A Novel Technique to Replace S-box in Traditional Cryptosystems Using Logical Properties of Mersenne Prime Number and Binary Logical Operations

The S-Box (Substitution Box) is a crucial component in many cryptographic algorithms, serving to provide non-linearity and resistance against linear and differential cryptanalysis. However, traditional S-Boxes have known vulnerabilities, which can be exploited by advanced cryptanalysis techniques, undermining the overall security of the cryptosystem. This paper introduces a novel approach for replacing the traditional S- Box with a novel technique designed to enhance cryptographic security. The proposed method leverages mainly the logical properties of Mersenne's prime number to create an adaptable and complex non-linear transformation along with simple logical operations. These provide resistance to both known and emerging cryptanalytic attacks. Comparative analysis with existing cryptosystems demonstrates significant improvements in security strength, performance and resilience against cryptanalysis. The justification of these has been validated with image data using Mersenne prime number 2<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">521</sup>-1, which is a NIST recommended prime. Demonstrated using image data, the proposed algorithm shows promise in advancing next-generation encryption techniques capable of resisting sophisticated attack vectors, thereby strengthening data confidentiality and integrity.