The Number Field Sieve in the Medium Prime Case

@inproceedings{Joux2006TheNF,
  title={The Number Field Sieve in the Medium Prime Case},
  author={Antoine Joux and Reynald Lercier and Nigel P. Smart and Frederik Vercauteren},
  booktitle={CRYPTO},
  year={2006}
}
In this paper, we study several variations of the number field sieve to compute discrete logarithms in finite fields of the form Fpn , with p a medium to large prime. We show that when n is not too large, this yields a Lpn(1/3) algorithm with efficiency similar to that of the regular number field sieve over prime fields. This approach complements the recent results of Joux and Lercier on the function field sieve. Combining both results, we deduce that computing discrete logarithms have… CONTINUE READING
Highly Influential
This paper has highly influenced 13 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS

From This Paper

Figures, tables, and topics from this paper.

Citations

Publications citing this paper.
Showing 1-10 of 69 extracted citations

References

Publications referenced by this paper.
Showing 1-10 of 19 references

A course in computational algebraic number theory, volume 138 of Graduate Texts in Mathematics

  • H. Cohen
  • 1993
Highly Influential
4 Excerpts

Discrete logarithms and local units

  • O. Schirokauer
  • Philos. Trans. Roy. Soc. London Ser. A,
  • 1993
Highly Influential
9 Excerpts

Discrete logarithms in Fp18 - 101 digits

  • R. Lercier, F. Vercauteren
  • NMBRTHRY mailing list,
  • 2005
1 Excerpt

Similar Papers

Loading similar papers…