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

Authors:	Igor A Semaev

Institution:	43-2 Profsoyuznaya Street, Apartment \#723, 117420 Moscow, Russia

Abstract:	In this paper we propose an algorithm for evaluation of logarithms in the finite fields $F_{p^n}$ , where the number has a small primitive factor . The heuristic estimate of the complexity of the algorithm is equal to $\exp((c+o(1))(\log p\,r\log^2r)^{1/3})$ , where grows to $\infty$ , and is limited by a polynomial in . 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 of small degrees.

Keywords:	Cryptography discrete logarithms finite fields

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