Pseudo-Randomness of Discrete-Log Sequences from Elliptic Curves

Authors:
Zhixiong Chen;Ning Zhang;Guozhen Xiao
Affiliations:
Department of Mathematics, Putian Univ., Putian, China 351100 and Key Lab of Network Security and Cryptology, Fujian Normal University, Fuzhou, China 350007;Ministry of Education Key Lab of Computer Networks and Information Security, Xidian University, Xi'an, China 710071;Ministry of Education Key Lab of Computer Networks and Information Security, Xidian University, Xi'an, China 710071
Venue:
Information Security and Cryptology
Year:
2007

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Abstract

We investigate an upper bound on the discrepancy and a lower bound on the linear complexity of a class of sequences, derived from elliptic curves by using discrete logarithm in this paper. The results indicate that these sequences may have `nice' pseudo-random properties. The important tool in the proof is certain character sums estimate along elliptic curves. In addition, we apply linear recurrence relation over elliptic curves to output binary sequences with very interesting pseudo-random behavior.