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

  title={Discrete Logarithms in GF(P) Using the Number Field Sieve},
  author={Daniel M. Gordon},
  journal={SIAM J. Discret. Math.},
  • 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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