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

In this paper we propose an algorithm for evaluation of logarithms in the finite fields Fpn , where the number pn − 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 log2 r)1/3), where n grows to ∞, 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 ≡ D(x), which has a great deal of solutions—pairs of polynomials C(x), D(x) of small degrees.

• Type: Journal
• Year: 1998
• Where: MOC
• Authors: Igor A. Semaev
• Keywords: Algorithm, Heuristic Estimate, MOC 1998, Small Primitive Factor