Hill-Enigma-SPN: A Novel Substitution–Permutation Network Cipher with GF(2) Matrix-Rotor Scheduling and Argon2id Key Derivation

This paper introduces Hill-Enigma-SPN (HESPN), a 128-bit byte-oriented substitution–permutation network that extends the Hill cipher to address its classical weaknesses, including linearity, the absence of a nonlinear substitution layer, and the lack of memory-hard key derivation. HESPN combines four innovations: a rotor-scheduled admissible GF(2) matrix diffusion layer inspired by Enigma, AES S-box substitution, a round-dependent inter-byte permutation, and Argon2id memory-hard key derivation. Empirical evaluation across three experimental sessions shows behavior comparable to AES on the evaluated metrics: plaintext avalanche averages about 64 bits at 12 rounds; maximum observed differential probability reaches 2×10⁻⁵; and linear bias remains at the statistical noise floor. Algebraic degree grows across rounds, saturating at the maximum observable degree by round 12. A branch number B ≥ 4 is formally proved for all admissible matrices. Estimated C throughput is ~80 MB/s. Compared with AES, PRESENT, SAFER+, SHARK, Serpent, and MD-Hill SPN, HESPN combines rotor-scheduled GF(2) diffusion, proven branch number, AES S-boxes, and Argon2id key derivation in a single design.