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A Quasi-polynomial Algorithm For Discrete Logarithm In Finite Fields Of Small Characteristic.pdf

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Preview of A quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic
🔗 Source: eprint.iacr.org
📊 Size: 460 KB
👤 Author: Razvan Barbulescu, Pierrick Gaudry, Antoine Joux, Emmanuel Thomé
⬇️ Downloads: 119

Summary

A quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic is proposed, with a complexity of nO(log n) where n is the bit-size of the input, which is smaller than any L(ϵ) for ϵ > 0. The algorithm applies to finite fields that admit a sparse medium subfield representation and uses a descent approach with elementary algorithmic building blocks, avoiding Gröbner basis algorithms. The complexity result relies on three key heuristics, and experiments validate these heuristics on practical instances. The algorithm improves the complexity of discrete logarithm computations in a larger range of finite fields, becoming Lqk(α + o(1)) when q grows as Lqk(α), and is asymptotically faster than the Function Field Sieve algorithm in almost all the range previously covered by this algorithm.

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A quasi-polynomial algorithm for discrete logarithm in finite fields of small characteristic is proposed, with a complexity of nO(log n) where n is the...

Technical Information

  • File Format: PDF
  • File Size: 460 KB
  • Pages: 16
  • Language: EN
  • Author: Razvan Barbulescu, Pierrick Gaudry, Antoine Joux, Emmanuel Thomé
  • Total Downloads: 119
  • Last Updated: 3 weeks ago

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