KHAN Cipher

A High-Performance Stream Cipher Native to Python/C++, Powered by Primitive Roots.

Architecture Overview

KHAN is built on a mathematically rigorous sequence derived from Full Reptend Primes (Primitive Roots Modulo P).

• Key Derivation (HMAC-SHA256): Secure master key mapping and salt handling.
• State Generation (Full Reptend Primes): Predictable zero-bias sequences mathematically derived from primitive root fractional expansion.
• C++ XOR Diffusion Matrix: High-speed symmetric stream combining native Python abstractions with a C++17 -O3 optimized backend.

State Space Analysis

The keystream features an unbounded internal state space based on the properties of $p$, while remaining perfectly keyed by a strict 256-bit symmetric input, creating non-linear sequence generation distributions verified by SP 800-22.

Features

• Non-Linear Sequence Generation
• Symmetric Keystream Construction
• Zero-Latency Diffusion: C++ bulk_xor compiler flags targeting native architecture achieve multi-gigabyte/second throughputs.
• High Entropy: Achieves 7.99/8.0 Byte-wise Shannon Entropy, passing all 15 NIST STS suites.

Installation

GCC or Clang is required to compile the C++ cryptographic extensions on your system.

pip install -e .

Developer Quick Start

import os
from khan_cipher.core import encrypt, decrypt

master_key = os.urandom(32)
plaintext = b"CONFIDENTIAL: Cloudflare Edge Node routing tables update. Payload highly sensitive."

# Encrypt
payload = encrypt(plaintext, master_key)

# The resulting payload contains: [Salt (16) | IV (16) | Ciphertext (N) | MAC (32)]

# Decrypt
decrypted = decrypt(payload, master_key)
assert plaintext == decrypted

Formal Verification

The primitive root bijections mapped internally are formally modeled in Lean 4. The proofs tracking the permutation cycles without bias reside in docs/KHAN_Theorems.lean.

Benchmarks

To run the automated Python visualization limits, spectral analysis, and parse NIST p-values:

python benchmarks/run_all.py

Security Notice

Disclaimer: This algorithm is an academic exploration of primitive root cryptographic properties. It has not undergone formal multi-year cryptanalysis by standard bodies. Do not use for production secrets.