Design a Compact Non-linear S-Box with Multiple-Affine Transformations

Abstract

The present paper introduces a new method of S-Box construction which work as a byte-oriented substitution scheme. The S-Box design considers the core part for the building most block cipher algorithms and play a major role in generating confusion property. Modern ciphers build with different types of S-Box of half-byte (nibble of 4-bit) or full-byte 8-bit as lookup tables with distinct mathematical Boolean functions (BFs). The proposed method generates the S-box based on multiplications of multiple different affine transforms with multiple distinct overlapped vectors of 8-bit to achieve high nonlinearity. The construction of S-box focused on use an irreducible polynomial of order eight over Galois Field GF (28). The proposed S-box quit similar to the S-box of Advance Encryption Standard (AES) but with more algebraic complexity and high non-linearity factor