Journal of Symbolic Computation
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 with two large primes (extended abstract)
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Sparse matrix computations on parallel processor arrays
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Solving Large Sparse Linear Systems over Finite Fields
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Discrete Logarithms: The Past and the Future
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Designs, Codes and Cryptography
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
Fast Multiplication in Finite Fields GF(2N)
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
The Function Field Sieve Is Quite Special
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Fast arithmetic architectures for public-key algorithms over Galois fields GF((2n)m)
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
A heterogeneous computing environment to solve the 768-bit RSA challenge
Cluster Computing
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
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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Numerous cryptosystems have been designed to be secure under the assumption that the computation of discrete alogarithms is infeasible. This paper reports on an aggressive attempt to discover the size of fields of characteristic two for which the computation of discrete logarithms is feasible. We discover several things that were previously overlooked in the implementation of Coppersmith's algorithm, some positive, and some negative. As a result of this work we have shown that fields as large as GF(2503) can definitely be attacked.