### Cover and Decomposition Index Calculus on Elliptic Curves made practical. Application to a seemingly secure curve over $\F_{p^6}$

Antoine Joux and Vanessa Vitse

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. Note: Extended version of the accepted paper at Eurocrypt 2012. ##### Metadata Available format(s) Publication info Published elsewhere. Unknown where it was published Keywords elliptic curvediscrete logarithmindex calculusWeil descentdecomposition attack Contact author(s) vanessa vitse @ prism uvsq fr History 2012-01-30: last of 3 revisions 2011-01-14: received See all versions Short URL https://ia.cr/2011/020 License CC BY BibTeX @misc{cryptoeprint:2011/020, author = {Antoine Joux and Vanessa Vitse}, title = {Cover and Decomposition Index Calculus on Elliptic Curves made practical. Application to a seemingly secure curve over$\F_{p^6}\$},
howpublished = {Cryptology ePrint Archive, Paper 2011/020},
year = {2011},
note = {\url{https://eprint.iacr.org/2011/020}},
url = {https://eprint.iacr.org/2011/020}
}

Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.