Large Family of Sequences from Elliptic Curves over Residue Class Rings

Shengqiang LI; Zhixiong CHEN; Liang ZHOU

doi:10.1587/transfun.E93.A.1827

Regular Section

Large Family of Sequences from Elliptic Curves over Residue Class Rings

Shengqiang LI, Zhixiong CHEN, Liang ZHOU

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Keywords: elliptic curves, exponential sums, binary sequences, well-distribution measure, correlation measure

JOURNAL RESTRICTED ACCESS

2010 Volume E93.A Issue 10 Pages 1827-1832

DOI https://doi.org/10.1587/transfun.E93.A.1827

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Abstract

An upper bound is established for certain exponential sums on the rational points of an elliptic curve over a residue class ring $\mathbb{Z}_N$, 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 $\mathbb{Z}_N$.

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