Elliptic curve analogue of Legendre sequences

Author： Chen Zhixiong  

Publisher： Springer Publishing Company

ISSN： 0026-9255

Source： Monatshefte für Mathematik, Vol.154, Iss.1, 2008-05, pp. : 1-10

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Abstract

The Legendre symbol is applied to the rational points over an elliptic curve to output a family of binary sequences with strong pseudorandom properties. That is, both the well-distribution measure and the correlation measure of order k, which are evaluated by using estimation of certain character sums along elliptic curves, of the resulting binary sequences are “small”. A lower bound on the linear complexity profile of these sequences is also presented. Our results indicate that the behavior of such sequences is very similar to that of the Legendre sequences.

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