The Tower Number Field Sieve

@article{Barbulescu2015TheTN,
  title={The Tower Number Field Sieve},
  author={Razvan Barbulescu and Pierrick Gaudry and Thorsten Kleinjung},
  journal={IACR Cryptology ePrint Archive},
  year={2015},
  volume={2015},
  pages={505}
}
The security of pairing-based crypto-systems relies on the difficulty to compute discrete logarithms in finite fields Fpn where n is a small integer larger than 1. The state-of-art algorithm is the number field sieve (NFS) together with its many variants. When p has a special form (SNFS), as in many pairings constructions, NFS has a faster variant due to Joux and Pierrot. We present a new NFS variant for SNFS computations, which is better for some cryptographically relevant cases, according to… CONTINUE READING
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