Designs, Codes and Cryptography

, Volume 86, Issue 5, pp 1113–1129 | Cite as

On the elliptic curve endomorphism generator

  • László Mérai


For an elliptic curve \({E}\) over a finite field we define the point sequence \((P_n)\) recursively by \(P_n=\vartheta (P_{n-1})=\vartheta ^n(P_0)\) with an endomorphism \(\vartheta \in {{\mathrm{End}}}({E})\) and with some initial point \(P_0\) on \({E}\). We study the distribution and the linear complexity of sequences obtained from \((P_n)\).


Elliptic curves Complex multiplication Character sums Linear complexity Power generator 

Mathematics Subject Classification

11T23 65C10 14H52 94A55 94A60 



The author would like to thank Arne Winterhof and Igor Shparlinski for helpful comments. The author is partially supported by the Austrian Science Fund FWF Project F5511-N26 which is part of the Special Research Program “Quasi-Monte Carlo Methods: Theory and Applications”.


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Authors and Affiliations

  1. 1.Johann Radon Institute for Computational and Applied MathematicsAustrian Academy of SciencesLinzAustria

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