finally

Cryptography/redacted-remainders/README.md

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+# to-do

Cryptography/redacted-remainders/challenge.yml

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+name: "Redacted Remainders"
+category: Cryptography
+description: |-
+  It's 4 AM right now and I'm so tired, surely nothing bad will happen if I publish this challenge right?
+
+  Author: ringoshiro
+
+##### DON'T CHANGE
+value: 500
+type: dynamic
+extra:
+    initial: 500
+    decay: 30
+    minimum: 100
+##### DON'T CHANGE
+
+flags:
+  - BEECTF{b1t5_0f_ch1n3s3_c03ff5}
+
+tags:
+  - medium
+
+files:
+  - dist/chall.py
+  - dist/output.txt
+
+state: hidden
+
+version: "0.1"

Cryptography/redacted-remainders/dist/chall.py

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+from Crypto.Util.number import getPrime, inverse, bytes_to_long
+import random, math
+from textwrap import wrap
+
+LR = 0.28
+GROUP = 4
+FKP = 24
+FKS = 24
+
+def mask_bits_as_r(bs: str, hr: float, fp: int, fs: int) -> str:
+    n = len(bs)
+    alw_ids = list(range(n))
+    if fp > 0:
+        alw_ids = alw_ids[fp:]
+    if fs > 0:
+        alw_ids = [i for i in alw_ids if i < n - fs]
+    to_hide_target = int(hr * len(alw_ids))
+    to_hide = set(random.sample(alw_ids, k=min(to_hide_target, len(alw_ids))))
+    masked = []
+    for i, b in enumerate(bs):
+        if (fp and i < fp) or (fs and i >= n - fs):
+            masked.append(b)
+        elif i in to_hide:
+            masked.append('r')
+        else:
+            masked.append(b)
+    return ''.join(masked)
+
+def groupify(s: str, size: int) -> str:
+    return ' '.join(wrap(s, size))
+
+def int_to_bin(x: int) -> str:
+    return bin(x)[2:]
+
+flag = open("flag.txt", "rb").read().strip()
+e = 4099
+while True:
+    p = getPrime(128)
+    q = getPrime(128)
+    n = p * q
+    phi = (p - 1) * (q - 1)
+    if math.gcd(e, phi) != 1:
+        continue
+    d = inverse(e, phi)
+    dp = d % (p - 1)
+    dq = d % (q - 1)
+    kp = (e * dp - 1) // (p - 1)
+    kq = (e * dq - 1) // (q - 1)
+    if kp == 0 or kq == 0:
+        continue
+    break
+m = bytes_to_long(flag)
+if m >= n:
+    raise ValueError("flag too large for modulus")
+c = pow(m, e, n)
+dp_bits = int_to_bin(dp)
+dq_bits = int_to_bin(dq)
+masked_dp = mask_bits_as_r(dp_bits, LR, FKP, FKS)
+masked_dq = mask_bits_as_r(dq_bits, LR, FKP, FKS)
+dp = groupify(masked_dp, GROUP)
+dq = groupify(masked_dq, GROUP)
+with open("output.txt", "w") as f:
+    f.write(f"n={n}\n")
+    f.write(f"e={e}\n")
+    f.write(f"c={c}\n")
+    f.write(f"dp={dp}\n")
+    f.write(f"dq={dq}\n")

Cryptography/redacted-remainders/dist/output.txt

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+n=59213204637068816907517582537717244881250709490610600160235894584144862180589
+e=4099
+c=52598477212363693322221974252387327725937369173109674066499283883678096102095
+dp=1010 0010 0100 1111 1100 1101 r01r 0011 0101 r010 00r1 0r0r 11r0 0101 0r00 0001 rr01 1r01 1rr1 1r01 r1r1 rr01 01r1 001r 0r01 1111 1000 1011 1101 1110 1010 11
+dq=1010 1110 0110 1001 1000 1011 0101 11rr 1000 0101 1100 110r 1r10 r110 0rr1 011r 110r rrr0 1r1r 01rr r110 1011 0rr1 1100 110r r1r0 1101 0001 0010 1001 1101 011