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Thirteenth Algorithmic Number Theory Symposium ANTS-XIII
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Computation of discrete logarithms in finite fields
Emmanuel Thomé
Abstract: The Number Field Sieve was invented as a factoring algorithm nearly three decades ago, and its analogues for computing discrete logarithms over finite fields are only a few years more recent. Over time, several record computations for discrete logarithms were obtained. The recent period has seen a surge of interest in the topic. On the one hand, in practical terms, recent computations have a significant impact on cryptographic parameters that are purportedly still in use. On the other hand, improvements to the algorithm adapt well to select cases (for example the cryptanalysis of some pairing-based cryptosystems), and lead to adjust (sometimes significantly) some claims on the security levels.
Files available: slides