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Inferring Sequences Produced by a Linear Congruential Generator on Elliptic Curves Using Coppersmith's Methods

Thierry Mefenza 1, 2
1 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
DI-ENS - Département d'informatique de l'École normale supérieure, CNRS - Centre National de la Recherche Scientifique : UMR 8548, Inria de Paris
Abstract : We analyze the security of the Elliptic Curve Linear Con-gruential Generator (EC-LCG). We show that this generator is insecure if sufficiently many bits are output at each iteration. In 2007, Gutierrez and Ibeas showed that this generator is insecure given a certain amount of most significant bits of some consecutive values of the sequence. Using the Coppersmith's methods, we are able to improve their security bounds.
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Submitted on : Friday, October 14, 2016 - 3:07:30 PM
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Thierry Mefenza. Inferring Sequences Produced by a Linear Congruential Generator on Elliptic Curves Using Coppersmith's Methods. COCOON 2016, Aug 2016, Ho Chi Minh City, Vietnam. pp.12, ⟨10.1007/978-3-319-42634-1_24⟩. ⟨hal-01381658⟩

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