchpFlTO0w6uP3LDl47wzr5kzeYgMRVTI5+u+dNrZgP9mCHWihUwCcIAwStEnk+rehm+YiOHITqp5kGD8PXmjeKfUBhYWVod1appmAHI7fs8+LxYPjApYFsrfuADXXYzuHq6nvWs8p9EyzKmYhB5WHX10DHsHCOSahtGjvlC9Tf7z5LlneI6zXCZ2Ute6yT/QWLzuPYVMqAMogFW5lQnIjd5BZxS8W2xU8RNPpBN/uefJquSgahHwel7rSoRDcX9BIqFjVmsA2zqGqnL9eah7db/wvKppsSjBdGojomTuL0+73nR5mRlrwfU3siB/yvUQk2OSJzRhen2Z5k0gMOKLU6l3vcbvuQMCFDUHwxrkd2/I1eCbC0P1gnoj7NGKzKPmx/2yLhvB5vep1ZE9oMa9OAcXy/+t8eY5nNRJ5wNN4H8wr7yASiUj5zLWFt80lfBU+wwfIqBcu6f7rN097TvUXwNPKwu6+nPOXP1zPss55GUOGMuxYCLUBFq6FsOeplgf8tEi+SEoYzzQPRs7qk/HZJ0anLS+ydkKDxxBRFOFssTs909umrkgMkpW+RMbISiTn7W62fUEEJuu7fMAAAAAAAAAAAAAAAAABhEVGiQqMGUCMCBBrw6jMWG8ni7AghbGflvAk+Gvc+p5fVhxyVSDCdgWSEgUflkibr6I6JczHF+0rwIxAIRiiR6pYoEPgZtAVV0O1uaJ2cNCvATCr3outlvkxkr7JpSahazZFltQuz5+PYTF6w== + +[RFC-KAT-MLDSA65-ECDSA-brainpoolP256r1-SHA512] +tcId = id-MLDSA65-ECDSA-brainpoolP256r1-SHA512 +pk = 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+ +[RFC-KAT-MLDSA87-ECDSA-P384-SHA512] +tcId = id-MLDSA87-ECDSA-P384-SHA512 +pk = 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+ +[RFC-KAT-MLDSA87-ECDSA-P521-SHA512] +tcId = id-MLDSA87-ECDSA-P521-SHA512 +pk = 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diff --git a/src/tests/test_dilithium.cpp b/src/tests/test_dilithium.cpp index 06d527347bc..bd1ae3d3f59 100644 --- a/src/tests/test_dilithium.cpp +++ b/src/tests/test_dilithium.cpp @@ -21,6 +21,8 @@ #include "test_rng.h" #endif +#include + namespace Botan_Tests { namespace { @@ -288,4 +290,66 @@ BOTAN_REGISTER_TEST("pubkey", "dilithium_keygen", Dilithium_Keygen_Tests); } // namespace +#if defined(BOTAN_HAS_DILITHIUM_COMMON) + +class MLDSA_Param_Tests final : public Test { + public: + struct Test_Case { + bool expect_success; + std::string param; + bool randomized_signature; + }; + + std::vector run() override { + std::string test_name = "MLDSA_Param_Tests"; + std::vector results; + auto rng = Test::new_rng(test_name); + + const std::string msg = "The quick brown fox jumps over the lazy dog."; + const std::vector msgvec(msg.data(), msg.data() + msg.size()); + + const Botan::Dilithium_PrivateKey priv_key(*rng, Botan::DilithiumMode::ML_DSA_4x4); + + const std::vector sign_params = { + Test_Case{true, std::string(""), true}, + Test_Case{true, std::string("Randomized,Pure"), true}, + Test_Case{true, std::string("Deterministic,ctx_hex=00AABB"), false}, + Test_Case{false, std::string("ctx_hex=,ctx_hex="), true}, + Test_Case{false, std::string("Randomized,Deterministic"), false}, + Test_Case{false, std::string("ctx=AA"), true}, + Test_Case{false, std::string("X"), true}, + Test_Case{false, std::string("ctx=A"), true}}; + + for(const auto& [expect_success, param_str, random_sig] : sign_params) { + Test::Result result(std::format("{}: param string = '{}'", test_name, param_str)); + std::unique_ptr signer; + bool exc = false; + try { + signer = std::make_unique(Botan::PK_Signer(priv_key, *rng, param_str)); + } catch(Botan::Exception&) { + exc = true; + } + result.test_bool_eq(std::format("parameters string '{}' for ML-DSA op was valid", param_str), + !exc && signer, + expect_success); + if(exc) { + results.push_back(result); + continue; + } + auto verifier = Botan::PK_Verifier(*priv_key.public_key(), param_str); + auto signature = signer->sign_message(msgvec, *rng); + auto signature2 = signer->sign_message(msgvec, *rng); + result.test_bool_eq( + std::format("signature randomization (param = '{}')", param_str), signature != signature2, random_sig); + result.test_is_true("signature verification", verifier.verify_message(msgvec, signature)); + results.push_back(result); + } + + return results; + } +}; + +BOTAN_REGISTER_TEST("pubkey", "mldsa_op_params", MLDSA_Param_Tests); +#endif + } // namespace Botan_Tests diff --git a/src/tests/test_ffi.cpp b/src/tests/test_ffi.cpp index fdc379c5140..7c1631d631d 100644 --- a/src/tests/test_ffi.cpp +++ b/src/tests/test_ffi.cpp @@ -9,6 +9,7 @@ #include "tests.h" #include +#include #if defined(BOTAN_HAS_FFI) #include @@ -4545,6 +4546,8 @@ class FFI_Signature_Roundtrip_Test : public FFI_Test { virtual std::vector modes() const = 0; virtual const char* hash_algo_or_padding() const = 0; + virtual std::string make_mode_for_key_loading(std::string_view mode) { return std::string(mode); } + public: void ffi_test(Test::Result& result, botan_rng_t rng) override { const std::vector message1 = {'H', 'e', 'l', 'l', 'o', ' '}; @@ -4569,9 +4572,13 @@ class FFI_Signature_Roundtrip_Test : public FFI_Test { botan_privkey_t priv_loaded; botan_pubkey_t pub_loaded; TEST_FFI_OK(private_key_load_function(), - (&priv_loaded, priv_bytes.get().data(), priv_bytes.get().size(), mode)); - TEST_FFI_OK(public_key_load_function(), - (&pub_loaded, pub_bytes.get().data(), pub_bytes.get().size(), mode)); + (&priv_loaded, + priv_bytes.get().data(), + priv_bytes.get().size(), + make_mode_for_key_loading(mode).c_str())); + TEST_FFI_OK( + public_key_load_function(), + (&pub_loaded, pub_bytes.get().data(), pub_bytes.get().size(), make_mode_for_key_loading(mode).c_str())); // re-encode and compare to the first round ViewBytesSink priv_bytes2; @@ -4840,6 +4847,28 @@ class FFI_ML_DSA_Test final : public FFI_Signature_Roundtrip_Test { const char* hash_algo_or_padding() const override { return ""; } }; +class FFI_MLDSA_Composite_Test final : public FFI_Signature_Roundtrip_Test { + public: + std::string name() const override { return "FFI MLDSA-Composite"; } + + private: + const char* algo() const override { return "MLDSA44-RSA2048-PKCS15-SHA256"; } + + privkey_loader_fn_t private_key_load_function() const override { return botan_privkey_load_mldsa_composite; } + + pubkey_loader_fn_t public_key_load_function() const override { return botan_pubkey_load_mldsa_composite; } + + std::vector modes() const override { + return { + "", + }; + } + + const char* hash_algo_or_padding() const override { return ""; } + + std::string make_mode_for_key_loading(std::string_view) override { return std::string(algo()); } +}; + class FFI_SLH_DSA_Test final : public FFI_Signature_Roundtrip_Test { public: std::string name() const override { return "FFI SLH-DSA"; } @@ -5756,6 +5785,7 @@ BOTAN_REGISTER_TEST("ffi", "ffi_kyber768", FFI_Kyber768_Test); BOTAN_REGISTER_TEST("ffi", "ffi_kyber1024", FFI_Kyber1024_Test); BOTAN_REGISTER_TEST("ffi", "ffi_ml_kem", FFI_ML_KEM_Test); BOTAN_REGISTER_TEST("ffi", "ffi_ml_dsa", FFI_ML_DSA_Test); +BOTAN_REGISTER_TEST("ffi", "ffi_mldsa_composite", FFI_MLDSA_Composite_Test); BOTAN_REGISTER_TEST("ffi", "ffi_slh_dsa", FFI_SLH_DSA_Test); BOTAN_REGISTER_TEST("ffi", "ffi_frodokem", FFI_FrodoKEM_Test); BOTAN_REGISTER_TEST("ffi", "ffi_cmce", FFI_Classic_McEliece_Test); diff --git a/src/tests/test_mldsa_composite.cpp b/src/tests/test_mldsa_composite.cpp new file mode 100644 index 00000000000..37563949f3b --- /dev/null +++ b/src/tests/test_mldsa_composite.cpp @@ -0,0 +1,546 @@ +/* + * Tests for MLDSA-composite + * - KAT tests using the KAT vectors from + * https://datatracker.ietf.org/doc/html/draft-ietf-lamps-pq-composite-sigs-15 + * Used the corresponding JSON file at https://github.com/lamps-wg/draft-composite-sigs/blob/main/src/testvectors.json + * + * (C) 2026 Falko Strenzke (MTG AG) + * + * Botan is released under the Simplified BSD License (see license.txt) + */ + +#include "tests.h" + +#include +#include +#include +#include +#include +#if defined(BOTAN_HAS_MLDSA_COMPOSITE) + + #include + #include + #include + #include + #include + #include + #include + #include + #include + #include + #include + #include + #include + + #include "test_pubkey.h" + #include "test_rng.h" + #if defined(BOTAN_HAS_X509_CERTIFICATES) + #include + #include + #endif + +#endif + +namespace Botan_Tests { + +#if defined(BOTAN_HAS_MLDSA_COMPOSITE) + +namespace { + +std::vector decode_var_base64(const VarMap& vars, std::string_view var) { + const auto var_b64 = vars.get_req_str(var); + const auto var_sv = Botan::base64_decode(var_b64); + return std::vector(var_sv.begin(), var_sv.end()); +} + +void mimic_speed_test(Botan::RandomNumberGenerator& rng, Test::Result& result) { + // test for a real-life bug that occurred because of lazy evaluation of the 2nd signature verification. + #if !defined BOTAN_HAS_RSA + return; + #else + std::vector message; + std::vector signature; + std::vector bad_signature; + rng.random_vec(message, 48); + auto sk = Botan::create_private_key("MLDSA65-RSA3072-PKCS15-SHA512", rng, ""); + const char* padding = ""; + Botan::PK_Signer sig(*sk, rng, padding, Botan::Signature_Format::Standard, ""); + auto pk = sk->public_key(); + Botan::PK_Verifier ver(*pk, padding, Botan::Signature_Format::Standard, ""); + signature = sig.sign_message(message, rng); + bad_signature = signature; + bad_signature[0] ^= 1; + result.test_bool_eq("first valid signature", ver.verify_message(message, signature), true); + ver.verify_message(message, bad_signature); + // 2nd run after invalid signature + signature = sig.sign_message(message, rng); + result.test_bool_eq("2nd valid signature", ver.verify_message(message, signature), true); + #endif +} + +void sign_and_verify(const Botan::Private_Key& priv_key, + const Botan::Public_Key& pub_key, + Botan::RandomNumberGenerator& rng, + Test::Result& test_result, + std::string_view test_context) { + const char* message_cstr = "The quick brown fox jumps over the lazy dog."; + std::vector message(message_cstr, message_cstr + strlen(message_cstr)); + Botan::PK_Signer signer(priv_key, rng, ""); + signer.update(message); + std::vector signature = signer.signature(rng); + const size_t sig_max_len = signer.signature_length(); + test_result.test_sz_lte("signature not larger than indicated by signature OP", signature.size(), sig_max_len); + + Botan::PK_Verifier verifier(pub_key, ""); + verifier.update(message); + test_result.test_bool_eq( + std::format("verification of correct signature ({})", test_context), verifier.check_signature(signature), true); + + verifier.update(message); + test_result.test_bool_eq( + std::format("verification of correct signature (repeated use of only verifier with update) ({})", test_context), + verifier.check_signature(signature), + true); + + // test sign_message() with already used signature-op and already used verify-op + for(size_t i = 0; i < 2; i++) { + signature = signer.sign_message(message, rng); // PK_Ops::Signature_with_Hash::update() is called before signing + test_result.test_bool_eq( + std::format( + "verification of correct signature (repeated use of signer and verifier with sign/verify_message) ({})", + test_context), + verifier.verify_message(message, signature), + true); + } + + // test update() with already used signature-op and already used verify-op + signer.update(message); + signature = signer.signature(rng); + verifier.update(message); + test_result.test_bool_eq( + std::format("verification of correct signature (repeated use of signer and verifier with update) ({})", + test_context), + verifier.check_signature(signature), + true); +} +} // namespace + +// + +class MLDSA_Composite_Key_Detail_Tests : public Test { + public: + static Test::Result run_detail_test(Botan::MLDSA_Composite_Param::id_t id) { + auto param = Botan::MLDSA_Composite_Param::from_id_supported_or_throw(id); + const std::string test_name = std::string("MLDSA_Composite_Key_Detail_") + param.id_str(); + Test::Result result(test_name); + auto rng = Test::new_rng(test_name); + + const Botan::MLDSA_Composite_PrivateKey priv_key_generated(*rng, param); + Botan::MLDSA_Composite_PrivateKey priv_key_generated_cp(priv_key_generated); + const Botan::MLDSA_Composite_PrivateKey priv_key_other(*rng, param); + + auto pub_key_generated = priv_key_generated.public_key(); + const Botan::Public_Key* pub_key_cast = static_cast(&priv_key_generated); + + auto message = std::vector(); + Botan::PK_Signer signer(priv_key_generated, *rng, ""); + signer.update(message); + std::vector signature = signer.signature(*rng); + + Botan::PK_Verifier