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Pré-Publication, Document De Travail Année : 2015

Cover and Decomposition Index Calculus on Elliptic Curves made practical

Vanessa Vitse
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Résumé

We present a new " cover and decomposition " attack on the elliptic curve discrete logarithm problem, that combines Weil descent and decomposition-based index calculus into a single discrete logarithm algorithm. This attack applies, at least theoretically, to all composite degree extension fields, and is particularly well-suited for curves defined over Fp6. We give a real-size example 3 of discrete logarithm computations on a curve over a 156-bit degree 6 extension field, which would not have been practically attackable using previously known algorithms. A shorter version of this work was presented at the EUROCRYPT 2012 conference.
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Dates et versions

hal-01121942 , version 1 (02-03-2015)

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  • HAL Id : hal-01121942 , version 1

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Antoine Joux, Vanessa Vitse. Cover and Decomposition Index Calculus on Elliptic Curves made practical: Application to a previously unreachable curve over Fp6. 2015. ⟨hal-01121942⟩
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