Cover and Decomposition Index Calculus on Elliptic Curves made practical. Application to a seemingly secure curve over $\F_{p^6}$.
Talk by Vanessa Vitse
Date: 20.04.11 Time: 11.00 - 13.00 Room:
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 over a 130-bit degree 6 extension field.