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Challenges with Assessing the Impact of NFS Advances on the Security of Pairing-based Cryptography
finite fields discrete logarithm problem tower number field sieve
2016/12/7
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...
Faster individual discrete logarithms in non-prime finite fields with the NFS and FFS algorithms
finite field discrete logarithm number field sieve
2016/7/13
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. ...
Improving NFS for the discrete logarithm problem in non-prime finite fields
Discrete logarithm computation NFS
2016/6/12
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...
A note on the practical complexity of the NFS in the medium prime case: Smoothness of Norms
DLP NFS pairing based cryptography
2013/4/18
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 ...
Non-Wafer-Scale Sieving Hardware for the NFS：Another Attempt to Cope with 1024-bit
RSA cryptanalytic hardware factoring integers
2008/12/29
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...