Generalized Galois-Fibonacci Matrix Generators Pseudo-Random Sequences

The article discusses various options for constructing binary generators of pseudo-random numbers (PRN) based on the so-called generalized Galois and Fibonacci matrices. terms "Galois matrix" "Fibonacci are borrowed from theory cryptography, in which linear feedback shift registers (LFSR) PRN according to schemes widely used. matrix generate identical sequences as LFSR generators. transition classical (PRNG) is accompanied by expanding variety generators, leading a significant increase their cryptographic resistance. This effect achieved both due rise number elements forming matrices because synthesized primitive generating polynomials that not necessarily primitive. Classical (and equivalents) have drawback: they susceptible Berlekamp-Messi (BM) attacks. Generalized PRNG free BM attack. last property consequence such feature algorithm. algorithm cracking solves problem calculating only unknown – polynomial generator. For variants PRNG, it becomes necessary determine two parameters: an irreducible element produces matrix. turns out be unsolvable since designed calculate one parameter. research results solving problems over field odd characteristics.