Elliptic curve analogue of Legendre sequences

. 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...

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Bibliographic Details
Published inMonatshefte für Mathematik Vol. 154; no. 1; pp. 1 - 10
Main Author Chen, Zhixiong
Format Journal Article
LanguageEnglish
Published Vienna Springer-Verlag 01.05.2008
Subjects
Mathematics
Mathematics and Statistics
Key words: Pseudorandom binary sequences, elliptic curves, character sums, correlation
2000 Mathematics Subject Classification: 11G20, 94A60, 11K45, 11L40
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ISSN0026-9255
1436-5081
DOI10.1007/s00605-008-0520-x

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Summary:. 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.
ISSN:0026-9255
1436-5081
DOI:10.1007/s00605-008-0520-x