A kilobit hidden SNFS discrete logarithm computation

Abstract : 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 back-doored 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 weak primes found in use in the wild.
Type de document :
Pré-publication, Document de travail

Contributeur : Emmanuel Thomé <>
Soumis le : vendredi 7 octobre 2016 - 16:40:05
Dernière modification le : jeudi 17 novembre 2016 - 13:05:47
Document(s) archivé(s) le : dimanche 8 janvier 2017 - 12:16:07


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  • HAL Id : hal-01376934, version 1
  • ARXIV : 1610.02874


Joshua Fried, Pierrick Gaudry, Nadia Heninger, Emmanuel Thomé. A kilobit hidden SNFS discrete logarithm computation. 2016. <hal-01376934>



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