Advancing Cryptographic Security With a New Delannoy-Derived Chaotic S-Box

Abstract

The S-Box (Substitution Box) plays a crucial role in cryptographic security by introducing non-linearity and confusion into the encryption process. It enhances the resistance against cryptanalytic attacks, such as differential and linear cryptanalysis, by providing a complex and unpredictable transformation of input data. This study has exploited the constructs of Delannoy Numbers and the chaotic map to come up with a novel and secured S-Box. The non-linearity and confusion effects have been poured into the potential S-Box by swapping the randomly selected non-overlapping vectors of numbers from arbitrary rows and columns of the S-Box. A filter has been embedded in the proposed algorithm to avoid the swapping of vectors in case they overlap with each other. This process has been iterated a number of times to boost the security effects. 5D multi-wing hyperchaotic map has been used to spawn the streams of random numbers. By means of extensive testing and analysis, we demonstrate the improved cryptographic characteristics of the designed S-boxes over traditional designs. In particular, advanced security considerations have been used, including non-linearity (NL), bit-independence criteria (BIC), strict-avalanche criteria (SAC), differential probability (DP), and bijectivity. This study unquestionably contributes significantly to the ever-evolving field of network security.

Keywords

• Chaos
• Delannoy numbers
• S-box
• symmetric key
• cyber security