Generators of pseudo random sequences of galois

Generators of pseudo random sequences of galois

A. Ya. Beletsky, E. A. Beletsky

 

Abstract

The questions of Galois and Fibonacci random size n primitive matrices creation over thesimple field GF( p) is considered. The synthesis is based on usage of irreducible polynomial fn of degreen and primitive elements of extended field GF( pn ) , which is generated by polynomial fn . The ways oflinked primitive matrices of Galois and Fibonacci are offered. The possibilities of such matricesapplication are described

Keywords

Irreducible and primitive polynomials; primitive matrices; linear shift registers; generators of Galois sequences

References

Ivanov, M. A.; Chugunkov, I. V. Theory, application and evaluation of the quality of pseudorandom sequences. Moscow: Kudits-OBRAZ, 2003. (In Russian).

Lidl, R.; Niederreiter, H. Finite fields. Monograph in 2 vols. Addison Wesley, 1983.

Volkovich, S. L.; Geranin, V. O.; Movchan, T. V.; Pisarenko, L. D. Introduction to algebraic theory of noiseproof coding. yiv: UkrINTEI, 2002. (In Russian).

Ivanov, M. A. Cryptographic methods of information security in computer systems and networks. Moscow: Kudits-OBRAZ, 2001. (In Russian).

Beletsky, A. Ja.; Beletsky, A. A.; Beletsky, E. A. Gray Transformations. Monograph in 2 vols. vol.1. Fundamentals of the theory. Kyiv: NAU Publishing House, 2001. (In Russian).

Gantmakher, F. R. Theory of Matrices. – Moscow: Nauka, 1968. (In Russian).

Fomichev V. M. Discrete mathematics and cryptology. Moscow.: Dialog-MIFI, 2003. 400 p.