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
Factoring numbers using singular integers
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
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
An implementation of the general number field sieve
CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
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
NFS with Four Large Primes: An Explosive Experiment
CRYPTO '95 Proceedings of the 15th 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
The Magic Words are Squeamish Ossifrage
ASIACRYPT '94 Proceedings of the 4th International Conference on the Theory and Applications of Cryptology: Advances in Cryptology
A World Wide Number Field Sieve Factoring Record: On to 512 Bits
ASIACRYPT '96 Proceedings of the International Conference on the Theory and Applications 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
Computing Discrete Logarithms with the General Number Field Sieve
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
A Multiple Polynominal General Number Field Sieve
ANTS-II Proceedings of the Second International Symposium on Algorithmic Number Theory
On the Reduction of Composes Relations from the Number Field Sieve
ANTS-II Proceedings of the Second 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
Strategies in Filtering in the Number Field Sieve
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
A block Lanczos algorithm for finding dependencies over GF(2)
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
Factorization of a 512-bit RSA modulus
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
The Function Field Sieve Is Quite Special
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Journal of Algorithms
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
Analysis of the efficiency of the Chor-Rivest cryptosystem implementation in a safe-parameter range
Information Sciences: an International Journal
Oracle-Assisted Static Diffie-Hellman Is Easier Than Discrete Logarithms
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Journal of Algorithms
When e-th roots become easier than factoring
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
An experiment of number field sieve over GF(p) of low hamming weight characteristic
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
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
An algorithm to solve the discrete logarithm problem with the number field sieve
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
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
Pairing-Based cryptography at high security levels
IMA'05 Proceedings of the 10th international conference on Cryptography and Coding
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In this paper, 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.