The Number Field Sieve in the Medium Prime Case

  title={The Number Field Sieve in the Medium Prime Case},
  author={Antoine Joux and Reynald Lercier and Nigel P. Smart and Frederik Vercauteren},
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
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