  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.
