Cover and Decomposition Index Calculus on Elliptic Curves Made Practical [chapter]

Antoine Joux, Vanessa Vitse
2012 Lecture Notes in Computer Science  
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 F p 6 . We give a real-size example of discrete logarithm computations on a curve over a 151-bit degree 6 extension field, which would not have
more » ... n practically attackable using previously known algorithms.
doi:10.1007/978-3-642-29011-4_3 fatcat:23ppmsbcyrgf7atw55jgrbgztq