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In the past two years there have been several advances in Number Field Sieve (NFS) algorithms for computing discrete logarithms in finite fields \fpn\fpn where pp is prime and n>1n>1 is a small intege...
Computing discrete logarithms in finite fields is a main concern in cryptography. The best algorithms known are the Number Field Sieve and its variants in large and medium characteristic fields (e.g. ...
The aim of this work is to investigate the hardness of the discrete logarithm problem in fields GF(pn) where n is a small integer greater than 1. Though less studied than the small characteristic case...
This paper shows, assuming standard heuristics regarding the number-field sieve, that a "batch NFS" circuit of area L^{1.181...+o(1)} factors L^{0.5+o(1)} separate B-bit RSA keys in time L^{1.022...+o...
During an ongoing examination of the behaviour, in practice, of the Number Field Sieve (NFS) in the medium prime case we have noticed numerous interesting patterns. In this paper we present findings o...
In this contribution we investigate practical issues with imple- menting the NFS algorithm to solve the DLP arising in XTR-based cryptosys- tems. We can transform original XTR-DLP to a DLP instance ...
Significant progress in the design of special purpose hardware for supporting the Number Field Sieve (NFS) has been made. From a practical cryptanalytic point of view, however, none of the published...

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