verifier(*pub_key_cast, ""); + verifier.update(message); + result.test_bool_eq("verification of correct signature ", verifier.check_signature(signature), true); + const auto priv_key_sv = priv_key_generated.private_key_bits(); + const std::vector priv_key_v(priv_key_sv.begin(), priv_key_sv.end()); + const auto false_private_keys = generate_false_keys(priv_key_v, param.mldsa_privkey_size()); + + const auto pub_key_bits = pub_key_generated->public_key_bits(); + const auto false_public_keys = generate_false_keys(pub_key_bits, param.mldsa_pubkey_size()); + + try { + const Botan::MLDSA_Composite_PublicKey pub_key_dec(param.id(), pub_key_bits); + Botan::MLDSA_Composite_PublicKey pub_key2(pub_key_dec); + auto priv_key2(priv_key_generated_cp); + priv_key_generated_cp = priv_key_other; // must not influence the copy made above + sign_and_verify(priv_key2, pub_key2, *rng, result, "use copied keys"); + priv_key_generated_cp = priv_key_generated; // back to normal + + pub_key2 = pub_key_dec; + priv_key2 = priv_key_generated; + priv_key_generated_cp = priv_key_other; // must not influence the assignemt made above + sign_and_verify(priv_key2, pub_key2, *rng, result, "use assigned keys"); + priv_key_generated_cp = priv_key_generated; // back to normal + // + mimic_speed_test(*rng, result); + + } catch(const Botan::Exception& e) { + result.test_failure(std::format("Exception during key operations: {}", e.what())); + } + + for(const auto& false_private_key_enc : false_private_keys) { + bool exc = false; + try { + Botan::MLDSA_Composite_PrivateKey(param.id(), false_private_key_enc); + } catch(const Botan::Exception& e) { + exc = true; + } + result.test_bool_eq("decoding of false private key", exc, true); + } + for(const auto& false_public_key_enc : false_public_keys) { + bool exc = false; + try { + Botan::MLDSA_Composite_PublicKey(param.id(), false_public_key_enc); + } catch(const Botan::Exception& e) { + exc = true; + } + result.test_bool_eq("decoding of false public key", exc, true); + } + return result; + } + + std::vector run() override { + const std::vector params { + #if defined(BOTAN_HAS_RSA) + Botan::MLDSA_Composite_Param::from_id_supported_or_throw( + Botan::MLDSA_Composite_Param::id_t::MLDSA44_RSA2048_PKCS15_SHA256), + #endif + #if defined(BOTAN_HAS_ED25519) + Botan::MLDSA_Composite_Param::from_id_supported_or_throw( + Botan::MLDSA_Composite_Param::id_t::MLDSA44_Ed25519_SHA512), + #endif + #if defined BOTAN_HAS_ECDSA && BOTAN_HAS_PCURVES_BRAINPOOL256R1 + Botan::MLDSA_Composite_Param::from_id_supported_or_throw( + Botan::MLDSA_Composite_Param::id_t::MLDSA65_ECDSA_brainpoolP256r1_SHA512), + Botan::MLDSA_Composite_Param::from_id_supported_or_throw( + Botan::MLDSA_Composite_Param::id_t::MLDSA87_ECDSA_P521_SHA512), + #endif + #if defined BOTAN_HAS_ED448 && defined BOTAN_HAS_SHAKE + Botan::MLDSA_Composite_Param::from_id_supported_or_throw( + Botan::MLDSA_Composite_Param::id_t::MLDSA87_Ed448_SHAKE256), + #endif + }; + std::vector result; + result.reserve(params.size()); + for(const auto& param : params) { + result.push_back(run_detail_test(param.id())); + } + return result; + } + + private: + static std::vector> generate_false_keys(const std::span correct_key, + size_t mldsa_key_size) { + std::vector> result; + result.push_back(std::vector()); + result.push_back(std::vector(1)); + result.push_back(std::vector(2)); + result.push_back(std::vector(correct_key.begin(), correct_key.begin() + mldsa_key_size - 1)); + result.push_back(std::vector(correct_key.begin(), correct_key.begin() + mldsa_key_size)); + result.push_back(std::vector(correct_key.begin(), correct_key.begin() + mldsa_key_size + 1)); + result.push_back(std::vector(correct_key.begin(), correct_key.begin() + correct_key.size() - 1)); + + return result; + } +}; + +BOTAN_REGISTER_TEST("pubkey", "mldsa_composite_key_detail", MLDSA_Composite_Key_Detail_Tests); + +class MLDSA_Composite_Sig_Detail_Tests : public Test { + public: + static Test::Result run_detail_test(Botan::MLDSA_Composite_Param::id_t id) { + auto param = Botan::MLDSA_Composite_Param::from_id_supported_or_throw(id); + const std::string test_name = std::string("MLDSA_Composite_Signature_Detail_") + param.id_str(); + Test::Result result(test_name); + auto rng = Test::new_rng(test_name); + + auto priv_key_generated(Botan::create_private_key(param.id_str(), *rng)); + + auto pub_key_generated = priv_key_generated->public_key(); + Botan::Public_Key* pub_key_cast = static_cast(priv_key_generated.get()); + + auto message = std::vector(); + Botan::PK_Signer signer(*priv_key_generated, *rng, ""); + signer.update(message); + std::vector signature = signer.signature(*rng); + + const auto false_signatures = generate_false_signatures(signature, param.mldsa_signature_size()); + + Botan::PK_Verifier verifier(*pub_key_cast, ""); + verifier.update(message); + result.test_bool_eq("verification of correct signature ", verifier.check_signature(signature), true); + + for(const auto& false_signature : false_signatures) { + Botan::PK_Verifier verifier2(*pub_key_cast, ""); + verifier2.update(message); + result.test_bool_eq("verification of false signature", verifier2.check_signature(false_signature), false); + verifier2.update(message); + result.test_is_true( + std::format( + "verification of correct signature after failed verification, false signature length = {}, length of correct signature = {}", + false_signature.size(), + signature.size()), + verifier2.check_signature(signature)); + } + return result; + } + + std::vector run() override { + const std::vector params { + #if defined(BOTAN_HAS_RSA) + Botan::MLDSA_Composite_Param::from_id_supported_or_throw( + Botan::MLDSA_Composite_Param::id_t::MLDSA44_RSA2048_PKCS15_SHA256), + #endif + #if defined(BOTAN_HAS_PSS) + Botan::MLDSA_Composite_Param::from_id_supported_or_throw( + Botan::MLDSA_Composite_Param::id_t::MLDSA44_RSA2048_PSS_SHA256), + #endif + #if defined(BOTAN_HAS_ED25519) + Botan::MLDSA_Composite_Param::from_id_supported_or_throw( + Botan::MLDSA_Composite_Param::id_t::MLDSA44_Ed25519_SHA512), + #endif + #if defined BOTAN_HAS_ECDSA && defined BOTAN_HAS_PCURVES_BRAINPOOL256R1 + Botan::MLDSA_Composite_Param::from_id_supported_or_throw( + Botan::MLDSA_Composite_Param::id_t::MLDSA65_ECDSA_brainpoolP256r1_SHA512), + #endif + #if defined BOTAN_HAS_ED448 && defined BOTAN_HAS_SHAKE + Botan::MLDSA_Composite_Param::from_id_supported_or_throw( + Botan::MLDSA_Composite_Param::id_t::MLDSA87_Ed448_SHAKE256) + #endif + }; + + std::vector result; + result.reserve(params.size()); + for(const auto& param : params) { + result.push_back(run_detail_test(param.id())); + } + return result; + } + + private: + static std::vector> generate_false_signatures(std::span correct_signature, + size_t mldsa_signature_size) { + std::vector> result; + result.push_back(std::vector()); + result.push_back(std::vector(1)); + result.push_back( + std::vector(correct_signature.begin(), correct_signature.begin() + mldsa_signature_size)); + result.push_back( + std::vector(correct_signature.begin(), correct_signature.begin() + mldsa_signature_size + 1)); + + std::vector flip_start(correct_signature.begin(), correct_signature.end()); + flip_start[0] ^= 1; + result.push_back(flip_start); + + std::vector flip_end(correct_signature.begin(), correct_signature.end()); + flip_end[flip_end.size() - 1] ^= 1; + result.push_back(flip_end); + + std::vector flip_start_of_trad(correct_signature.begin(), correct_signature.end()); + flip_start_of_trad[mldsa_signature_size] ^= 1; + result.push_back(flip_start_of_trad); + + return result; + } +}; + +BOTAN_REGISTER_TEST("pubkey", "mldsa_composite_sig_detail", MLDSA_Composite_Sig_Detail_Tests); + +class MLDSA_Composite_RT_Tests : public Test { + public: + static Test::Result run_detail_test(Botan::MLDSA_Composite_Param::id_t id) { + auto param = Botan::MLDSA_Composite_Param::from_id_supported_or_throw(id); + const std::string test_name = std::string("MLDSA_Composite_round_trip_") + param.id_str(); + Test::Result result(test_name); + auto rng = Test::new_rng(test_name); + if(!param.is_supported()) { + result.test_throws("create MLDSA-composite private key for non-supported parameter", + [&]() { Botan::create_private_key(param.id_str(), *rng); }); + return result; + } + + auto priv_key_generated = Botan::create_private_key(param.id_str(), *rng); + if(nullptr == priv_key_generated) { + result.test_bool_eq("generated private key non-null", false, true); + } else { + auto pub_key_generated = priv_key_generated->public_key(); + if(nullptr == pub_key_generated) { + result.test_bool_eq("generated pub key key non-null", false, true); + } else { + sign_and_verify(*priv_key_generated, *pub_key_generated, *rng, result, "produced with generated key"); + } + } + const uint64_t rep_cnt = options().run_long_tests() ? 150 : 1; + for(uint64_t i = 1; i < rep_cnt; i++) { + Botan::secure_vector private_enc = priv_key_generated->private_key_bits(); + if(test_name.find("ECDSA") != std::string::npos) { + check_encoded_ecdsa_private_key(private_enc, result); + } + std::vector public_enc = priv_key_generated->public_key_bits(); + const Botan::MLDSA_Composite_PrivateKey priv_key_redec(priv_key_generated->algorithm_identifier(), + private_enc); + const Botan::MLDSA_Composite_PublicKey pub_key_redec(priv_key_generated->algorithm_identifier(), + public_enc); + sign_and_verify(priv_key_redec, pub_key_redec, *rng, result, "produced with re-decoded key"); + } + return result; + } + + std::vector run() override { + auto all_params = Botan::MLDSA_Composite_Param::all_supported_param_sets(); + std::vector result; + result.reserve(all_params.size()); + for(const auto& param : all_params) { + result.push_back(run_detail_test(param.id())); + } + return result; + } + + private: + static void check_encoded_ecdsa_private_key(std::span composite_private_key, Test::Result& result) { + Botan::OID key_parameters; + Botan::secure_vector private_key_bits; + const Botan::secure_vector public_key_bits; + if(composite_private_key.size() < 33) { + result.test_failure("encoded ECDSA component private key is too short"); + } + const std::vector ecdsa_private_enc(composite_private_key.begin() + 32, composite_private_key.end()); + try { + Botan::BER_Decoder(ecdsa_private_enc) + .start_sequence() + .decode_and_check(1, "Unknown version code for ECC key") + .decode(private_key_bits, Botan::ASN1_Type::OctetString) + .decode_optional(key_parameters, Botan::ASN1_Type(0), Botan::ASN1_Class::ExplicitContextSpecific) + .end_cons() + .verify_end(); + } catch(const Botan::Exception& e) { + result.test_failure(std::format("verify ECDSA private format decoding: {}", e.what())); + } + } +}; + +BOTAN_REGISTER_TEST("pubkey", "mldsa_composite_roundtrips", MLDSA_Composite_RT_Tests); + + #if defined(BOTAN_TARGET_OS_HAS_FILESYSTEM) + +class MLDSA_Composite_KAT_Tests : public Text_Based_Test { + public: + MLDSA_Composite_KAT_Tests() : + Text_Based_Test("pubkey/mldsa_composite.vec", "tcId,pk,x5c,sk,sk_pkcs8,s,sWithContext") {} + + Test::Result run_one_test(const std::string& name, const VarMap& vars) override { + auto rng = std::make_unique(Botan::hex_decode( + "061550234D158C5EC95595FE04EF7A25767F2E24CC2BC479D09D86DC9ABCFDE7056A8C266F9EF97ED08541DBD2E1FFA1")); + bool pubkey_valid = true; + bool privkey_valid = true; + bool exc_during_pubkey_decoding = false; + bool exc_during_privkey_decoding = false; + if(name.ends_with("pubkey-invalid")) { + pubkey_valid = false; + } + if(name.ends_with("privkey-invalid")) { + privkey_valid = false; + } + Test::Result result(name); + auto tcId = vars.get_req_str("tcId"); + if(tcId.starts_with("id-")) { + tcId = tcId.substr(3); + } + const auto pk = vars.get_req_str("pk"); + const auto pk_bin = Botan::base64_decode(pk); + + const auto sk = vars.get_req_str("sk"); + const auto sk_bin = Botan::base64_decode(sk); + + const auto sig_bin = Botan::base64_decode(vars.get_req_str("s")); + + const auto comp_parm_opt = Botan::MLDSA_Composite_Param::from_id_str(tcId); + // support