Conference abstracts

Session A3 - Computational Number Theory

July 11, 14:50 ~ 15:30 - Room B6

A kilobit hidden SNFS discrete logarithm computation

Nadia Heninger

University of Pennsylvania, United States   -   nadiah@cis.upenn.edu

We perform a special number field sieve discrete logarithm computation in a 1024-bit prime field. To our knowledge, this is the first kilobit-sized discrete logarithm computation ever reported for prime fields. This computation took a little over two months of calendar time on an academic cluster using the open-source CADO-NFS software.

Our chosen prime $p$ looks random, and $p-1$ has a 160-bit prime factor, in line with recommended parameters for the Digital Signature Algorithm. However, our $p$ has been trapdoored in such a way that the special number field sieve can be used to compute discrete logarithms in $\mathbb{F}_p^*$, yet detecting that $p$ has this trapdoor seems out of reach. Twenty-five years ago, there was considerable controversy around the possibility of backdoored parameters for DSA. Our computations show that trapdoored primes are entirely feasible with current computing technology. We also describe special number field sieve discrete log computations carried out for multiple conspicuously weak primes found in use in the wild.

Joint work with Joshua Fried (University of Pennsylvania), Pierrick Gaudry (INRIA, CNRS, Université de Lorraine) and Emmanuel Thomé (INRIA, CNRS, Université de Lorraine).

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