Annals of Communications in Mathematics

AbstractThis paper establishes a k-analogue of the lambda gamma function and in troduces a k-Riemann zeta function and a k-lambda Riemann zeta function. In addition, the paper establishes a relationship between the k-analogue of the lambda gamma function, the k-Riemann zeta function and the k-lambda Riemann zeta function. Finally, the paper establishes some properties of the k-analogue of the lambda gamma function similar to existing properties satisfied by the classical gamma function, the k-analogue of the gamma function and the lambda gamma function.

Abstract:Digital communication among individuals, institutions, and enterprises across internet-based platforms has grown substantially over the past decades. This sharp increase has greatly exposed sensitive information to adversarial attacks and to substantial data losses. Although many cryptosystems have been proposed and implemented to address these challenges, daily reports continue to reveal successful attacks. In this paper, we propose a symmetric-key cryptosystem to improve message security. The proposed system combines the classical Hill cipher with columnar transposition. It uses four distinct keys: two square key matrices and two additional keys termed ‘key-within-key’ (𝜔). The Hill cipher is enhanced by expanding the character space to include all printable ASCII characters, mitigating known-plaintext attacks. The key space is doubled by using the transpose of the key matrix as a second key. Encryption is performed in two rounds, each round employing two of the four keys; decryption follows the reverse process. Matlab simulation conducted was observed to display efficient results.