of composite algorithms also depends on whether Botan's build configuration supports the individual traditional component algorithm. + if(!comp_parm_opt.has_value() or !comp_parm_opt.value().is_supported()) { + return result; + } + + const auto comp_parm = comp_parm_opt.value(); + + const char* message = "The quick brown fox jumps over the lazy dog."; + std::unique_ptr pubkey; + std::unique_ptr privkey; + + try { + pubkey = std::make_unique(comp_parm.id(), pk_bin); + } catch(const Botan::Exception& e) { + exc_during_pubkey_decoding = true; + } + result.test_bool_eq("pubkey decoding OK", !exc_during_pubkey_decoding, pubkey_valid); + if(exc_during_pubkey_decoding) { + return result; + } + Botan::PK_Verifier verifier(*pubkey, ""); + verifier.update(message); + result.test_bool_eq("verification of correct signature", verifier.check_signature(sig_bin), true); + + try { + privkey = std::make_unique(comp_parm.id(), sk_bin); + } catch(const Botan::Exception& e) { + exc_during_privkey_decoding = true; + } + result.test_bool_eq("privkey decoding OK", !exc_during_privkey_decoding, privkey_valid); + if(exc_during_privkey_decoding) { + return result; + } + sign_and_verify(*privkey, *pubkey, *rng, result, "produced by decoded private key"); + return result; + } +}; + +BOTAN_REGISTER_TEST("pubkey", "mldsa_composite_kat", MLDSA_Composite_KAT_Tests); + + #if defined(BOTAN_HAS_X509_CERTIFICATES) + +class MLDSA_Composite_X509_Tests : public Text_Based_Test { + public: + MLDSA_Composite_X509_Tests() : + Text_Based_Test("pubkey/mldsa_composite.vec", "tcId,x5c,sk_pkcs8", "pk,sk,s,sWithContext") {} + + Test::Result run_one_test(const std::string& name, const VarMap& vars) override { + auto rng = std::make_unique(Botan::hex_decode( + "061550234D158C5EC95595FE04EF7A25767F2E24CC2BC479D09D86DC9ABCFDE7056A8C266F9EF97ED08541DBD2E1FFA1")); + Test::Result result(name); + + auto tcId = vars.get_req_str("tcId"); + if(tcId.starts_with("id-")) { + tcId = tcId.substr(3); + } + + const std::vector x5c = decode_var_base64(vars, "x5c"); + const auto comp_parm_opt = Botan::MLDSA_Composite_Param::from_id_str(tcId); + + Botan::X509_Certificate cert(x5c); + if(comp_parm_opt.has_value() and comp_parm_opt.value().is_supported()) { + auto ver_res = cert.verify_signature(*cert.subject_public_key()); + result.test_is_true("signature of certificate verifies", + ver_res.first == Botan::Certificate_Status_Code::OK); + } else { + // doesn't throw Not_Implemented, but seems to catch that one and wrap it into another exception. + result.test_throws("verify certificate with unsupported MLDSA-composite parameters" + + (comp_parm_opt.has_value() ? " " + comp_parm_opt.value().id_str() : ""), + [&] { cert.verify_signature(*cert.subject_public_key()); }); + return result; + } + + const std::shared_ptr private_key = + Botan::PKCS8::load_key(decode_var_base64(vars, "sk_pkcs8")); + + sign_and_verify(*private_key, + *cert.subject_public_key(), + *rng, + result, + "PKCS#8 private key signs and cert's public key verifies"); + return result; + } +}; + +BOTAN_REGISTER_TEST("pubkey", "mldsa_composite_x509", MLDSA_Composite_X509_Tests); + #endif + #endif +#endif +} // namespace Botan_Tests From c8be7acf6be1c6b34b5cfd4a49ff08f73c8276e1 Mon Sep 17 00:00:00 2001 From: Falko Strenzke <30287971+falko-strenzke@users.noreply.github.com> Date: Mon, 22 Jun 2026 12:42:00 +0200 Subject: [PATCH 02/25] Update doc/api_ref/pubkey.rst --- doc/api_ref/pubkey.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/doc/api_ref/pubkey.rst b/doc/api_ref/pubkey.rst index eb072fbf8ef..94f1fb8d7d0 100644 --- a/doc/api_ref/pubkey.rst +++ b/doc/api_ref/pubkey.rst @@ -168,7 +168,7 @@ Currently two flavors of Dilithium are implemented in separate Botan modules: * ``dilithium_aes``, that uses AES instead of Keccak-based primitives. This mode is deprecated and will be removed in a future release. -ML-DSA (draft-ietf-lamps-pq-composite-sigs-15) +ML-DSA-composite (draft-ietf-lamps-pq-composite-sigs-15) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Composite signature algorithms combining ML-DSA with a traditional signature algorithm. All variants defined in draft-ietf-lamps-pq-composite-sigs-15 are supported. Each is modelled as a From 1d4cca304727fd410ae9a87ef804d6baadc120a2 Mon Sep 17 00:00:00 2001 From: Falko Strenzke <30287971+falko-strenzke@users.noreply.github.com> Date: Mon, 22 Jun 2026 12:42:36 +0200 Subject: [PATCH 03/25] Update src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h --- src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h index de701ba0946..be171ca5f9f 100644 --- a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h +++ b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h @@ -37,7 +37,7 @@ class BOTAN_PUBLIC_API(3, 0) MLDSA_Composite_Param { MLDSA65_Ed25519_SHA512, MLDSA87_Ed448_SHAKE256, }; - +static inline const char* generic_algo_name = "MLDSA-Composite";¬ static std::vector all_param_sets(); static std::vector all_supported_param_sets(); From 5e2939f10df1f672bf1c3ee9b3861d6e7a4a6a89 Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Mon, 22 Jun 2026 12:44:13 +0200 Subject: [PATCH 04/25] remove unused vars --- src/lib/pubkey/mldsa-composite/mldsa_comp.cpp | 4 ---- src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h | 1 - 2 files changed, 5 deletions(-) diff --git a/src/lib/pubkey/mldsa-composite/mldsa_comp.cpp b/src/lib/pubkey/mldsa-composite/mldsa_comp.cpp index a887369e93a..b9473e99813 100644 --- a/src/lib/pubkey/mldsa-composite/mldsa_comp.cpp +++ b/src/lib/pubkey/mldsa-composite/mldsa_comp.cpp @@ -31,8 +31,6 @@ namespace Botan { namespace { std::span mldsa_pubkey_subspan(const MLDSA_Composite_Param& param, std::span key_bits) { - const OID oid(param.mldsa_oid_str()); - const AlgorithmIdentifier aid(oid, AlgorithmIdentifier::Encoding_Option::USE_EMPTY_PARAM); if(key_bits.size() <= param.mldsa_pubkey_size()) { throw Invalid_Argument(fmt("encoded MLDSA component public key is too short (len = {})", key_bits.size())); } @@ -40,8 +38,6 @@ std::span mldsa_pubkey_subspan(const MLDSA_Composite_Param& param } std::span mldsa_privkey_subspan(const MLDSA_Composite_Param& param, std::span key_bits) { - const OID oid(param.mldsa_oid_str()); - const AlgorithmIdentifier aid(oid, AlgorithmIdentifier::Encoding_Option::USE_EMPTY_PARAM); if(key_bits.size() <= param.mldsa_privkey_size()) { throw Invalid_Argument("encoded MLDSA component private key is too short"); } diff --git a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h index be171ca5f9f..7737788d28c 100644 --- a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h +++ b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h @@ -104,7 +104,6 @@ static inline const char* generic_algo_name = "MLDSA-Composite";¬ std::string curve() const { return std::string(this->m_curve); } std::string get_traditional_algo_param_str() const; - size_t traditional_pubkey_encoded_size() const; size_t mldsa_privkey_size() const { return 32; } From 2a44db31c7bdc6d8105f988ab6ee812ff186f05d Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Mon, 22 Jun 2026 12:50:00 +0200 Subject: [PATCH 05/25] fix header guard --- src/lib/ffi/ffi_pkey_algs.cpp | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/src/lib/ffi/ffi_pkey_algs.cpp b/src/lib/ffi/ffi_pkey_algs.cpp index 0e7ee1a7a27..5afa569b8c9 100644 --- a/src/lib/ffi/ffi_pkey_algs.cpp +++ b/src/lib/ffi/ffi_pkey_algs.cpp @@ -7,8 +7,6 @@ */ #include -#include -#include #include #include @@ -89,6 +87,10 @@ #include #endif +#if defined(BOTAN_HAS_MLDSA_COMPOSITE) + #include +#endif + #if defined(BOTAN_HAS_SLH_DSA_WITH_SHA2) || defined(BOTAN_HAS_SLH_DSA_WITH_SHAKE) #include #endif From 8c367c79dd0563cd2cfcba3d5d07f4372e67ae5e Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Mon, 22 Jun 2026 13:29:48 +0200 Subject: [PATCH 06/25] fix compilation error --- src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h | 4 +++- 1 file changed, 3 insertions(+), 1 deletion(-) diff --git a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h index 7737788d28c..6ddff3f78c0 100644 --- a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h +++ b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h @@ -37,7 +37,9 @@ class BOTAN_PUBLIC_API(3, 0) MLDSA_Composite_Param { MLDSA65_Ed25519_SHA512, MLDSA87_Ed448_SHAKE256, }; -static inline const char* generic_algo_name = "MLDSA-Composite";¬ + + static inline const char* generic_algo_name = "MLDSA-Composite"; + static std::vector all_param_sets(); static std::vector all_supported_param_sets(); From adcdad208f28fd844e8846a1cc660925cda0ceda Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Mon, 22 Jun 2026 18:06:33 +0200 Subject: [PATCH 07/25] new mldsa-comp parameterization --- doc/api_ref/pubkey.rst | 2 +- src/cli/perf_pk_sig.cpp | 64 ++++--------------- .../mldsa-composite/mldsa_comp_parameters.cpp | 3 + src/lib/pubkey/pk_algs.cpp | 45 ++++++++----- src/tests/test_ffi.cpp | 16 ++++- src/tests/test_mldsa_composite.cpp | 62 ++++++++---------- 6 files changed, 86 insertions(+), 106 deletions(-) diff --git a/doc/api_ref/pubkey.rst b/doc/api_ref/pubkey.rst index 94f1fb8d7d0..efa9a9060e8 100644 --- a/doc/api_ref/pubkey.rst +++ b/doc/api_ref/pubkey.rst @@ -169,7 +169,7 @@ Currently two flavors of Dilithium are implemented in separate Botan modules: This mode is deprecated and will be removed in a future release. ML-DSA-composite (draft-ietf-lamps-pq-composite-sigs-15) -~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Composite signature algorithms combining ML-DSA with a traditional signature algorithm. All variants defined in draft-ietf-lamps-pq-composite-sigs-15 are supported. Each is modelled as a distinct algorithm in Botan. The module for the composite algorithms is given by `mldsa-composite`, but note that diff --git a/src/cli/perf_pk_sig.cpp b/src/cli/perf_pk_sig.cpp index 67e9f62aaa6..989db2445fc 100644 --- a/src/cli/perf_pk_sig.cpp +++ b/src/cli/perf_pk_sig.cpp @@ -408,69 +408,29 @@ BOTAN_REGISTER_PERF_TEST("ML-DSA", PerfTest_ML_DSA); #endif -} // namespace - #if defined(BOTAN_HAS_MLDSA_COMPOSITE) -template class PerfTest_MLDSA_Composite final : public PerfTest_PKSig { public: - std::string algo() const override { return Botan::MLDSA_Composite_Param::from_id_supported_or_throw(A).id_str(); } + std::string algo() const override { return Botan::MLDSA_Composite_Param::generic_algo_name; } std::string hash() const override { return ""; } std::vector keygen_params(const PerfConfig& /*config*/) const override { - return {Botan::MLDSA_Composite_Param::from_id_supported_or_throw(A).id_str()}; + const auto all_params = Botan::MLDSA_Composite_Param::all_supported_param_sets(); + std::vector result; + result.reserve(all_params.size()); + for(const auto& param : all_params) { + result.push_back(param.id_str()); + } + return result; } }; -// NOLINTNEXTLINE(cppcoreguidelines-macro-usag) - #define BOTAN_REGISTER_PERF_TEST_TMPL(name, Perf_Class) \ - /* NOLINTNEXTLINE(cert-err58-cpp) */ \ - const Botan_CLI::PerfTest::Registration reg_perf_##Perf_Class##_##name( \ - #name, []() -> std::unique_ptr { \ - /* NOLINTNEXTLINE(bugprone-macro-parentheses) */ \ - return std::make_unique>(); \ - }) - - #if defined(BOTAN_HAS_RSA) -BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA44_RSA2048_PKCS15_SHA256, PerfTest_MLDSA_Composite); -BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA65_RSA3072_PKCS15_SHA512, PerfTest_MLDSA_Composite); -BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA65_RSA4096_PKCS15_SHA512, PerfTest_MLDSA_Composite); - #endif - #if defined(BOTAN_HAS_PSS) -BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA44_RSA2048_PSS_SHA256, PerfTest_MLDSA_Composite); -BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA65_RSA3072_PSS_SHA512, PerfTest_MLDSA_Composite); -BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA65_RSA4096_PSS_SHA512, PerfTest_MLDSA_Composite); -BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA87_RSA3072_PSS_SHA512, PerfTest_MLDSA_Composite); -BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA87_RSA4096_PSS_SHA512, PerfTest_MLDSA_Composite); - #endif - #if defined(BOTAN_HAS_ECDSA) - #if BOTAN_HAS_PCURVES_SECP256R1 -BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA44_ECDSA_P256_SHA256, PerfTest_MLDSA_Composite); -BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA65_ECDSA_P256_SHA512, PerfTest_MLDSA_Composite); - #endif - #if BOTAN_HAS_PCURVES_SECP384R1 -BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA65_ECDSA_P384_SHA512, PerfTest_MLDSA_Composite); -BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA87_ECDSA_P384_SHA512, PerfTest_MLDSA_Composite); - #endif - #if BOTAN_HAS_PCURVES_BRAINPOOL256R1 -BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA65_ECDSA_brainpoolP256r1_SHA512, PerfTest_MLDSA_Composite); - #endif - #if BOTAN_HAS_PCURVES_BRAINPOOL384R1 -BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA87_ECDSA_brainpoolP384r1_SHA512, PerfTest_MLDSA_Composite); - #endif - #if BOTAN_HAS_PCURVES_SECP521R1 -BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA87_ECDSA_P521_SHA512, PerfTest_MLDSA_Composite); - #endif - #endif - #if defined(BOTAN_HAS_ED25519) -BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA44_Ed25519_SHA512, PerfTest_MLDSA_Composite); -BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA65_Ed25519_SHA512, PerfTest_MLDSA_Composite); - #endif - #if defined(BOTAN_HAS_ED448) && defined(BOTAN_HAS_SHAKE) -BOTAN_REGISTER_PERF_TEST_TMPL(MLDSA87_Ed448_SHAKE256, PerfTest_MLDSA_Composite); - #endif +BOTAN_REGISTER_PERF_TEST("MLDSA-Composite", PerfTest_MLDSA_Composite); + #endif +} // namespace + } // namespace Botan_CLI diff --git a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp index 75673e468f5..1e2193d8c8f 100644 --- a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp +++ b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp @@ -14,6 +14,7 @@ #include #include #include +#include #include namespace Botan { @@ -257,9 +258,11 @@ std::optional MLDSA_Composite_Param::from_id(MLDSA_Compos MLDSA_Composite_Param MLDSA_Composite_Param::from_id_supported_or_throw(MLDSA_Composite_Param::id_t id) { const auto result = from_id(id); if(!result.has_value()) { + std::cout << "MLDSA_Composite_Param::from_id_supported_or_throw has no value\n"; throw Botan::Invalid_Argument("no parameter found for provided MLDSA composite id (enum)"); } if(!result.value().is_supported()) { + std::cout << "MLDSA_Composite_Param::from_id_supported_or_throw is not supported\n"; throw Not_Implemented("Parameter set " + result.value().id_str() + " is not supported by Botan's build configuration"); } diff --git a/src/lib/pubkey/pk_algs.cpp b/src/lib/pubkey/pk_algs.cpp index ca1b6a29244..53835e9d46f 100644 --- a/src/lib/pubkey/pk_algs.cpp +++ b/src/lib/pubkey/pk_algs.cpp @@ -273,12 +273,17 @@ std::unique_ptr load_public_key(const AlgorithmIdentifier& alg_id, #endif #if defined(BOTAN_HAS_MLDSA_COMPOSITE) - if(alg_name.starts_with("MLDSA")) { - auto comp_parm = MLDSA_Composite_Param::from_id_str(alg_name); - if(comp_parm.has_value()) { - return std::make_unique(comp_parm->id(), key_bits); + { + auto mldsa_comp_param_opt = MLDSA_Composite_Param::from_algo_id(alg_id); + if(mldsa_comp_param_opt.has_value()) { + auto& comp_parm = mldsa_comp_param_opt.value(); + if(comp_parm.is_supported()) { + return std::make_unique(alg_id, key_bits); + } else { + throw Not_Implemented(fmt("MLDSA-composite is supported, but the requested parameter set {} is not", + alg_id.get_oid().to_string())); + } } - // we continue the search as there might be other algorithms defined with leading "MLDSA" } #endif @@ -450,12 +455,17 @@ std::unique_ptr load_private_key(const AlgorithmIdentifier& alg_id, #endif #if defined(BOTAN_HAS_MLDSA_COMPOSITE) - if(alg_name.starts_with("MLDSA")) { - auto comp_parm = MLDSA_Composite_Param::from_id_str(alg_name); - if(comp_parm.has_value()) { - return std::make_unique(comp_parm->id(), key_bits); + { + auto mldsa_comp_param_opt = MLDSA_Composite_Param::from_algo_id(alg_id); + if(mldsa_comp_param_opt.has_value()) { + auto& comp_parm = mldsa_comp_param_opt.value(); + if(comp_parm.is_supported()) { + return std::make_unique(alg_id, key_bits); + } else { + throw Not_Implemented(fmt("MLDSA-composite is supported, but the requested parameter set {} is not", + alg_id.get_oid().to_string())); + } } - // we continue the search as there might be other algorithms defined with leading "MLDSA" } #endif @@ -647,13 +657,16 @@ std::unique_ptr create_private_key(std::string_view alg_name, #endif #if defined(BOTAN_HAS_MLDSA_COMPOSITE) - - if(alg_name.starts_with("MLDSA")) { - auto comp_parm = MLDSA_Composite_Param::from_id_str(alg_name); - if(comp_parm.has_value()) { - return std::make_unique(rng, comp_parm.value()); + { + if(alg_name == MLDSA_Composite_Param::generic_algo_name) { + auto comp_param = MLDSA_Composite_Param::from_id_str_or_throw(params); + if(comp_param.is_supported()) { + return std::make_unique(rng, comp_param); + } else { + throw Not_Implemented( + fmt("MLDSA-composite is supported, but the requested parameter set {} is not", params)); + } } - // we continue, there might be other algorithms defined with leading "MLDSA" } #endif diff --git a/src/tests/test_ffi.cpp b/src/tests/test_ffi.cpp index 7c1631d631d..a96365d04fd 100644 --- a/src/tests/test_ffi.cpp +++ b/src/tests/test_ffi.cpp @@ -36,6 +36,10 @@ #include #endif +#if defined(BOTAN_HAS_MLDSA_COMPOSITE) + #include +#endif + namespace Botan_Tests { namespace { @@ -4852,7 +4856,7 @@ class FFI_MLDSA_Composite_Test final : public FFI_Signature_Roundtrip_Test { std::string name() const override { return "FFI MLDSA-Composite"; } private: - const char* algo() const override { return "MLDSA44-RSA2048-PKCS15-SHA256"; } + const char* algo() const override { return Botan::MLDSA_Composite_Param::generic_algo_name; } privkey_loader_fn_t private_key_load_function() const override { return botan_privkey_load_mldsa_composite; } @@ -4860,7 +4864,15 @@ class FFI_MLDSA_Composite_Test final : public FFI_Signature_Roundtrip_Test { std::vector modes() const override { return { - "", + #if defined(BOTAN_HAS_RSA) + "MLDSA44-RSA2048-PSS-SHA256", + #endif + #if defined(BOTAN_HAS_ED25519) + "MLDSA44-Ed25519-SHA512", + #endif + #if defined(BOTAN_HAS_ECDSA) && defined(BOTAN_HAS_PCURVES_BRAINPOOL256R1) + "MLDSA65-ECDSA-brainpoolP256r1-SHA512", + #endif }; } diff --git a/src/tests/test_mldsa_composite.cpp b/src/tests/test_mldsa_composite.cpp index 37563949f3b..97fcf6a8e80 100644 --- a/src/tests/test_mldsa_composite.cpp +++ b/src/tests/test_mldsa_composite.cpp @@ -62,7 +62,12 @@ void mimic_speed_test(Botan::RandomNumberGenerator& rng, Test::Result& result) { std::vector signature; std::vector bad_signature; rng.random_vec(message, 48); - auto sk = Botan::create_private_key("MLDSA65-RSA3072-PKCS15-SHA512", rng, ""); + auto sk = + Botan::create_private_key(Botan::MLDSA_Composite_Param::generic_algo_name, rng, "MLDSA65-RSA3072-PKCS15-SHA512"); + result.test_not_null("generated private key is non-null", sk); + if(sk == nullptr) { + return; + } const char* padding = ""; Botan::PK_Signer sig(*sk, rng, padding, Botan::Signature_Format::Standard, ""); auto pk = sk->public_key(); @@ -136,6 +141,7 @@ class MLDSA_Composite_Key_Detail_Tests : public Test { auto rng = Test::new_rng(test_name); const Botan::MLDSA_Composite_PrivateKey priv_key_generated(*rng, param); + Botan::MLDSA_Composite_PrivateKey priv_key_generated_cp(priv_key_generated); const Botan::MLDSA_Composite_PrivateKey priv_key_other(*rng, param); @@ -253,7 +259,13 @@ class MLDSA_Composite_Sig_Detail_Tests : public Test { Test::Result result(test_name); auto rng = Test::new_rng(test_name); - auto priv_key_generated(Botan::create_private_key(param.id_str(), *rng)); + auto priv_key_generated( + Botan::create_private_key(Botan::MLDSA_Composite_Param::generic_algo_name, *rng, param.id_str())); + + result.test_not_null("generated private key is not null", priv_key_generated); + if(!priv_key_generated) { + return result; + } auto pub_key_generated = priv_key_generated->public_key(); Botan::Public_Key* pub_key_cast = static_cast(priv_key_generated.get()); @@ -285,28 +297,8 @@ class MLDSA_Composite_Sig_Detail_Tests : public Test { } std::vector run() override { - const std::vector params { - #if defined(BOTAN_HAS_RSA) - Botan::MLDSA_Composite_Param::from_id_supported_or_throw( - Botan::MLDSA_Composite_Param::id_t::MLDSA44_RSA2048_PKCS15_SHA256), - #endif - #if defined(BOTAN_HAS_PSS) - Botan::MLDSA_Composite_Param::from_id_supported_or_throw( - Botan::MLDSA_Composite_Param::id_t::MLDSA44_RSA2048_PSS_SHA256), - #endif - #if defined(BOTAN_HAS_ED25519) - Botan::MLDSA_Composite_Param::from_id_supported_or_throw( - Botan::MLDSA_Composite_Param::id_t::MLDSA44_Ed25519_SHA512), - #endif - #if defined BOTAN_HAS_ECDSA && defined BOTAN_HAS_PCURVES_BRAINPOOL256R1 - Botan::MLDSA_Composite_Param::from_id_supported_or_throw( - Botan::MLDSA_Composite_Param::id_t::MLDSA65_ECDSA_brainpoolP256r1_SHA512), - #endif - #if defined BOTAN_HAS_ED448 && defined BOTAN_HAS_SHAKE - Botan::MLDSA_Composite_Param::from_id_supported_or_throw( - Botan::MLDSA_Composite_Param::id_t::MLDSA87_Ed448_SHAKE256) - #endif - }; + const std::vector params = + Botan::MLDSA_Composite_Param::all_supported_param_sets(); std::vector result; result.reserve(params.size()); @@ -353,22 +345,22 @@ class MLDSA_Composite_RT_Tests : public Test { Test::Result result(test_name); auto rng = Test::new_rng(test_name); if(!param.is_supported()) { - result.test_throws("create MLDSA-composite private key for non-supported parameter", - [&]() { Botan::create_private_key(param.id_str(), *rng); }); + result.test_throws( + "create MLDSA-composite private key for non-supported parameter", [&]() { + Botan::create_private_key(Botan::MLDSA_Composite_Param::generic_algo_name, *rng, param.id_str()); + }); return result; } - auto priv_key_generated = Botan::create_private_key(param.id_str(), *rng); + auto priv_key_generated = + Botan::create_private_key(Botan::MLDSA_Composite_Param::generic_algo_name, *rng, param.id_str()); + result.test_not_null("generated private key is non-null", priv_key_generated); if(nullptr == priv_key_generated) { - result.test_bool_eq("generated private key non-null", false, true); - } else { - auto pub_key_generated = priv_key_generated->public_key(); - if(nullptr == pub_key_generated) { - result.test_bool_eq("generated pub key key non-null", false, true); - } else { - sign_and_verify(*priv_key_generated, *pub_key_generated, *rng, result, "produced with generated key"); - } + return result; } + auto pub_key_generated = priv_key_generated->public_key(); + sign_and_verify(*priv_key_generated, *pub_key_generated, *rng, result, "produced with generated key"); + const uint64_t rep_cnt = options().run_long_tests() ? 