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

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.

References

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