Investigation of Matrix Encryption Algorithms

ABSTRACT: There are many applications that have been developed in order to protect information from any public network attacks. One of the important aspects for secure transformation of information is cryptography, which is the focus of this thesis. We only focus on the Hill cipher algorithm. The Hill cipher can be broken by known plaintext-ciphertext attack due to its linearity. There are several Hill cipher modifications, which have been proposed in the literature of cryptography to make it stronger. In this study, we deal with two different kinds of Hill cipher modifications which use interweaving, interlacing and 16 iterations. Both proposed ciphers have a substantial avalanche effect and are supposed to resist any cryptanalytic attack. However, it is not discussed why interweaving and interlacing with the iteration strengthen the Hill cipher and why the number of iterations is taken to be 16. We show that strength of proposed ciphers is due to non-linear transformation used in bit-level permutations and investigate effect of number of iterations on the avalanche effect. We modify Hill cipher modifications [7, 8] by introducing columns swapping HC (CSHC) that uses swapping of columns of the binary bits of the plaintext characters instead of interlacing and interweaving as in [7, 8]. Another modification is arbitrary permutation Hill cipher (APHC) that uses an arbitrary permutation not known to an opponent instead of a fixed permutation (interweaving, interlacing and etc.). In these ciphers 1 or 2 iterations are used instead of 16 iterations as in [7, 8]. The test results obtained by comparison analysis of two new proposed ciphers indicate that any bit-level permutations can provide a considerable avalanche effect and two iterations can be used instead of 16. Keyword: Hill cipher, linear transformation, Iteration, permutation, Avalanche effect v ……………………………………………………………………………………………………………………………………………………………………………………………………………………