RANDOMIZED DES USING IRREDUCIBLE POLYNOMIAL OVER GALOIS FIELD GF(73)

Abstract

Multiplicative inverses under an irreducible polynomial over Galois Field GF(p^m) play important role in cryptography. The substitution box of Advanced Encryption Standard is designed in 1999 with multiplicative inverses under the first irreducible polynomial over GF(2^8). In the present paper, a recently published pseudorandom number generator GF7 designed over GF(7^3) in 2016, is intuitively incorporated into the Data Encryption Standard algorithm to modify it by increasing its randomness as well as security. Following the method proposed by National Institute of Standards and Technology, the statistical randomness testing is done on a large number of output ciphers obtained by the algorithm. The statistical result shows tremendous improvement in randomness for the proposed modified algorithm.