A Cryptographic Approach Using Partial Affine Bijective Mapping and Recursive Hill Cipher

Abstract

This study introduces a hybrid encryption framework that integrates Partial Affine Bijective Mapping with a Recursive Hill Cipher, employing modulo 27 arithmetic to encompass all 26 English alphabetic characters along with the space symbol. In the proposed scheme, plaintext is initially converted into its numeric representation through partial affine bijective mapping. Subsequently, encryption is performed using a Hill Cipher, wherein the key matrix is recursively updated across successive rounds. This recursive key evolution significantly strengthens the cryptographic system by expanding the effective key space, enhancing statistical randomness, and mitigating susceptibility to classical cryptanalytic techniques such as frequency analysis and brute-force attack. In this paper, the proposed framework is further extended to modulo 37 arithmetic to additionally incorporate numeric digits (0–9), thereby improving its applicability to alphanumeric data without altering the core encryption structure.