Welcome to the resource topic for 2011/020
Title:
Cover and Decomposition Index Calculus on Elliptic Curves made practical. Application to a seemingly secure curve over \F_{p^6}
Authors: Antoine Joux, Vanessa Vitse
Abstract:We present a new variant of cover and decomposition attacks on the elliptic curve discrete logarithm problem, that combines Weil descent and decomposition-based index calculus into a single discrete logarithm algorithm. This variant applies, at least theoretically, to all composite degree extension fields, and is particularly well-suited for curves defined over \F_{p^6}. We give a real-size example of discrete logarithm computations on a seemingly secure curve defined over a 130$-bit degree 6 extension field.
ePrint: https://eprint.iacr.org/2011/020
Talk: https://www.youtube.com/watch?v=X2W8YEppLbI
Slides: https://iacr.org/cryptodb/archive/2012/EUROCRYPT/presentation/24240.pdf
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