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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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An algorithm for evaluation of discrete logarithms in some nonprime finite fields
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by Igor A. Semaev PDF
Math. Comp. 67 (1998), 1679-1689 Request permission


In this paper we propose an algorithm for evaluation of logarithms in the finite fields $F_{p^n}$, where the number $p^n-1$ has a small primitive factor $r$. The heuristic estimate of the complexity of the algorithm is equal to $\exp ((c+o(1))(\log p r\log ^2r)^{1/3})$, where $n$ grows to $\infty$, and $p$ is limited by a polynomial in $n$. The evaluation of logarithms is founded on a new congruence of the kind of D. Coppersmith, $C(x)^k\equiv D(x)$, which has a great deal of solutions—pairs of polynomials $C(x),D(x)$ of small degrees.
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Additional Information
  • Igor A. Semaev
  • Affiliation: 43-2 Profsoyuznaya Street, Apartment #723, 117420 Moscow, Russia
  • Received by editor(s): March 30, 1993
  • Received by editor(s) in revised form: August 30, 1995
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 1679-1689
  • MSC (1991): Primary 11T71, 11Y16, 94A60
  • DOI:
  • MathSciNet review: 1474656