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Recently, several algorithms using number field sieves have been given to factor a number n in heuristic expected time Lₙ 1/3; c, where \ Lₙ [ v ;c = \ (c + o (1) ) (n) ᵛ (n) ^{1 - v \} \] for n. This paper presents an algorithm to solve the discrete logarithm problem for GF (p) with heuristic expected running time Lₚ 1/3; 3^2/3. For umbers of a special form, there is an asymptotically slower but more practical version of the algorithm.
Daniel M. Gordon (Mon,) studied this question.