Criptografy applications of primitive matrices Galois and Fibonacci
DOI:
https://doi.org/10.18372/2410-7840.15.4777Keywords:
irreducible polynomials, primitive ma-trices, primitive elements of the field GaloisAbstract
Formation of pseudo-random sequences of binary numbers is the actual problem being solved in cryptography. The most common method of generating pseudo-random sequences is based on linear shift registers of maximal order linear feedback is uniquely described by the classical Galois and Fibonacci matrices. The paper deals with the synthesis of generalized primitive matrices Galois and Fibonacci (and their dual versions) of any order n over Galois prime field of characteristic p. Synthesis of matrices based on the use of irreducible polynomials of degree n fn characteristic p and primitive elements of the extended Galois field generated by the polynomial fn. We discuss the prospects of using such matrices in the construction of pseudorandom sequence of generalized p-ary numbers. Developed conversion operators of any generalized matrix of all the others. Proposed stylized representation of feedbacks in the LSR-generators of pseudo-random sequences.
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