Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
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
Function field sieve method for discrete logarithms over finite fields
Information and Computation
Using number fields to compute logarithms in finite fields
Mathematics of Computation
The Special Function Field Sieve
SIAM Journal on Discrete Mathematics
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
Computing Discrete Logarithms with the General 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
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
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The modification of the number field sieve which Joux and Lercier recently used to compute logarithms in a prime field of a record 120 decimal digits makes use of the notion of a virtual logarithm of a prime ideal in a number ring. We provide necessary and sufficient conditions for their method to succeed and give an explicit formula for the virtual logarithm of an ideal.