Decimation of M Sequences As a Way of Obtaining Primitive Polynomials

Abstract

One approach to obtain a cryptographically strong encryption gamma is to use linear-feedback shift registers defined by primitive polynomials. The ability to quickly select the appropriate polynomial can provide the required degree of security of the stream cipher. Currently, primitive polynomials for sufficiently large degrees are known, but usually these are so-called sparse polynomials. To increase the correlational stability, it is necessary to be able to quickly generate new primitive polynomials of the given degrees, which is the focus of this study.