A kilobit hidden SNFS discrete logarithm computation
Joshua Fried (1), Pierrick Gaudry (2), Nadia Heninger (1), Emmanuel, Thom\'e (2) ((1) CIS (2) CARAMBA)

TL;DR
This paper reports the first kilobit-sized discrete logarithm computation in a 1024-bit prime field using the special number field sieve, demonstrating the feasibility of trapdoored primes and highlighting the importance of verifiably random primes for security.
Contribution
It presents the first known kilobit-sized discrete logarithm computation in a prime field and introduces a trapdoor mechanism that can be exploited with current computing resources.
Findings
Trapdoored primes are feasible with current technology.
The computation took just over two months on an academic cluster.
No trapdoored primes were found in widespread use.
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 looks random, and 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 , 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…
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Taxonomy
TopicsAdvanced Data Storage Technologies · Cryptography and Residue Arithmetic · Coding theory and cryptography
