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Elliptic curve analogue of Legendre sequences

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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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Authors and Affiliations

  1. Putian University, Putian and Fujian Normal University, Fuzhou, Fujian, China

    Zhixiong Chen

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  1. Zhixiong Chen
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Correspondence to Zhixiong Chen.

Additional information

Research partially supported by the Science and Technology Foundation of Putian City (No. 2005S04), the Open Funds of Key Lab of Fujian Province University Network Security and Cryptology (No. 07B005) and the Foundation of the Education Department of Fujian Province (No. JA07164).

Author’s addresses: Department of Mathematics, Putian University, Putian, Fujian 351100, China; and Key Lab of Network Security and Cryptology, Fujian Normal University, Fuzhou, Fujian 350007, China

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Chen, Z. Elliptic curve analogue of Legendre sequences. Monatsh Math 154, 1–10 (2008). https://doi.org/10.1007/s00605-008-0520-x

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  • DOI: https://doi.org/10.1007/s00605-008-0520-x

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