150 : 1; for(uint64_t i = 1; i < rep_cnt; i++) { Botan::secure_vector private_enc = priv_key_generated->private_key_bits(); From 9ca6421e54294e80ae348cd7b43cb2e0cb58023c Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Tue, 23 Jun 2026 08:20:52 +0200 Subject: [PATCH 08/25] adapt doc to new parameter model --- doc/api_ref/pubkey.rst | 16 ++++++---------- 1 file changed, 6 insertions(+), 10 deletions(-) diff --git a/doc/api_ref/pubkey.rst b/doc/api_ref/pubkey.rst index efa9a9060e8..e37f988421d 100644 --- a/doc/api_ref/pubkey.rst +++ b/doc/api_ref/pubkey.rst @@ -168,13 +168,10 @@ Currently two flavors of Dilithium are implemented in separate Botan modules: * ``dilithium_aes``, that uses AES instead of Keccak-based primitives. This mode is deprecated and will be removed in a future release. -ML-DSA-composite (draft-ietf-lamps-pq-composite-sigs-15) +ML-DSA-composite (draft-ietf-lamps-pq-composite-sigs-19) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -Composite signature algorithms combining ML-DSA with a traditional signature algorithm. All -variants defined in draft-ietf-lamps-pq-composite-sigs-15 are supported. Each is modelled as a -distinct algorithm in Botan. The module for the composite algorithms is given by `mldsa-composite`, but note that -naturally only those algorithm combinations are available for which the respective module -support is compiled. +Composite signature algorithms combining ML-DSA with a traditional signature algorithm. All variants defined in draft-ietf-lamps-pq-composite-sigs-19 are supported. Each is modelled as a specific parameter value of the generic algorithm +``MLDSA-Composite``. The module for the composite algorithms is given by `mldsa-composite`, but note that naturally only those algorithm combinations are available for which the respective module support is compiled. ML-KEM (FIPS 203) @@ -1049,10 +1046,9 @@ Botan implements the following signature algorithms: #. ML-DSA (Dilithium). Takes and optional parameter string formed by comma-separated list of the following format ``[(Deterministic|Randomized),][Pure,][ctx_hex=]``, where the ordering of the comma-separated elements is arbitrary. The specification of ``Pure`` is redundant since currently only the pure variant of ML-DSA is implemented. The defaults of the other values are ``Randomized`` and an empty context parameter (`ctx_hex`). Non-empty context parameters are only supported by ML-DSA, but not by Dilithium. ``Deterministic`` or ``Randomized`` may also be specified in a verification operation thought it has no effect there. - -#. ML-DSA-composite (draft-ietf-lamps-pq-composite-sigs-15). - Takes no parameters. The following algorithms are defined and are accessed by the respective - string value: MLDSA44-RSA2048-PKCS15-SHA256, MLDSA65-RSA3072-PKCS15-SHA512, +#. ML-DSA-composite (draft-ietf-lamps-pq-composite-sigs-19). + The algorithm is identified by the generic algorithm name "MLDSA-Composite" defined in the variable `MLDSA_Composite_Param::generic_algo_name`. It requires a parameter identifying the specific algorithm combination. The following + parameter sets are principally available: MLDSA44-RSA2048-PKCS15-SHA256, MLDSA65-RSA3072-PKCS15-SHA512, MLDSA65-RSA4096-PKCS15-SHA512, MLDSA44-RSA2048-PSS-SHA256, MLDSA65-RSA3072-PSS-SHA512, MLDSA65-RSA4096-PSS-SHA512, MLDSA87-RSA3072-PSS-SHA512, MLDSA87-RSA4096-PSS-SHA512, MLDSA44-ECDSA-P256-SHA256, MLDSA65-ECDSA-P256-SHA512, MLDSA65-ECDSA-P384-SHA512, From a794bbb8b4ed7638e92d33bd0513736e45429c54 Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Wed, 24 Jun 2026 13:45:53 +0200 Subject: [PATCH 09/25] change API algo name --- doc/api_ref/pubkey.rst | 2 +- src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/doc/api_ref/pubkey.rst b/doc/api_ref/pubkey.rst index e37f988421d..6a655f0fc99 100644 --- a/doc/api_ref/pubkey.rst +++ b/doc/api_ref/pubkey.rst @@ -1047,7 +1047,7 @@ Botan implements the following signature algorithms: #. ML-DSA (Dilithium). Takes and optional parameter string formed by comma-separated list of the following format ``[(Deterministic|Randomized),][Pure,][ctx_hex=]``, where the ordering of the comma-separated elements is arbitrary. The specification of ``Pure`` is redundant since currently only the pure variant of ML-DSA is implemented. The defaults of the other values are ``Randomized`` and an empty context parameter (`ctx_hex`). Non-empty context parameters are only supported by ML-DSA, but not by Dilithium. ``Deterministic`` or ``Randomized`` may also be specified in a verification operation thought it has no effect there. #. ML-DSA-composite (draft-ietf-lamps-pq-composite-sigs-19). - The algorithm is identified by the generic algorithm name "MLDSA-Composite" defined in the variable `MLDSA_Composite_Param::generic_algo_name`. It requires a parameter identifying the specific algorithm combination. The following + The algorithm is identified by the generic algorithm name "ML-DSA-Composite". It requires a parameter identifying the specific algorithm combination. The following parameter sets are principally available: MLDSA44-RSA2048-PKCS15-SHA256, MLDSA65-RSA3072-PKCS15-SHA512, MLDSA65-RSA4096-PKCS15-SHA512, MLDSA44-RSA2048-PSS-SHA256, MLDSA65-RSA3072-PSS-SHA512, MLDSA65-RSA4096-PSS-SHA512, MLDSA87-RSA3072-PSS-SHA512, MLDSA87-RSA4096-PSS-SHA512, diff --git a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h index 6ddff3f78c0..c35646c0c5b 100644 --- a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h +++ b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h @@ -38,7 +38,7 @@ class BOTAN_PUBLIC_API(3, 0) MLDSA_Composite_Param { MLDSA87_Ed448_SHAKE256, }; - static inline const char* generic_algo_name = "MLDSA-Composite"; + static inline const char* generic_algo_name = "ML-DSA-Composite"; static std::vector all_param_sets(); From 80637fa42bd9c62226b0e7fa18f93f59cf2a6ed8 Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Thu, 25 Jun 2026 14:53:37 +0200 Subject: [PATCH 10/25] fix some CI failures --- src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp | 9 +++++++-- src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h | 7 +++---- 2 files changed, 10 insertions(+), 6 deletions(-) diff --git a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp index 1e2193d8c8f..b7475892cce 100644 --- a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp +++ b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp @@ -13,9 +13,10 @@ #include #include #include + +#include + #include -#include -#include namespace Botan { @@ -360,6 +361,10 @@ std::string MLDSA_Composite_Param::get_traditional_algo_param_str() const { return ""; } +OID MLDSA_Composite_Param::object_identifier() const { + return OID_Map::global_registry().str2oid(this->m_id_str); +} + bool MLDSA_Composite_Param::is_supported() const { switch(m_id) { case MLDSA44_RSA2048_PKCS15_SHA256: diff --git a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h index c35646c0c5b..246b05a93ad 100644 --- a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h +++ b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.h @@ -11,7 +11,6 @@ #include #include #include -#include namespace Botan { @@ -45,7 +44,7 @@ class BOTAN_PUBLIC_API(3, 0) MLDSA_Composite_Param { static std::vector all_supported_param_sets(); /** - * @brief Create a paramters object from the provided id. If the parameters are not supported by the build configuration of the library, throw a Not_Implemented exception. + * @brief Create a parameters object from the provided id. If the parameters are not supported by the build configuration of the library, throw a Not_Implemented exception. * * @param id The id of the parameter set to create. * @@ -69,7 +68,7 @@ class BOTAN_PUBLIC_API(3, 0) MLDSA_Composite_Param { * @brief * Find out whether the library build supports this parameter. * - * @return true if the parameter is supported, false otherwhise + * @return true if the parameter is supported, false otherwise */ bool is_supported() const; @@ -79,7 +78,7 @@ class BOTAN_PUBLIC_API(3, 0) MLDSA_Composite_Param { AlgorithmIdentifier get_traditional_algorithm_id() const; - OID object_identifier() const { return OID_Map::global_registry().str2oid(this->m_id_str); } + OID object_identifier() const; std::string mldsa_param_str() const; From ce7dc677110d53f50e0b2ad20dda1ae99a720cff Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Thu, 25 Jun 2026 15:44:27 +0200 Subject: [PATCH 11/25] adapt supported function from mlkem-composite branch --- .../mldsa-composite/mldsa_comp_parameters.cpp | 104 +++++------------- 1 file changed, 27 insertions(+), 77 deletions(-) diff --git a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp index b7475892cce..2a5ce56aa62 100644 --- a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp +++ b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp @@ -16,6 +16,7 @@ #include +#include #include namespace Botan { @@ -259,11 +260,9 @@ std::optional MLDSA_Composite_Param::from_id(MLDSA_Compos MLDSA_Composite_Param MLDSA_Composite_Param::from_id_supported_or_throw(MLDSA_Composite_Param::id_t id) { const auto result = from_id(id); if(!result.has_value()) { - std::cout << "MLDSA_Composite_Param::from_id_supported_or_throw has no value\n"; throw Botan::Invalid_Argument("no parameter found for provided MLDSA composite id (enum)"); } if(!result.value().is_supported()) { - std::cout << "MLDSA_Composite_Param::from_id_supported_or_throw is not supported\n"; throw Not_Implemented("Parameter set " + result.value().id_str() + " is not supported by Botan's build configuration"); } @@ -366,87 +365,38 @@ OID MLDSA_Composite_Param::object_identifier() const { } bool MLDSA_Composite_Param::is_supported() const { - switch(m_id) { - case MLDSA44_RSA2048_PKCS15_SHA256: - [[fallthrough]]; - case MLDSA65_RSA3072_PKCS15_SHA512: - [[fallthrough]]; - case MLDSA65_RSA4096_PKCS15_SHA512: + constexpr auto supported = std::to_array({ #if defined BOTAN_HAS_RSA - return true; -#else - return false; + MLDSA44_RSA2048_PKCS15_SHA256, MLDSA65_RSA3072_PKCS15_SHA512, MLDSA65_RSA4096_PKCS15_SHA512, + #if defined BOTAN_HAS_PSS + MLDSA44_RSA2048_PSS_SHA256, MLDSA65_RSA3072_PSS_SHA512, MLDSA65_RSA4096_PSS_SHA512, MLDSA87_RSA3072_PSS_SHA512, + MLDSA87_RSA4096_PSS_SHA512, + #endif #endif - case MLDSA44_RSA2048_PSS_SHA256: - [[fallthrough]]; - case MLDSA65_RSA3072_PSS_SHA512: - [[fallthrough]]; - case MLDSA65_RSA4096_PSS_SHA512: - [[fallthrough]]; - case MLDSA87_RSA3072_PSS_SHA512: - [[fallthrough]]; - case MLDSA87_RSA4096_PSS_SHA512: - -#if defined BOTAN_HAS_RSA && defined BOTAN_HAS_PSS - return true; -#else - return false; -#endif - case MLDSA44_ECDSA_P256_SHA256: - [[fallthrough]]; - /* NOLINTNEXTLINE(bugprone-branch-clone) */ - case MLDSA65_ECDSA_P256_SHA512: -#if defined BOTAN_HAS_ECDSA && defined BOTAN_HAS_PCURVES_SECP256R1 - return true; -#else - return false; -#endif - case MLDSA65_ECDSA_P384_SHA512: - [[fallthrough]]; - /* NOLINTNEXTLINE(bugprone-branch-clone) */ - case MLDSA87_ECDSA_P384_SHA512: -#if defined BOTAN_HAS_ECDSA && defined BOTAN_HAS_PCURVES_SECP384R1 - return true; -#else - return false; -#endif - case MLDSA65_ECDSA_brainpoolP256r1_SHA512: -#if defined BOTAN_HAS_ECDSA && defined BOTAN_HAS_PCURVES_BRAINPOOL256R1 - return true; -#else - return false; +#if defined(BOTAN_HAS_ECDSA) + #if defined(BOTAN_HAS_PCURVES_GENERIC) || defined(BOTAN_HAS_PCURVES_SECP256R1) + MLDSA44_ECDSA_P256_SHA256, MLDSA65_ECDSA_P256_SHA512, + #endif + #if defined(BOTAN_HAS_PCURVES_GENERIC) || defined(BOTAN_HAS_PCURVES_SECP384R1) + MLDSA65_ECDSA_P384_SHA512, MLDSA87_ECDSA_P384_SHA512, + #endif + #if defined(BOTAN_HAS_PCURVES_GENERIC) || defined(BOTAN_HAS_PCURVES_BRAINPOOL256R1) + MLDSA65_ECDSA_brainpoolP256r1_SHA512, + #endif + #if defined(BOTAN_HAS_PCURVES_GENERIC) || defined(BOTAN_HAS_PCURVES_BRAINPOOL384R1) + MLDSA87_ECDSA_brainpoolP384r1_SHA512, + #endif + #if defined(BOTAN_HAS_PCURVES_GENERIC) || defined(BOTAN_HAS_PCURVES_SECP521R1) + MLDSA87_ECDSA_P521_SHA512, + #endif #endif - case MLDSA87_ECDSA_brainpoolP384r1_SHA512: -#if defined BOTAN_HAS_ECDSA && defined BOTAN_HAS_PCURVES_BRAINPOOL384R1 - return true; -#else - return false; -#endif - case MLDSA87_ECDSA_P521_SHA512: -#if defined BOTAN_HAS_ECDSA && defined BOTAN_HAS_PCURVES_BRAINPOOL512R1 - return true; -#else - return false; -#endif - case MLDSA_Composite_Param::id_t::MLDSA44_Ed25519_SHA512: - [[fallthrough]]; - /* NOLINTNEXTLINE(bugprone-branch-clone) */ - case MLDSA_Composite_Param::id_t::MLDSA65_Ed25519_SHA512: #if defined BOTAN_HAS_ED25519 - return true; -#else - return false; + MLDSA44_Ed25519_SHA512, MLDSA65_Ed25519_SHA512, #endif - /* NOLINTNEXTLINE(bugprone-branch-clone) */ - case MLDSA_Composite_Param::id_t::MLDSA87_Ed448_SHAKE256: #if defined BOTAN_HAS_ED448 && defined BOTAN_HAS_SHAKE - return true; -#else - return false; + MLDSA87_Ed448_SHAKE256, #endif - } - // should be dead code, needed for compiler (why?) - return false; + }); + return std::find(supported.begin(), supported.end(), m_id) != supported.end(); } - } // namespace Botan From