Algorithmica
Finding irreducible polynomials over finite fields
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
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
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Factoring numbers using singular integers
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Rigorous, subexponential algorithms for discrete logarithms over finite fields
Rigorous, subexponential algorithms for discrete logarithms over finite fields
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
Factoring with cyclotomic polynomials
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Fast Arithmetic for Public-Key Algorithms in Galois Fields with Composite Exponents
IEEE Transactions on Computers
The generalized Weil pairing and the discrete logarithm problem on elliptic curves
Theoretical Computer Science - Latin American theorotical informatics
Speeding up Exponentiation using an Untrusted Computational Resource
Designs, Codes and Cryptography
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There are numerous subexponential algorithms for computing discrete logarithms over certain classes of finite fields. However, there appears to be no published subexponential algorithm for computing discrete logarithms over all finite fields. We present such an algorithm and a heuristic argument that there exists a c 驴 R 0 such that for all sufficiently large prime powers pn, the algorithm computes discrete logarithms over GF(pn) within expected time: ec(log(pn)log log(pn))1/2.