Primitive matrix Galois in cryptographic applications

Abstract

The article discusses the formation of generalized Galoisprimitive matrices of arbitrary order n , the elements ofwhich belong to the prime field GF(2) . Synthesis ofmatrices based on the use of irreducible polynomials ofdegree n and primitive elements of the extended field(2 ) n GF , which generated by polynomials. The methodsof constructing conjugate primitive matrices Galois andunambiguously related matrices Fibonacci. Discussesways to use these matrices in cryptographic applicationsto solve the problem of the generalized linear generatorsof pseudo-random sequences Galois of maximal period.The analysis of the binary pseudo-random sequencesgenerated by linear generators Galois in feedback registersthat use primitive polynomials of small degree in therange of four to six.