Galois generalized matrices in stream ciphers

The matrix terms Galois and Fibonacci borrowed from the theory of cryptography. These matrices connected by so-called right-hand transposition (a transposing of the relative to the auxiliary diagonal). In cryptography makes extensive use of pseudorandom number generators in Galois and Fibonacci schemes. With the help of these matrices, the same binary sequence can form as the LFSRs generated. In addition to the matrices named in work, other matrices have introduced. These include conjugate matrices Galois and Fibonacci, those created by classical (the left-hand) transpose, inverse to the basis matrices, and those inverse to the conjugate matrices. Traditional pseudorandom number generators have a significant disadvantage, which is that they are subject to the Berlekemp-Messi attack. Two main approaches proposed to prevent such attacks. The first of them assume the change from classical generators to generalized pseudorandom number generators. The second constructive way of protection against the Berlekemp-Messi attack is the construction of generators pseudorandom number based on transformations of similarity of traditional or generalized generators. This study aims to develop algorithms for the synthesis of generalized Galois of the maximum period and to establish interrelationships of Galois matrices. © 2020 Begell House Inc.. All rights reserved.