an:01871627
Zbl 1099.11074
Joux, Antoine; Lercier, Reynald
Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the Gaussian integer method
EN
Math. Comput. 72, No. 242, 953-967 (2003).
00092922
2003
j
11Y16 11T71 11Y40 68Q25 94A60
Summary: 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.