A Scalable Symmetric Cryptographic Scheme Based on Latin Square, Permutations, and Reed-Muller Codes for Resilient Encryption

Symmetric cryptography is essential for secure communication as it ensures confidentiality by using shared secret keys. This paper proposes a novel substitution-permutation network (SPN) that integrates Latin squares, permutations, and Reed-Muller (RM) codes to achieve robust security and resilience. As an adaptive design using binary representation with base-n Latin square mappings for non-linear substitutions, it supports any n (Codeword length and Latin square order), k (RM code dimension), d (RM code minimum distance) parameters aligned with the Latin square and RM(n,k,d) codes. The scheme employs 2log2n-round transformations using log2n permutations ρz, where in the additional log2n rounds, row and column pairs are swapped for each pair of rounds, with key-dependent πz permutations for round outputs and fixed ρz permutations for codeword shuffling, ensuring strong diffusion. The scheme leverages dynamic Latin square substitutions for confusion and a vast key space, with permutations ensuring strong diffusion and RM(n,k,d) codes correcting transmission errors and enhancing robustness against fault-based attacks. Precomputed components optimize deployment efficiency. The paper presents mathematical foundations, security primitives, and experimental results, including avalanche effect analysis, demonstrating flexibility and balancing enhanced security with computational and storage overhead.