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Using number fields to compute logarithms in finite fields
 Math. Comp
"... Abstract. We describe an adaptation of the number field sieve to the problem of computing logarithms in a finite field. We conjecture that the running time of the algorithm, when restricted to finite fields of an arbitrary but fixed degree, is Lq[1/3; (64/9) 1/3 + o(1)], where q is the cardinality o ..."
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Abstract. We describe an adaptation of the number field sieve to the problem of computing logarithms in a finite field. We conjecture that the running time of the algorithm, when restricted to finite fields of an arbitrary but fixed degree, is Lq[1/3; (64/9) 1/3 + o(1)], where q is the cardinality of the field, Lq[s; c] =exp(c(log q) s (log log q) 1−s), and the o(1) is for q →∞.Thenumber field sieve factoring algorithm is conjectured to factor a number the size of q inthesameamountoftime. 1.