Recent advances in computing discrete logarithms in finite fields
Speaker: Pierrick Gaudry
Abstract: The discrete logarithm problem in finite fields is the basis of the security of many deployed cryptographic products. Prime fields (of the form Z/pZ, for a prime p) are frequently used, and in the realm of pairing-friendly elliptic curves, fields of cardinality p^k are involved, where k is around 10.
In this lecture, we will give an overview of the Number Field Sieve algorithm, which is the best known algorithm for these settings. We will then focus on recent advances in the p^k case, where tools from lattice theory come to the rescue to speed-up the computations.