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

Source abstract

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