4, 8, 32, 64 bit Substitution Box generation using Irreducible or Reducible Polynomials over Galois Field GF(p^q) for Smart Applications
This work addresses the need for flexible S-Box generation in cryptography, but it appears incremental as it extends existing methods to broader Galois fields without demonstrating new performance gains.
The paper tackles the problem of generating substitution boxes (S-Boxes) for encryption by using irreducible or reducible polynomials over Galois fields GF(p^q), enabling the creation of S-Boxes with bit sizes like 4, 8, 32, and 64 for smart applications.
Substitution Box or S-Box had been generated using 4-bit Boolean Functions (BFs) for Encryption and Decryption Algorithm of Lucifer and Data Encryption Standard (DES) in late sixties and late seventies respectively. The S-box of Advance Encryption Standard have also been generated using Irreducible Polynomials over Galois field GF(2^8) adding an additive constant in early twenty first century. In this paper Substitution Boxes have been generated from Irreducible or Reducible Polynomials over Galois field GF(p^q). Binary Galois fields have been used to generate Substitution Boxes. Since the Galois Field Number or the Number generated from coefficients of a polynomial over a particular Binary Galois field (2q) is similar to log 2 q+1 bit BFs. So generation of log 2 q+1 bit S-boxes is Possible. Now if p = prime or non-prime number then generation of S-Boxes is possible using Galois field GF (p^q). where, q = p-1.