A Multi-Layered Cryptosystem to Improve the Hill Cipher Using Graph-Based Chaotic Logistic Maps, Dynamic Key Generation, and Nonlinear Transformations

The classical Hill cipher is inadequate for modern use because its key matrix is fixed and the cipher is linear, hence vulnerable to known-plaintext attacks. This paper proposes an experimental hybrid cryptosystem that extends the Hill cipher with chaotic dynamics and graph-based key derivation. A logistic map, run in its chaotic regime, generates the weights of a complete undirected weighted graph; a low-weight Hamiltonian path extracted from it (exact search for , greedy heuristic otherwise) supplies the Vigenère key and enters the Caesar shift, while the affine parameters, an invertible Hill matrix (mod 26 or 256), a key-dependent S-box, a byte permutation, a mixing matrix, the chaotic stream, and (through SHA-256) the round keys and the IV are derived from the same chaotic source; a per-message 128-bit nonce is mixed into the chaotic state so that the IV, the round keys, the classical-layer keystream and an HMAC-SHA256 key are all unique to each message. The plaintext passes through a classical layer (Caesar, Vigenère, affine, chaotic XOR, Hill) and then through a 16-byte SPN-like block layer in CBC mode. Experiments on a 1,898-byte mixed Arabic/English text confirm exact reversibility; a change of the seed makes decryption fail and changes about of the ciphertext bits; the ciphertext byte distribution is close to uniform; and all seven tested NIST SP 800-22 statistics passed at (Table 4). Because every component is derived from the seed and a few public parameters, the effective key space is bounded by the seed space (about at 50-digit precision) rather than by the product of the component spaces. The unoptimised prototype runs at roughly 34 kbit/s. The construction is wrapped in an Encrypt-then-MAC frame (nonce ciphertext tag) which rules out padding-oracle attacks [58]; the 10-round block layer follows the AES-128 parameter choice for 128-bit blocks [9], and empirical diffusion tests reach full diffusion after 3–4 rounds, leaving a safety margin of . The scheme provides confidentiality and integrity but has not been subjected to formal cryptanalysis, and should be regarded as an experimental and educational design.