International Association
for Cryptologic Research

In this paper, we study the

discrete logarithm problem in finite fields related to pairing-based

curves. We start with a precise analysis of the

state-of-the-art algorithms for computing discrete logarithms that

are suitable for finite fields related to pairing-friendly

constructions. To improve upon these algorithms, we extend the

Special Number Field Sieve to compute discrete logarithms in

$\\F_{p^{n}}$, where $p$ has an adequate sparse representation. Our

improved algorithm works for the whole range of applicability of the

Number Field Sieve.