The t-Modified Self-Shrinking Generator

Abstract

Pseudo-random sequences exhibit interesting properties with applications in many and distinct areas ranging from reliable communications to number generation or cryptography. Inside the family of decimation-based sequence generators, the modified self-shrinking generator (an improved version of the self-shrinking generator) is one of its best-known elements. In fact, such a generator divides the PN-sequence produced by a maximum-length LFSR into groups of three bits. When the sum of the first two bits in a group is one, then the generator returns the third bit, otherwise the bit is discarded. In this work, we introduce a generalization of this generator, where the PN-sequence is divided into groups of t bits, \(t\ge 2\). It is possible to check that the properties of the output sequences produced by this family of generators have the same or better properties than those of the classic modified self-shrunken sequences. Moreover, the number of sequences generated by this new family with application in stream cipher cryptography increases dramatically.