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

@article{Gordon1993DiscreteLI,
title={Discrete Logarithms in GF(P) Using the Number Field Sieve},
author={Daniel M. Gordon},
journal={SIAM J. Discret. Math.},
year={1993},
volume={6},
pages={124-138}
}
• D. M. Gordon
• Published 1 February 1993
• Mathematics, Computer Science
• SIAM J. Discret. Math.
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…
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