Algorithmica
Computation of discrete logarithms in prime fields
Designs, Codes and Cryptography
Discrete logarithms in GF(P) using the number field sieve
SIAM Journal on Discrete Mathematics
A course in computational algebraic number theory
A course in computational algebraic number theory
Solving Large Sparse Linear Systems over Finite Fields
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Journal of Algorithms
| Hi-index | 0.00 |
The security of the digital signature algorithm (DSA) and Diffie-Hellman key exchange is based on the difficulty of the discrete logarithm problems (DLP) over prime field GF(p), and thus it is important to evaluate the difficulty of the DLP over GF(p) for discussing the security of these protocols. The number field sieve (NFS) is asymptotically the fastest algorithm to solve the DLP over GF(p). NFS was first proposed by Gordon and then it was improved by Schirokauer and Joux-Lercier. On the other hand, Schirokauer presented a new variant of NFS, which is particularly efficient for the characteristic p with low weight (p has a signed binary representation of low Hamming weight). In this paper, we implement the NFS proposed by Joux-Lercier and Schirokauer, and then we compare the running time of the NFS using the polynomials by Joux-Lercier and Schirokauer with respect to low weight primes of 100 bits or 110 bits.