Large Family of Sequences from Elliptic Curves over Residue Class Rings

Shengqiang LI
Zhixiong CHEN
Liang ZHOU

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E93-A    No.10    pp.1827-1832
Publication Date: 2010/10/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E93.A.1827
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Cryptography and Information Security
elliptic curves,  exponential sums,  binary sequences,  well-distribution measure,  correlation measure,  

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An upper bound is established for certain exponential sums on the rational points of an elliptic curve over a residue class ring ZN , N=pq for two distinct odd primes p and q. The result is a generalization of an estimate of exponential sums on rational point groups of elliptic curves over finite fields. The bound is applied to showing the pseudorandomness of a large family of binary sequences constructed by using elliptic curves over ZN .