Algorithmica
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
Discrete logarithms in GF(P) using the number field sieve
SIAM Journal on Discrete Mathematics
Discrete Logarithms: The Past and the Future
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Special prime numbers and discrete logs in finite prime fields
Mathematics of Computation
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
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Recently, Shirokauer's algorithm to solve the discrete logarithm problem modulo a prime p has been modified by Matyukhin, yielding an algorithm with running time $L_{p}[\frac{1}{3},1.09018...]$, which is, at the present time, the best known estimate of the complexity of finding discrete logarithms over prime finite fields and which coincides with the best known theoretical running time for factoring integers, obtained by Coppersmith. In this paper, another algorithm to solve the discrete logarithm problem in $\mathbb{F}^{*}_{p}$ for p prime is presented. The global running time is again $L_{p}[\frac{1}{3},1.09018...]$, but in contrast with Matyukhins method, this algorithm enables us to calculate individual logarithms in a separate stage in time $L_{p}[\frac{1}{3},3^{1/3}]$, once a $L_{p}[\frac{1}{3},1.09018...]$ time costing pre-computation stage has been executed. We describe the algorithm as derived from [6] and estimate its running time to be $L_{p}[\frac{1}{3},(\frac{64}{9})^{1/3}]$, after which individual logarithms can be calculated in time $L_{p}[\frac{1}{3},3^{1/3}]$.