Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


An algorithm for evaluation
of discrete logarithms in some
nonprime finite fields

Author: Igor A. Semaev
Journal: Math. Comp. 67 (1998), 1679-1689
MSC (1991): Primary 11T71, 11Y16, 94A60
MathSciNet review: 1474656
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: 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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation of the American Mathematical Society with MSC (1991): 11T71, 11Y16, 94A60

Retrieve articles in all journals with MSC (1991): 11T71, 11Y16, 94A60

Additional Information

Igor A. Semaev
Affiliation: 43-2 Profsoyuznaya Street, Apartment #723, 117420 Moscow, Russia

PII: S 0025-5718(98)00969-7
Keywords: Cryptography, discrete logarithms, finite fields
Received by editor(s): March 30, 1993
Received by editor(s) in revised form: August 30, 1995
Article copyright: © Copyright 1998 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia