Using number fields to compute logarithms in finite fields

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 . The number field sieve factoring algorithm is conjectured to factor a number the size of q in the same amount of time.

• Type: Journal
• Year: 2000
• Where: MOC
• Authors: Oliver Schirokauer
• Keywords: Finite Fields, Fixed Degree, MOC 2000, Number Field