Significant role of the specific prime number p = 257 in the improvement of cryptosystems

Abstract

Cryptology is the significant science which is inseparable from the means of communication of secrets. In a safe manner, it has the main objective of transmitting (potentially sensitive) information between two interlocutors. One distinguishes mainly two “dual” disciplines within cryptology: (a) cryptography, which is interested in the security of information. (b) cryptanalysis, which seeks to attack it. One have a starting set of 256 elements, we add a new element to this set to form a set of 257 elements. In this paper, we consider a finite field that contains 257 elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are given by the integers modulo p when p is a prime number. For our case ℤ/pℤ, p = 257. We apply it to affine ciphers and show that this cipher looks like a permutation cipher. The idea based on this result, is to use the affine ciphers with the modulo 257 (as an initial permutation) in any specific algorithm of ciphering. Besides, one finishes with the decryption affine with the modulo 257 like an inverse permutation. This is to significantly increase the security of the specific encryption algorithm and to lengthen the 16-bits encryption key.