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On the linear complexity profile of some sequences derived from elliptic curves

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Abstract

For a given elliptic curve \(\mathbf {E}\) over a finite field of odd characteristic and a rational function f on \(\mathbf {E}\) we first study the linear complexity profiles of the sequences f(nG), \(n=1,2,\dots \) which complements earlier results of Hess and Shparlinski. We use Edwards coordinates to be able to deal with many f where Hess and Shparlinski’s result does not apply. Moreover, we study the linear complexities of the (generalized) elliptic curve power generators \(f(e^nG)\), \(n=1,2,\dots \) We present large families of functions f such that the linear complexity profiles of these sequences are large.

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Acknowledgments

The authors are 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”. The first author is also partially supported by Hungarian National Foundation for Scientific Research, Grant No. K100291.

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  1. Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Altenbergerstr. 69, 4040, Linz, Austria

    László Mérai & Arne Winterhof

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  1. László Mérai
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  2. Arne Winterhof
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Correspondence to László Mérai.

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Communicated by R. Steinwandt.

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Mérai, L., Winterhof, A. On the linear complexity profile of some sequences derived from elliptic curves. Des. Codes Cryptogr. 81, 259–267 (2016). https://doi.org/10.1007/s10623-015-0140-0

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  • DOI: https://doi.org/10.1007/s10623-015-0140-0

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