비선형 수열의 상호상관관계 함수

Abstract

In this thesis we propose a new Shrinking Generator(SG) which is called Linear Feedback Shift Register(LFSR) Cellular Automata(CA) Shrinking Generator(LCSG) using an LFSR with control register and CA with generator register. The proposed shrunken sequences generated by LCSG have longer periods and high complexities than the shrunken sequences generated by the known method. Also we analyze the generated sequences using LCSG. Especially we propose a new method for the calculation of the periodic cross-correlation of -sequences and GMW sequences generated by the same primitive polynomial. Our method is different from the Games's method. And we introduce a collection of families of nonlinear binary pseudorandom sequences generated by -sequences and Kasami sequences. Each sequence within a family has period . There are sequences within a family. Also the maximum over all auto correlation values and cross-correlation values equals to . Moreover we introduce the extended sequences of sequences generated by GMW sequences and No sequences. And we analyze cross-correlations of the extended sequences. Also we give extended sequences which are constructed from Legendre sequences. And we calculate the cross-correlation function of a Kasami sequence and a No sequence that have been generated by the same primitive polynomial with the periodic cross-correlation function of two smaller -sequences. Our method is different from the Games's method. Finally we give a proof for finding the values of the cross-correlation function when , where , and derive the linear span of the sequences in the proposed sequence family in some cases.