Residues of prime numbers as entries for the S-Box

Abstract

The byte substitution table which is known as the S-Box is one of the major steps of the Advances Encryption Standard (AES). Its entries are pre-computed and stored on lookup tables (ROMs) to avoid tedious real time computations using Galois Field. However, in many situations, storing data weakens the overall security as it gives a hacker a chance to put a foot at the door. To harden against such vulnerability, a modified approach that avoids onerous Galois Field operations is necessary. To that end, a replacement that is based on the field of residues of prime numbers is proposed The replacement uses a reduced lookup table. The advantage of the reduced lookup table over the one originally proposed for AES is demonstrated. The paper also justifies the need for speeding up byte substitution.