On a Class of Pseudorandom Sequences From Elliptic Curves Over Finite Fields

Author

Hu, Honggang ; Hu, Lei ; Feng, Dengguo

Author_Institution

Chinese Acad. of Sci., Beijing

Volume

53

Issue

7

fYear

2007

fDate

7/1/2007 12:00:00 AM

Firstpage

2598

Lastpage

2605

Abstract

Following the idea of Xing et al., we investigate a general method for constructing families of pseudorandom sequences with low correlation and large linear complexity from elliptic curves over finite fields in this correspondence. With the help of the tool of exponential sums on elliptic curves, we study their periods, linear complexities, linear complexity profiles, distributions of r-patterns, periodic correlation, partial period distributions, and aperiodic correlation in detail. The results show that they have nice randomness.

Keywords

correlation methods; random sequences; elliptic curves; finite fields; linear complexity; partial period distributions; periodic correlation; pseudorandom sequences; r-patterns; Digital signatures; Elliptic curve cryptography; Elliptic curves; Galois fields; Information security; Laboratories; Multiaccess communication; Public key cryptography; Random sequences; Upper bound; $r$-pattern; Aperiodic correlation; elliptic curve; exponential sum on elliptic curve; least period; linear complexity; periodic correlation; pseudorandom sequence;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2007.899532

Filename

4252333