Improvements to the
general number field sieve for discrete logarithms in prime fields. A
comparison with the Gaussian integer method.
Mathematics of Computation, 72(242):953-967, April 2003..
In this paper, we describe many improvements to the number
field sieve. Our main contribution consists of a new way to
compute individual logarithms with the number field sieve
without solving a very large linear system for each
logarithm. We show that, with these improvements, the number
field sieve outperforms the gaussian integer method in the
hundred digit range. We also illustrate our results by
successfully computing discrete logarithms with GNFS in a
large prime field.
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