dd0411e54cd3846c6cbd6b52a7aae8cbf37206fb Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Thu, 25 Jun 2026 17:22:54 +0200 Subject: [PATCH 12/25] fix minor findings from claude --- src/lib/pubkey/mldsa-composite/mldsa_comp.cpp | 9 +++++---- src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp | 2 +- 2 files changed, 6 insertions(+), 5 deletions(-) diff --git a/src/lib/pubkey/mldsa-composite/mldsa_comp.cpp b/src/lib/pubkey/mldsa-composite/mldsa_comp.cpp index b9473e99813..cf208298f58 100644 --- a/src/lib/pubkey/mldsa-composite/mldsa_comp.cpp +++ b/src/lib/pubkey/mldsa-composite/mldsa_comp.cpp @@ -32,7 +32,7 @@ namespace Botan { namespace { std::span mldsa_pubkey_subspan(const MLDSA_Composite_Param& param, std::span key_bits) { if(key_bits.size() <= param.mldsa_pubkey_size()) { - throw Invalid_Argument(fmt("encoded MLDSA component public key is too short (len = {})", key_bits.size())); + throw Invalid_Argument(fmt("encoded MLDSA-composite public key is too short (len = {})", key_bits.size())); } return std::span(key_bits.begin(), param.mldsa_pubkey_size()); } @@ -136,7 +136,6 @@ class MLDSA_Composite_Signature_Operation final : public PK_Ops::Signature_with_ m_traditional_sig_op(trad_privkey->create_signature_op(rng, param.traditional_padding(), "")) {} std::vector raw_sign(std::span ph, RandomNumberGenerator& rng) override { - // PROBLEM: when called repeatedly, the computed pre-hash ph differs and leads to failed verifications. // M' = Prefix || Label || len(ctx) || ctx || PH( M ) std::string msg_str = "CompositeAlgorithmSignatures2025"; msg_str += m_parameters.label(); @@ -148,6 +147,7 @@ class MLDSA_Composite_Signature_Operation final : public PK_Ops::Signature_with_ auto sig = m_mldsa_sig_op->sign(rng); auto trad_sig = m_traditional_sig_op->sign(rng); +#if defined(BOTAN_HAS_ECDSA) if(m_parameters.traditional_algorithm() == "ECDSA") { BOTAN_ASSERT(trad_sig.size() % 2 == 0, "ECDSA signature size is not divisible by 2"); std::vector enc_sig; @@ -159,23 +159,24 @@ class MLDSA_Composite_Signature_Operation final : public PK_Ops::Signature_with_ enc.start_sequence().encode(r).encode(s).end_cons(); std::swap(trad_sig, enc_sig); } +#endif sig.insert(sig.end(), trad_sig.begin(), trad_sig.end()); return sig; } size_t signature_length() const override { size_t encoding_len = 0; +#if defined(BOTAN_HAS_ECDSA) if(m_parameters.traditional_algorithm() == "ECDSA") { encoding_len = 3 /* SEQ */ + 2 * 2 /* 2x INTEGER T+L */ + 2 * 1 /* 2x potential leading sign octet in INTEGER */; } +#endif return m_mldsa_sig_op->signature_length() + m_traditional_sig_op->signature_length() + encoding_len; } AlgorithmIdentifier algorithm_identifier() const override { return m_parameters.get_composite_algorithm_id(); } - private: - private: MLDSA_Composite_Param m_parameters; std::unique_ptr m_mldsa_sig_op; diff --git a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp index 2a5ce56aa62..0d1f7e303ec 100644 --- a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp +++ b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp @@ -342,7 +342,7 @@ AlgorithmIdentifier MLDSA_Composite_Param::get_mldsa_algorithm_id() const { AlgorithmIdentifier MLDSA_Composite_Param::get_traditional_algorithm_id() const { std::optional oid; if(0 == std::strcmp(this->m_traditional_algorithm, "ECDSA")) { - oid = OID::from_name(std::string("ECDSA/") + m_prehash_func); + oid = OID::from_name(std::string("ECDSA/") + m_traditional_padding); } else { oid = OID::from_name(this->m_traditional_algorithm); } From 2c51a30447cb2800d4b9e262b6b8bbff2edc2242 Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Mon, 6 Jul 2026 10:45:07 +0200 Subject: [PATCH 13/25] fix copy & paste errors --- src/lib/ffi/ffi_pkey_algs.cpp | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/src/lib/ffi/ffi_pkey_algs.cpp b/src/lib/ffi/ffi_pkey_algs.cpp index 5afa569b8c9..bc1aa0993bb 100644 --- a/src/lib/ffi/ffi_pkey_algs.cpp +++ b/src/lib/ffi/ffi_pkey_algs.cpp @@ -1427,7 +1427,7 @@ int botan_privkey_load_mldsa_composite(botan_privkey_t* key, return ffi_new_object(key, std::move(mldsa_composite_key)); }); #else - BOTAN_UNUSED(key, key_len, privkey, mldsa_mode); + BOTAN_UNUSED(key, key_len, privkey, mldsa_composite_algo); return BOTAN_FFI_ERROR_NOT_IMPLEMENTED; #endif } @@ -1436,7 +1436,7 @@ int botan_pubkey_load_mldsa_composite(botan_pubkey_t* key, const uint8_t pubkey[], size_t key_len, const char* mldsa_composite_algo) { -#if defined(BOTAN_HAS_ML_DSA) +#if defined(BOTAN_HAS_MLDSA_COMPOSITE) if(key == nullptr || pubkey == nullptr || mldsa_composite_algo == nullptr) { return BOTAN_FFI_ERROR_NULL_POINTER; } @@ -1454,7 +1454,7 @@ int botan_pubkey_load_mldsa_composite(botan_pubkey_t* key, return ffi_new_object(key, std::move(mldsa_composite_key)); }); #else - BOTAN_UNUSED(key, key_len, pubkey, mldsa_mode); + BOTAN_UNUSED(key, key_len, pubkey, mldsa_composite_algo); return BOTAN_FFI_ERROR_NOT_IMPLEMENTED; #endif } From 1abbe96c76b72c8ff42144d12e7310ed90843e9e Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Mon, 6 Jul 2026 16:37:42 +0200 Subject: [PATCH 14/25] fix signature size related test failure --- doc/api_ref/pubkey.rst | 18 +++++++--- src/lib/pubkey/mldsa-composite/mldsa_comp.h | 2 +- src/tests/test_ffi.cpp | 37 ++++++++++++++------- 3 files changed, 40 insertions(+), 17 deletions(-) diff --git a/doc/api_ref/pubkey.rst b/doc/api_ref/pubkey.rst index 6a655f0fc99..64233b3dcd1 100644 --- a/doc/api_ref/pubkey.rst +++ b/doc/api_ref/pubkey.rst @@ -170,9 +170,17 @@ Currently two flavors of Dilithium are implemented in separate Botan modules: ML-DSA-composite (draft-ietf-lamps-pq-composite-sigs-19) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -Composite signature algorithms combining ML-DSA with a traditional signature algorithm. All variants defined in draft-ietf-lamps-pq-composite-sigs-19 are supported. Each is modelled as a specific parameter value of the generic algorithm -``MLDSA-Composite``. The module for the composite algorithms is given by `mldsa-composite`, but note that naturally only those algorithm combinations are available for which the respective module support is compiled. - +Composite signature algorithms combining ML-DSA with a traditional signature +algorithm. All variants defined in draft-ietf-lamps-pq-composite-sigs-19 are +supported. Each is modelled as a specific parameter value of the generic +algorithm ``MLDSA-Composite``. The module for the composite algorithms is given +by `mldsa-composite`, but note that naturally only those algorithm combinations +are available for which the respective module support is compiled. + +One specific trait of these algorithms is that for the combinations with ECDSA, +due to variability in the encoded signature, the signature size returned by the +signature or verification operation instance is only an upper bound, and not the +exact size. ML-KEM (FIPS 203) ~~~~~~~~~~~~~~~~~ @@ -1047,7 +1055,9 @@ Botan implements the following signature algorithms: #. ML-DSA (Dilithium). Takes and optional parameter string formed by comma-separated list of the following format ``[(Deterministic|Randomized),][Pure,][ctx_hex=]``, where the ordering of the comma-separated elements is arbitrary. The specification of ``Pure`` is redundant since currently only the pure variant of ML-DSA is implemented. The defaults of the other values are ``Randomized`` and an empty context parameter (`ctx_hex`). Non-empty context parameters are only supported by ML-DSA, but not by Dilithium. ``Deterministic`` or ``Randomized`` may also be specified in a verification operation thought it has no effect there. #. ML-DSA-composite (draft-ietf-lamps-pq-composite-sigs-19). - The algorithm is identified by the generic algorithm name "ML-DSA-Composite". It requires a parameter identifying the specific algorithm combination. The following + The algorithm is identified by the generic algorithm name "ML-DSA-Composite". + It requires a parameter identifying the specific algorithm combination. The + following parameter sets are principally available: MLDSA44-RSA2048-PKCS15-SHA256, MLDSA65-RSA3072-PKCS15-SHA512, MLDSA65-RSA4096-PKCS15-SHA512, MLDSA44-RSA2048-PSS-SHA256, MLDSA65-RSA3072-PSS-SHA512, MLDSA65-RSA4096-PSS-SHA512, MLDSA87-RSA3072-PSS-SHA512, MLDSA87-RSA4096-PSS-SHA512, diff --git a/src/lib/pubkey/mldsa-composite/mldsa_comp.h b/src/lib/pubkey/mldsa-composite/mldsa_comp.h index e1ea7556b24..745bce4db74 100644 --- a/src/lib/pubkey/mldsa-composite/mldsa_comp.h +++ b/src/lib/pubkey/mldsa-composite/mldsa_comp.h @@ -30,7 +30,7 @@ class BOTAN_PUBLIC_API(3, 0) MLDSA_Composite_PublicKey : public virtual Public_K BOTAN_FUTURE_EXPLICIT MLDSA_Composite_PublicKey(const AlgorithmIdentifier& algo_id, std::span key_bits); - std::string algo_name() const override { return "MLDSA_Composite"; } + std::string algo_name() const override { return MLDSA_Composite_Param::generic_algo_name; } AlgorithmIdentifier algorithm_identifier() const override { return AlgorithmIdentifier(object_identifier(), AlgorithmIdentifier::USE_EMPTY_PARAM); diff --git a/src/tests/test_ffi.cpp b/src/tests/test_ffi.cpp index a96365d04fd..cdcf2f50d19 100644 --- a/src/tests/test_ffi.cpp +++ b/src/tests/test_ffi.cpp @@ -4550,7 +4550,12 @@ class FFI_Signature_Roundtrip_Test : public FFI_Test { virtual std::vector modes() const = 0; virtual const char* hash_algo_or_padding() const = 0; - virtual std::string make_mode_for_key_loading(std::string_view mode) { return std::string(mode); } + virtual void test_signature_length(size_t produced_sig_size, + size_t expected_sig_size, + std::string /*mode*/, + Test::Result& result) const { + result.test_sz_eq("reported sig lengths are equal", produced_sig_size, expected_sig_size); + } public: void ffi_test(Test::Result& result, botan_rng_t rng) override { @@ -4576,13 +4581,9 @@ class FFI_Signature_Roundtrip_Test : public FFI_Test { botan_privkey_t priv_loaded; botan_pubkey_t pub_loaded; TEST_FFI_OK(private_key_load_function(), - (&priv_loaded, - priv_bytes.get().data(), - priv_bytes.get().size(), - make_mode_for_key_loading(mode).c_str())); - TEST_FFI_OK( - public_key_load_function(), - (&pub_loaded, pub_bytes.get().data(), pub_bytes.get().size(), make_mode_for_key_loading(mode).c_str())); + (&priv_loaded, priv_bytes.get().data(), priv_bytes.get().size(), mode)); + TEST_FFI_OK(public_key_load_function(), + (&pub_loaded, pub_bytes.get().data(), pub_bytes.get().size(), mode)); // re-encode and compare to the first round ViewBytesSink priv_bytes2; @@ -4609,7 +4610,8 @@ class FFI_Signature_Roundtrip_Test : public FFI_Test { TEST_FFI_RC(BOTAN_FFI_ERROR_INSUFFICIENT_BUFFER_SPACE, botan_pk_op_sign_finish, (signer, rng, nullptr, &sig_output_length_out)); - result.test_sz_eq("reported sig lengths are equal", sig_output_length, sig_output_length_out); + + test_signature_length(sig_output_length_out, sig_output_length, mode, result); // Recreate signer and try again TEST_FFI_OK(botan_pk_op_sign_destroy, (signer)); @@ -4621,7 +4623,7 @@ class FFI_Signature_Roundtrip_Test : public FFI_Test { sig_output_length_out = sig_output_length * 2; Botan::secure_vector signature(sig_output_length_out); TEST_FFI_OK(botan_pk_op_sign_finish, (signer, rng, signature.data(), &sig_output_length_out)); - result.test_sz_eq("signature length", sig_output_length, sig_output_length_out); + test_signature_length(sig_output_length_out, sig_output_length, mode, result); signature.resize(sig_output_length_out); TEST_FFI_OK(botan_pk_op_sign_destroy, (signer)); @@ -4862,6 +4864,19 @@ class FFI_MLDSA_Composite_Test final : public FFI_Signature_Roundtrip_Test { pubkey_loader_fn_t public_key_load_function() const override { return botan_pubkey_load_mldsa_composite; } + void test_signature_length(size_t produced_sig_size, + size_t expected_sig_size, + std::string mode, + Test::Result& result) const override { + if((mode.find("ECDSA") != std::string::npos)) { + result.test_sz_lte( + "reported sig length is smaller or equal than limit", produced_sig_size, expected_sig_size); + } else { + result.test_sz_eq( + "reported sig length is different from expected length", produced_sig_size, expected_sig_size); + } + } + std::vector modes() const override { return { #if defined(BOTAN_HAS_RSA) @@ -4877,8 +4892,6 @@ class FFI_MLDSA_Composite_Test final : public FFI_Signature_Roundtrip_Test { } const char* hash_algo_or_padding() const override { return ""; } - - std::string make_mode_for_key_loading(std::string_view) override { return std::string(algo()); } }; class FFI_SLH_DSA_Test final : public FFI_Signature_Roundtrip_Test { From 462c6f15d3011a1eaea2613b3ac9e6006e38eed2 Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Mon, 6 Jul 2026 17:22:33 +0200 Subject: [PATCH 15/25] remove std::format --- src/lib/pubkey/mldsa-composite/mldsa_comp.cpp | 2 +- src/tests/test_dilithium.cpp | 8 +++----- 2 files changed, 4 insertions(+), 6 deletions(-) diff --git a/src/lib/pubkey/mldsa-composite/mldsa_comp.cpp b/src/lib/pubkey/mldsa-composite/mldsa_comp.cpp index cf208298f58..ebf7e2922d9 100644 --- a/src/lib/pubkey/mldsa-composite/mldsa_comp.cpp +++ b/src/lib/pubkey/mldsa-composite/mldsa_comp.cpp @@ -3,8 +3,8 @@ #include #include #include -#include #if defined BOTAN_HAS_ECDSA + #include #include #endif #if defined BOTAN_HAS_ED25519 diff --git a/src/tests/test_dilithium.cpp b/src/tests/test_dilithium.cpp index bd1ae3d3f59..d9cb1f895eb 100644 --- a/src/tests/test_dilithium.cpp +++ b/src/tests/test_dilithium.cpp @@ -21,8 +21,6 @@ #include "test_rng.h" #endif -#include - namespace Botan_Tests { namespace { @@ -321,7 +319,7 @@ class MLDSA_Param_Tests final : public Test { Test_Case{false, std::string("ctx=A"), true}}; for(const auto& [expect_success, param_str, random_sig] : sign_params) { - Test::Result result(std::format("{}: param string = '{}'", test_name, param_str)); + Test::Result result(std::string(test_name) + ": param string = '" + param_str + "'"); std::unique_ptr signer; bool exc = false; try { @@ -329,7 +327,7 @@ class MLDSA_Param_Tests final : public Test { } catch(Botan::Exception&) { exc = true; } - result.test_bool_eq(std::format("parameters string '{}' for ML-DSA op was valid", param_str), + result.test_bool_eq("parameters string '" + param_str + "' for ML-DSA op was valid", !exc && signer, expect_success); if(exc) { @@ -340,7 +338,7 @@ class MLDSA_Param_Tests final : public Test { auto signature = signer->sign_message(msgvec, *rng); auto signature2 = signer->sign_message(msgvec, *rng); result.test_bool_eq( - std::format("signature randomization (param = '{}')", param_str), signature != signature2, random_sig); + "signature randomization (param = '" + param_str + "')", signature != signature2, random_sig); result.test_is_true("signature verification", verifier.verify_message(msgvec, signature)); results.push_back(result); } From 9d137e00e8d2898e27d21d98f67f56d4d207e9c5 Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Tue, 7 Jul 2026 09:16:31 +0200 Subject: [PATCH 16/25] fix unused exception varialble --- src/tests/test_mldsa_composite.cpp | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/src/tests/test_mldsa_composite.cpp b/src/tests/test_mldsa_composite.cpp index 97fcf6a8e80..710243c2eb0 100644 --- a/src/tests/test_mldsa_composite.cpp +++ b/src/tests/test_mldsa_composite.cpp @@ -187,7 +187,7 @@ class MLDSA_Composite_Key_Detail_Tests : public Test { bool exc = false; try { Botan::MLDSA_Composite_PrivateKey(param.id(), false_private_key_enc); - } catch(const Botan::Exception& e) { + } catch(const Botan::Exception&) { exc = true; } result.test_bool_eq("decoding of false private key", exc, true); @@ -196,7 +196,7 @@ class MLDSA_Composite_Key_Detail_Tests : public Test { bool exc = false; try { Botan::MLDSA_Composite_PublicKey(param.id(), false_public_key_enc); - } catch(const Botan::Exception& e) { + } catch(const Botan::Exception&) { exc = true; } result.test_bool_eq("decoding of false public key", exc, true); @@ -459,7 +459,7 @@ class MLDSA_Composite_KAT_Tests : public Text_Based_Test { try { pubkey = std::make_unique(comp_parm.id(), pk_bin); - } catch(const Botan::Exception& e) { + } catch(const Botan::Exception&) { exc_during_pubkey_decoding = true; } result.test_bool_eq("pubkey decoding OK", !exc_during_pubkey_decoding, pubkey_valid); @@ -472,7 +472,7 @@ class MLDSA_Composite_KAT_Tests : public Text_Based_Test { try { privkey = std::make_unique(comp_parm.id(), sk_bin); - } catch(const Botan::Exception& e) { + } catch(const Botan::Exception&) { exc_during_privkey_decoding = true; } result.test_bool_eq("privkey decoding OK", !exc_during_privkey_decoding, privkey_valid); From cf645c99d2fc848085611dffa839841789c41124 Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Tue, 7 Jul 2026 09:29:32 +0200 Subject: [PATCH 17/25] remove std::format --- src/tests/test_mldsa_composite.cpp | 39 ++++++++++++++---------------- 1 file changed, 18 insertions(+), 21 deletions(-) diff --git a/src/tests/test_mldsa_composite.cpp b/src/tests/test_mldsa_composite.cpp index 710243c2eb0..5fa4a585cd2 100644 --- a/src/tests/test_mldsa_composite.cpp +++ b/src/tests/test_mldsa_composite.cpp @@ -11,7 +11,6 @@ #include "tests.h" -#include #include #include #include @@ -98,22 +97,22 @@ void sign_and_verify(const Botan::Private_Key& priv_key, Botan::PK_Verifier verifier(pub_key, ""); verifier.update(message); - test_result.test_bool_eq( - std::format("verification of correct signature ({})", test_context), verifier.check_signature(signature), true); + test_result.test_bool_eq("verification of correct signature (" + std::string(test_context) + ")", + verifier.check_signature(signature), + true); verifier.update(message); - test_result.test_bool_eq( - std::format("verification of correct signature (repeated use of only verifier with update) ({})", test_context), - verifier.check_signature(signature), - true); + test_result.test_bool_eq("verification of correct signature (repeated use of only verifier with update) (" + + std::string(test_context) + ")", + verifier.check_signature(signature), + true); // test sign_message() with already used signature-op and already used verify-op for(size_t i = 0; i < 2; i++) { signature = signer.sign_message(message, rng); // PK_Ops::Signature_with_Hash::update() is called before signing test_result.test_bool_eq( - std::format( - "verification of correct signature (repeated use of signer and verifier with sign/verify_message) ({})", - test_context), + "verification of correct signature (repeated use of signer and verifier with sign/verify_message) (" + + std::string(test_context) + ")", verifier.verify_message(message, signature), true); } @@ -122,11 +121,10 @@ void sign_and_verify(const Botan::Private_Key& priv_key, signer.update(message); signature = signer.signature(rng); verifier.update(message); - test_result.test_bool_eq( - std::format("verification of correct signature (repeated use of signer and verifier with update) ({})", - test_context), - verifier.check_signature(signature), - true); + test_result.test_bool_eq("verification of correct signature (repeated use of signer and verifier with update) (" + + std::string(test_context) + ")", + verifier.check_signature(signature), + true); } } // namespace @@ -180,7 +178,7 @@ class MLDSA_Composite_Key_Detail_Tests : public Test { mimic_speed_test(*rng, result); } catch(const Botan::Exception& e) { - result.test_failure(std::format("Exception during key operations: {}", e.what())); + result.test_failure(std::string("Exception during key operations: ") + e.what()); } for(const auto& false_private_key_enc : false_private_keys) { @@ -287,10 +285,9 @@ class MLDSA_Composite_Sig_Detail_Tests : public Test { result.test_bool_eq("verification of false signature", verifier2.check_signature(false_signature), false); verifier2.update(message); result.test_is_true( - std::format( - "verification of correct signature after failed verification, false signature length = {}, length of correct signature = {}", - false_signature.size(), - signature.size()), + "verification of correct signature after failed verification, false signature length = " + + std::to_string(false_signature.size()) + + ", length of correct signature = " + std::to_string(signature.size()), verifier2.check_signature(signature)); } return result; @@ -405,7 +402,7 @@ class MLDSA_Composite_RT_Tests : public Test { .end_cons() .verify_end(); } catch(const Botan::Exception& e) { - result.test_failure(std::format("verify ECDSA private format decoding: {}", e.what())); + result.test_failure(std::string("verify ECDSA private format decoding: ") + e.what()); } } }; From e28bc779b0beb66d2e2039bdf81e53e50f606b2e Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Tue, 7 Jul 2026 09:47:14 +0200 Subject: [PATCH 18/25] fix empty std::array for MSVC --- .../mldsa-composite/mldsa_comp_parameters.cpp | 28 +++++++++---------- 1 file changed, 14 insertions(+), 14 deletions(-) diff --git a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp index 0d1f7e303ec..17cae783d49 100644 --- a/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp +++ b/src/lib/pubkey/mldsa-composite/mldsa_comp_parameters.cpp @@ -16,7 +16,6 @@ #include -#include #include namespace Botan { @@ -365,38 +364,39 @@ OID MLDSA_Composite_Param::object_identifier() const { } bool MLDSA_Composite_Param::is_supported() const { - constexpr auto supported = std::to_array({ + bool result = false; #if defined BOTAN_HAS_RSA - MLDSA44_RSA2048_PKCS15_SHA256, MLDSA65_RSA3072_PKCS15_SHA512, MLDSA65_RSA4096_PKCS15_SHA512, + result = result || m_id == MLDSA44_RSA2048_PKCS15_SHA256 || m_id == MLDSA65_RSA3072_PKCS15_SHA512 || + m_id == MLDSA65_RSA4096_PKCS15_SHA512; #if defined BOTAN_HAS_PSS - MLDSA44_RSA2048_PSS_SHA256, MLDSA65_RSA3072_PSS_SHA512, MLDSA65_RSA4096_PSS_SHA512, MLDSA87_RSA3072_PSS_SHA512, - MLDSA87_RSA4096_PSS_SHA512, + result = result || m_id == MLDSA44_RSA2048_PSS_SHA256 || m_id == MLDSA65_RSA3072_PSS_SHA512 || + m_id == MLDSA65_RSA4096_PSS_SHA512 || m_id == MLDSA87_RSA3072_PSS_SHA512 || + m_id == MLDSA87_RSA4096_PSS_SHA512; #endif #endif #if defined(BOTAN_HAS_ECDSA) #if defined(BOTAN_HAS_PCURVES_GENERIC) || defined(BOTAN_HAS_PCURVES_SECP256R1) - MLDSA44_ECDSA_P256_SHA256, MLDSA65_ECDSA_P256_SHA512, + result = result || m_id == MLDSA44_ECDSA_P256_SHA256 || m_id == MLDSA65_ECDSA_P256_SHA512; #endif #if defined(BOTAN_HAS_PCURVES_GENERIC) || defined(BOTAN_HAS_PCURVES_SECP384R1) - MLDSA65_ECDSA_P384_SHA512, MLDSA87_ECDSA_P384_SHA512, + result = result || m_id == MLDSA65_ECDSA_P384_SHA512 || m_id == MLDSA87_ECDSA_P384_SHA512; #endif #if defined(BOTAN_HAS_PCURVES_GENERIC) || defined(BOTAN_HAS_PCURVES_BRAINPOOL256R1) - MLDSA65_ECDSA_brainpoolP256r1_SHA512, + result = result || m_id == MLDSA65_ECDSA_brainpoolP256r1_SHA512; #endif #if defined(BOTAN_HAS_PCURVES_GENERIC) || defined(BOTAN_HAS_PCURVES_BRAINPOOL384R1) - MLDSA87_ECDSA_brainpoolP384r1_SHA512, + result = result || m_id == MLDSA87_ECDSA_brainpoolP384r1_SHA512; #endif #if defined(BOTAN_HAS_PCURVES_GENERIC) || defined(BOTAN_HAS_PCURVES_SECP521R1) - MLDSA87_ECDSA_P521_SHA512, + result = result || m_id == MLDSA87_ECDSA_P521_SHA512; #endif #endif #if defined BOTAN_HAS_ED25519 - MLDSA44_Ed25519_SHA512, MLDSA65_Ed25519_SHA512, + result = result || m_id == MLDSA44_Ed25519_SHA512 || m_id == MLDSA65_Ed25519_SHA512; #endif #if defined BOTAN_HAS_ED448 && defined BOTAN_HAS_SHAKE - MLDSA87_Ed448_SHAKE256, + result = result || m_id == MLDSA87_Ed448_SHAKE256; #endif - }); - return std::find(supported.begin(), supported.end(), m_id) != supported.end(); + return result; } } // namespace Botan From 6159ba22789ba212d6ed9cad60ec835882e29089 Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Tue, 7 Jul 2026 10:02:27 +0200 Subject: [PATCH 19/25] fix code formatting --- src/tests/test_dilithium.cpp | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/src/tests/test_dilithium.cpp b/src/tests/test_dilithium.cpp index d9cb1f895eb..c66513ddb00 100644 --- a/src/tests/test_dilithium.cpp +++ b/src/tests/test_dilithium.cpp @@ -327,9 +327,8 @@ class MLDSA_Param_Tests final : public Test { } catch(Botan::Exception&) { exc = true; } - result.test_bool_eq("parameters string '" + param_str + "' for ML-DSA op was valid", - !exc && signer, - expect_success); + result.test_bool_eq( + "parameters string '" + param_str + "' for ML-DSA op was valid", !exc && signer, expect_success); if(exc) { results.push_back(result); continue; From 3948dd2752031a0bfa577e1a0d8e5e5df4538289 Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Tue, 7 Jul 2026 10:57:06 +0200 Subject: [PATCH 20/25] fix clang-tidy issues --- src/tests/test_dilithium.cpp | 2 +- src/tests/test_ffi.cpp | 4 ++-- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/src/tests/test_dilithium.cpp b/src/tests/test_dilithium.cpp index c66513ddb00..ef78e3c33b9 100644 --- a/src/tests/test_dilithium.cpp +++ b/src/tests/test_dilithium.cpp @@ -299,7 +299,7 @@ class MLDSA_Param_Tests final : public Test { }; std::vector run() override { - std::string test_name = "MLDSA_Param_Tests"; + const std::string test_name = "MLDSA_Param_Tests"; std::vector results; auto rng = Test::new_rng(test_name); diff --git a/src/tests/test_ffi.cpp b/src/tests/test_ffi.cpp index cdcf2f50d19..37a7eee4c61 100644 --- a/src/tests/test_ffi.cpp +++ b/src/tests/test_ffi.cpp @@ -4552,7 +4552,7 @@ class FFI_Signature_Roundtrip_Test : public FFI_Test { virtual void test_signature_length(size_t produced_sig_size, size_t expected_sig_size, - std::string /*mode*/, + const std::string& /*mode*/, Test::Result& result) const { result.test_sz_eq("reported sig lengths are equal", produced_sig_size, expected_sig_size); } @@ -4866,7 +4866,7 @@ class FFI_MLDSA_Composite_Test final : public FFI_Signature_Roundtrip_Test { void test_signature_length(size_t produced_sig_size, size_t expected_sig_size, - std::string mode, + const std::string& mode, Test::Result& result) const override { if((mode.find("ECDSA") != std::string::npos)) { result.test_sz_lte( From 08b92a56cb9b96165427159aba1ecfe34fabf179 Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Tue, 7 Jul 2026 10:59:53 +0200 Subject: [PATCH 21/25] fix conditional compilation --- src/tests/test_ffi.cpp | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/src/tests/test_ffi.cpp b/src/tests/test_ffi.cpp index 37a7eee4c61..15ee8de0c1e 100644 --- a/src/tests/test_ffi.cpp +++ b/src/tests/test_ffi.cpp @@ -4855,10 +4855,10 @@ class FFI_ML_DSA_Test final : public FFI_Signature_Roundtrip_Test { class FFI_MLDSA_Composite_Test final : public FFI_Signature_Roundtrip_Test { public: - std::string name() const override { return "FFI MLDSA-Composite"; } + std::string name() const override { return "FFI ML-DSA-Composite"; } private: - const char* algo() const override { return Botan::MLDSA_Composite_Param::generic_algo_name; } + const char* algo() const override { return "ML-DSA-Composite"; } privkey_loader_fn_t private_key_load_function() const override { return botan_privkey_load_mldsa_composite; } From 211a58be8bf6bee61abd7d35f155e61d7df7b25c Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Tue, 7 Jul 2026 14:38:36 +0200 Subject: [PATCH 22/25] fix cond. compilation filesystem --- src/tests/test_mldsa_composite.cpp | 14 ++++++++------ 1 file changed, 8 insertions(+), 6 deletions(-) diff --git a/src/tests/test_mldsa_composite.cpp b/src/tests/test_mldsa_composite.cpp index 5fa4a585cd2..72e9fef0f99 100644 --- a/src/tests/test_mldsa_composite.cpp +++ b/src/tests/test_mldsa_composite.cpp @@ -46,12 +46,6 @@ namespace Botan_Tests { namespace { -std::vector decode_var_base64(const VarMap& vars, std::string_view var) { - const auto var_b64 = vars.get_req_str(var); - const auto var_sv = Botan::base64_decode(var_b64); - return std::vector(var_sv.begin(), var_sv.end()); -} - void mimic_speed_test(Botan::RandomNumberGenerator& rng, Test::Result& result) { // test for a real-life bug that occurred because of lazy evaluation of the 2nd signature verification. #if !defined BOTAN_HAS_RSA @@ -411,6 +405,14 @@ BOTAN_REGISTER_TEST("pubkey", "mldsa_composite_roundtrips", MLDSA_Composite_RT_T #if defined(BOTAN_TARGET_OS_HAS_FILESYSTEM) +namespace { +std::vector decode_var_base64(const VarMap& vars, std::string_view var) { + const auto var_b64 = vars.get_req_str(var); + const auto var_sv = Botan::base64_decode(var_b64); + return std::vector(var_sv.begin(), var_sv.end()); +} +} // namespace + class MLDSA_Composite_KAT_Tests : public Text_Based_Test { public: MLDSA_Composite_KAT_Tests() : From 57b5a6d391e3528eb4eeb2a1064821ce28949097 Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Fri, 10 Jul 2026 07:04:28 +0200 Subject: [PATCH 23/25] add python tests --- src/python/botan3.py | 17 +++++++++++++++++ src/scripts/test_python.py | 14 ++++++++++++++ 2 files changed, 31 insertions(+) diff --git a/src/python/botan3.py b/src/python/botan3.py index 9c039eb1051..81aa05d1f58 100755 --- a/src/python/botan3.py +++ b/src/python/botan3.py @@ -449,6 +449,8 @@ def ffi_api(fn, args, allowed_errors=None): ffi_api(dll.botan_pubkey_x448_get_pubkey, [c_void_p, c_char_p]) ffi_api(dll.botan_privkey_load_ml_dsa, [c_void_p, c_void_p, c_int, c_char_p]) ffi_api(dll.botan_pubkey_load_ml_dsa, [c_void_p, c_void_p, c_int, c_char_p]) + ffi_api(dll.botan_privkey_load_mldsa_composite, [c_void_p, c_void_p, c_int, c_char_p]) + ffi_api(dll.botan_pubkey_load_mldsa_composite, [c_void_p, c_void_p, c_int, c_char_p]) ffi_api(dll.botan_privkey_load_slh_dsa, [c_void_p, c_void_p, c_int, c_char_p]) ffi_api(dll.botan_pubkey_load_slh_dsa, [c_void_p, c_void_p, c_int, c_char_p]) ffi_api(dll.botan_privkey_load_kyber, [c_void_p, c_char_p, c_int]) @@ -1633,6 +1635,14 @@ def load_slh_dsa(cls, slhdsa_mode: str, key: bytes) -> PublicKey: _DLL.botan_pubkey_load_slh_dsa(byref(pub.handle_()), key, len(key), _ctype_str(slhdsa_mode)) return pub + @classmethod + def load_mldsa_composite(cls, mldsa_composite_mode: str, key: bytes) -> PublicKey: + """Load an ML-DSA-Composite public key giving the mode as a string + (like "MLDSA44-ECDSA-P256-SHA256") and the raw encoding of the public key.""" + pub = PublicKey() + _DLL.botan_pubkey_load_mldsa_composite(byref(pub.handle_()), key, len(key), _ctype_str(mldsa_composite_mode)) + return pub + @classmethod def load_frodokem(cls, frodo_mode: str, key: bytes) -> PublicKey: pub = PublicKey() @@ -1879,6 +1889,13 @@ def load_ml_dsa(cls, mldsa_mode: str, key: bytes) -> PrivateKey: _DLL.botan_privkey_load_ml_dsa(byref(priv.handle_()), key, len(key), _ctype_str(mldsa_mode)) return priv + @classmethod + def load_mldsa_composite(cls, mldsa_composite_mode: str, key: bytes) -> PrivateKey: + """Return a private ML-DSA-Composite key""" + priv = PrivateKey() + _DLL.botan_privkey_load_mldsa_composite(byref(priv.handle_()), key, len(key), _ctype_str(mldsa_composite_mode)) + return priv + @classmethod def load_slh_dsa(cls, slh_dsa: str, key: bytes) -> PrivateKey: """Return a private SLH-DSA key""" diff --git a/src/scripts/test_python.py b/src/scripts/test_python.py index 359f3a842dd..d4f1b805bd2 100644 --- a/src/scripts/test_python.py +++ b/src/scripts/test_python.py @@ -1255,6 +1255,20 @@ def test_ml_dsa_raw_keys(self): self.assertEqual(sk_read.to_raw(), sk_bits) self.assertEqual(pk_read.to_raw(), pk_bits) + def test_ml_dsa_composite_raw_keys(self): + mldsa_composite_mode = "MLDSA44-ECDSA-P256-SHA256" + sk = botan.PrivateKey.create("ML-DSA-Composite", mldsa_composite_mode, botan.RandomNumberGenerator("user")) + pk = sk.get_public_key() + + sk_bits = sk.to_raw() + pk_bits = pk.to_raw() + + sk_read = botan.PrivateKey.load_mldsa_composite(mldsa_composite_mode, sk_bits) + pk_read = botan.PublicKey.load_mldsa_composite(mldsa_composite_mode, pk_bits) + + self.assertEqual(sk_read.to_raw(), sk_bits) + self.assertEqual(pk_read.to_raw(), pk_bits) + def test_slh_dsa_raw_keys(self): slhdsa_mode = "SLH-DSA-SHAKE-128f" sk = botan.PrivateKey.create("SLH-DSA", slhdsa_mode, botan.RandomNumberGenerator("user")) From d1dfddaf3857dc84debb86ce54020d0d21810860 Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Fri, 10 Jul 2026 08:29:03 +0200 Subject: [PATCH 24/25] add example --- src/examples/mldsa_composite.cpp | 38 ++++++++++++++++++++++++++++++++ 1 file changed, 38 insertions(+) create mode 100644 src/examples/mldsa_composite.cpp diff --git a/src/examples/mldsa_composite.cpp b/src/examples/mldsa_composite.cpp new file mode 100644 index 00000000000..bfb7d084bd4 --- /dev/null +++ b/src/examples/mldsa_composite.cpp @@ -0,0 +1,38 @@ +#include +#include +#include +#include + +#include +#include + +int main() { + // Create a random number generator used for key generation. + Botan::AutoSeeded_RNG rng; + + // create a new public/private key pair for the ML-DSA-44 / ECDSA-P256 + // composite signature scheme. + const auto param = + Botan::MLDSA_Composite_Param::from_id_supported_or_throw(Botan::MLDSA_Composite_Param::MLDSA44_ECDSA_P256_SHA256); + const Botan::MLDSA_Composite_PrivateKey private_key(rng, param); + const auto public_key = private_key.public_key(); + + // create Public Key Signer using the private key. + Botan::PK_Signer signer(private_key, rng, ""); + + // create and sign a message using the Public Key Signer. + Botan::secure_vector msg{0x01, 0x02, 0x03, 0x04}; + auto sig = signer.sign_message(msg, rng); + + // create Public Key Verifier using the public key + Botan::PK_Verifier verifier(*public_key, ""); + + // verify the signature for the previously generated message. + if(verifier.verify_message(msg, sig)) { + std::cout << "Success.\n"; + return 0; + } else { + std::cout << "Error.\n"; + return 1; + } +} From 4868858c6c2de7bed189529e86c26b16ac4e16d9 Mon Sep 17 00:00:00 2001 From: Falko Strenzke Date: Tue, 14 Jul 2026 13:26:31 +0200 Subject: [PATCH 25/25] fix some of TJ-91's commments --- src/lib/pubkey/mldsa-composite/mldsa_comp.cpp | 9 +++++++-- src/lib/pubkey/mldsa-composite/mldsa_comp.h | 2 +- 2 files changed, 8 insertions(+), 3 deletions(-) diff --git a/src/lib/pubkey/mldsa-composite/mldsa_comp.cpp b/src/lib/pubkey/mldsa-composite/mldsa_comp.cpp index ebf7e2922d9..c01213d11f8 100644 --- a/src/lib/pubkey/mldsa-composite/mldsa_comp.cpp +++ b/src/lib/pubkey/mldsa-composite/mldsa_comp.cpp @@ -48,7 +48,8 @@ std::span traditional_pubkey_subspan(const MLDSA_Composite_Param& std::span key_bits) { const size_t offset = param.mldsa_pubkey_size(); if(key_bits.size() <= 1 + offset) { - throw Invalid_Argument(fmt("encoded traditional component public key is too short (len = {})", key_bits.size())); + throw Invalid_Argument(fmt("encoded traditional component public key is too short, its length is only {} bytes", + key_bits.size() - offset)); } return std::span(key_bits.begin() + offset, key_bits.end()); } @@ -96,7 +97,11 @@ class MLDSA_Composite_Verification_Operation final : public PK_Ops::Verification BER_Decoder dec(trad_sig); BigInt ri; BigInt si; - dec.start_sequence().decode(ri).decode(si).end_cons(); + try { + dec.start_sequence().decode(ri).decode(si).end_cons(); + } catch(Exception&) { + return false; + } const auto group = Botan::EC_Group::from_name(m_parameters.curve()); const EC_Scalar r = EC_Scalar::from_bigint(group, ri); const EC_Scalar s = EC_Scalar::from_bigint(group, si); diff --git a/src/lib/pubkey/mldsa-composite/mldsa_comp.h b/src/lib/pubkey/mldsa-composite/mldsa_comp.h index 745bce4db74..bc84bccb170 100644 --- a/src/lib/pubkey/mldsa-composite/mldsa_comp.h +++ b/src/lib/pubkey/mldsa-composite/mldsa_comp.h @@ -47,7 +47,7 @@ class BOTAN_PUBLIC_API(3, 0) MLDSA_Composite_PublicKey : public virtual Public_K * This is justified by the assumption that composite algorithms are used in the assumption that * one of the component algorithms might be broken. * - * @return the mimium of the components' estimated strengths. + * @return the maximum of the components' estimated strengths. */ size_t estimated_strength() const override { return std::max(this->m_mldsa_pubkey->estimated_strength(), this->m_traditional_pubkey->estimated_strength());