## IACR paper details

Title | Inferring sequences produced by a linear congruential generator on elliptic curves missing high--order bits |
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Booktitle | IACR Eprint archive |
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Pages | |
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Year | 2007 |
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URL | http://eprint.iacr.org/2007/099 |
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Author | Jaime Gutierrez |
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Author | Alvar Ibeas |
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Abstract |
Let $p$ be a prime and let $E(\F_p)$ be an elliptic curve defined over
the finite field $\F_p$ of $p$ elements. For a given point $G \in
E(\F_p)$ the linear congruential genarator on elliptic curves (EC-LCG)
is a sequence $(U_n)$ of pseudorandom numbers defined by the relation
$$ U_n=U_{n-1}\oplus G=nG\oplus U_0,\quad n=1,2,\ldots,$$ where
$\oplus$ denote the group operation in $E(\F_p)$ and $U_0 \in E(\F_p)$
is the initial value or seed. We show that if $G$ and sufficiently
many of the most significants bits of two consecutive values $U_n,
U_{n+1}$ of the EC-LCG are given, one can recover the seed $U_0$ (even
in the case where the elliptic curve is private) provided that the
former value $U_n$ does not lie in a certain small subset of
exceptional values. We also estimate limits of a heuristic approach
for the case where $G$ is also unknown. This suggests that for
cryptographic applications EC-LCG should be used with great care. Our
results are somewhat similar to those known for the linear and
non-linear pseudorandom number congruential generator. |
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Search for the paper

@misc{eprint-2007-13381,
title={Inferring sequences produced by a linear congruential generator on elliptic curves missing high--order bits},
booktitle={IACR Eprint archive},
keywords={foundations /},
url={http://eprint.iacr.org/2007/099},
note={pseudorandom numbers, elliptic curves jaime.gutierrez@unican.es 13591 received 19 Mar 2007},
author={Jaime Gutierrez and Alvar Ibeas},
year=2007
}

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