Discrete Logarithms in $GF ( P )$ Using the Number Field Sieve

Recently, several algorithms using number field sieves have been given to factor a number n in heuristic expected time Lₙ [1/3; c], where \[ L_n [ v ;c ] = exp \{ ( c + o ( 1 ) ) ( log n )^v ( log log n )1 - v \} \] for n → ∞. This paper presents an algorithm to solve the discrete logarithm problem for $GF ( p )$ with heuristic expected running time Lₚ [ 1/3; 32/3]. For umbers of a special form, there is an asymptotically slower but more practical version of the algorithm.