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Research on Excellent Sequence of Period p^n over GF(q) with Genetic Algorithm | IEEE Conference Publication | IEEE Xplore

Research on Excellent Sequence of Period p^n over GF(q) with Genetic Algorithm


Abstract:

The pn-periodic q-ary sequence with high linear complexity and high k-error linear complexity is defined as excellent sequence. With appropriate fitness function and para...Show More

Abstract:

The pn-periodic q-ary sequence with high linear complexity and high k-error linear complexity is defined as excellent sequence. With appropriate fitness function and parameters, this paper design a genetic algorithm to generate the N-periodic q-ary excellent sequences, where N=27, 81, , 2187, and get some laws of k-error linear complexity and linear complexity, here p is an odd prime and q is a primitive root modulo p2.
Date of Conference: 10-14 August 2015
Date Added to IEEE Xplore: 21 July 2016
ISBN Information:
Conference Location: Beijing, China
School of Computer Engineering and Science, Shanghai University, Shanghai, China
School of Computer Engineering and Science, Shanghai University, Shanghai, China
School of Computer Engineering and Science, Shanghai University, Shanghai, China

I. Introduction

In the sixties of the 20th century, Massey proposed the Berlekamp-Massey algorithm. According to the algorithm[1], if the linear complexity of a sequence is , we can compute the entire sequence with continuous 2 bits. So a cryptographically secure sequence must have a high linear complexity. Later, more and more papers devoted to the study of the linear complexity[2]–[5]. However, a high linear complexity is not enough to ensure a sequence being cryptographically secure. For example, let be a period of an -periodic sequence . It is obviously that has the maximum possible linear complexity . But it is cryptographically weak. After changing every bit from 1 to 0, the linear complexity will decrease to zero. So such sequences are not secure for being used in cryptography. And we can conclude that a cryptographically secure sequence should have a stable linear complexity.

School of Computer Engineering and Science, Shanghai University, Shanghai, China
School of Computer Engineering and Science, Shanghai University, Shanghai, China
School of Computer Engineering and Science, Shanghai University, Shanghai, China

References

References is not available for this document.