Algorithmica
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
On random walks for Pollard's Rho method
Mathematics of Computation
Speeding Up Pollard's Rho Method for Computing Discrete Logarithms
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Random Cayley Digraphs and the Discrete Logarithm
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Near Optimal Bounds for Collision in Pollard Rho for Discrete Log
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Spectral analysis of pollard rho collisions
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Improved Pollard rho method for computing discrete logarithms over finite extension fields
Journal of Computational and Applied Mathematics
Cryptanalysis of RSA with a small parameter
ACISP'12 Proceedings of the 17th Australasian conference on Information Security and Privacy
Speeding up elliptic curve discrete logarithm computations with point halving
Designs, Codes and Cryptography
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Pollard's rho method is a randomized algorithm for computing discrete logarithms. It works by defining a pseudo-random sequence and then detecting a match in the sequence. Many improvements have been proposed, while few evaluation results and efficiency suggestions have been reported. This paper is devoted to a detailed study of the efficiency issues in Pollard's rho method. We describe an empirical performance analysis of several widely applied algorithms. This should provide a better combination of algorithms and a good choice of parameters for Pollard's rho method.