ENHANCING THE SECURITY OF HILL CYPHER ALGORITHM

Abstract

The Hill Cipher, a classical polygraphic substitution cipher, remains vulnerable to cryptanalytic attacks such as known-plaintext attacks due to its linear algebraic structure and dependence on invertible key matrices. This paper proposes a hybrid cryptographic framework that integrates the Hill Cipher with a transposition method to mitigate these vulnerabilities. By combining substitution and permutation techniques, the enhanced algorithm introduces non-linearity and disrupts statistical patterns in ciphertext, thereby improving resistance against frequency analysis and matrix-based attacks. The proposed method involves two stages: first, plaintext is encrypted using the Hill Cipher with a randomly generated invertible matrix, and second, the resulting ciphertext undergoes a columnar transposition process governed by a secret key. The transposition step scrambles the positional relationships of characters, obscuring residual patterns from the substitution phase. Security analysis demonstrates that the hybrid approach significantly increases the effective key space and complicates cryptanalysis by necessitating simultaneous recovery of both substitution and transposition keys. Experimental evaluations confirm that the augmented system resists known-plaintext attacks targeting the Hill Cipher’s linearity, as adversaries must now solve a compounded problem involving matrix inversion and transposition key derivation. Comparative results with the standard Hill Cipher highlight improved confusion and diffusion properties, measured through metrics such as entropy, avalanche effect, and n-gram frequency distribution uniformity. This work underscores the efficacy of hybridizing substitution and transposition mechanisms to fortify classical ciphers against modern cryptanalytic threats.