Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
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
Journal of Cryptology
Discrete logarithms in GF(P) using the number field sieve
SIAM Journal on Discrete Mathematics
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Solving homogeneous linear equations over GF(2) via block Wiedemann algorithm
Mathematics of Computation
Factoring with two large primes
Mathematics of Computation
Mathematics of Computation
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
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
ANTS-I Proceedings of the First 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
Strategies in Filtering in the Number Field Sieve
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
Arithmetic on superelliptic curves
Mathematics of Computation
A subexponential algorithm for the discrete logarithm problem with applications to cryptography
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
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
Unbelievable Security. Matching AES Security Using Public Key Systems
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
The Function Field Sieve Is Quite Special
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Implementing cryptographic pairings on smartcards
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
Hidden pairings and trapdoor DDH groups
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Algebraic attacks on clock-controlled stream ciphers
ACISP'06 Proceedings of the 11th Australasian conference on Information Security and Privacy
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We describe in this article how we have been able to extend the record for computationsof discrete logarithmsin characteristic 2 from the previousrecord over F2503 to a newer mark of F2607 , using Coppersmith's algorithm. This has been made possible by several practical improvementsto the algorithm. Although the computationsha ve been carried out on fairly standard hardware, our opinion is that we are nearing the current limitsof the manageable sizesfor thisalgorithm, and that going substantially further will require deeper improvements to the method.