Hill Cipher with Block Permutation Using a 97-Symbol Character Set: Entropy and Cryptanalytic Considerations

Abstract

This study investigates a Hill-cipher implementation over a 97-symbol character set followed by a fixed block permutation. The character set consists of the 94 printable standard ASCII symbols excluding space, supplemented by ¥, €, and ±, and is mapped bijectively to the finite field F₉₇. Invertible key matrices of sizes 3×3, 4×4, and 5×5 are evaluated using Shannon entropy and character-frequency distributions. For the experimental text, preprocessing removes spaces and symbols outside the defined set, producing 1,302 symbols with plaintext entropy 4.4800 bits. A representative 4×4 experiment yields ciphertext entropy 6.5545 bits, close to the theoretical maximum log₂(97)=6.5999 bits. Across three keys for each matrix size, the mean entropy values are 6.5209, 6.5443, and 6.5399 bits for 3×3, 4×4, and 5×5 matrices, respectively, showing no monotonic increase with matrix size. The block permutation changes symbol positions but preserves single-symbol frequencies and entropy. Moreover, because a fixed permutation matrix composed with a Hill key remains a linear transformation over F₉₇, the construction retains the known-plaintext vulnerability of Hill-type ciphers. Accordingly, the results demonstrate strong single-symbol statistical uniformity of the ciphertext, but should not be interpreted as evidence of modern cryptographic security.