Algorithmica
Discrete logarithms in finite fields and their cryptographic significance
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
Computation of discrete logarithms in prime fields
Designs, Codes and Cryptography
Function field sieve method for discrete logarithms over finite fields
Information and Computation
Designs, Codes and Cryptography
Solving Large Sparse Linear Systems over Finite Fields
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Massively Parallel Computation of Discrete Logarithms
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
The Solution of McCurley's Discrete Log Challenge
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Computation of Discrete Logarithms in F2607
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Lattice sieving and trial division
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Discrete Logarithms: The Effectiveness of the Index Calculus Method
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
Rigorous, subexponential algorithms for discrete logarithms over finite fields
Rigorous, subexponential algorithms for discrete logarithms over finite fields
The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Solving a 676-bit discrete logarithm problem in GF(36n)
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
The number field sieve in the medium prime case
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
The function field sieve in the medium prime case
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Key length estimation of pairing-based cryptosystems using ηT pairing
ISPEC'12 Proceedings of the 8th international conference on Information Security Practice and Experience
Algebraic curves and cryptography
Finite Fields and Their Applications
Breaking pairing-based cryptosystems using ηT pairing over GF(397)
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
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In this paper, we describe improvements to the function field sieve (FFS) for the discrete logarithm problem in Fpn, when p is small. Our main contribution is a new way to build the algebraic function fields needed in the algorithm. With this new construction, the heuristic complexity is as good as the complexity of the construction proposed by Adleman and Huang [2], i.e Lpn[1/3, c] = exp((c + o(1)) log(pn)1/3 log(log(pn))2/3) where c = (32/9)1/3. With either of these constructions the FFS becomes an equivalent of the special number field sieve used to factor integers of the form AN 卤 B. From an asymptotic point of view, this is faster than older algorithm such as Coppersmith's algorithm and Adleman's original FFS. From a practical viewpoint, we argue that our construction has better properties than the construction of Adleman and Huang. We demonstrate the efficiency of the algorithm by successfully computing discrete logarithms in a large finite field of characteristic two, namely F2521.