Random Walks Revisited: Extensions of Pollard's Rho Algorithm for Computing Multiple Discrete Logarithms

Authors:
Fabian Kuhn;René Struik
Affiliations:
-;-
Venue:
SAC '01 Revised Papers from the 8th Annual International Workshop on Selected Areas in Cryptography
Year:
2001

Citing 6
Cited 1

A subexponential algorithm for discrete logarithms over all finite fields

CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
On random walks for Pollard's Rho method

Mathematics of Computation
Faster Attacks on Elliptic Curve Cryptosystems

SAC '98 Proceedings of the Selected Areas in Cryptography
A subexponential algorithm for discrete logarithms over the rational subgroup of the jacobians of large genus hyperelliptic curves over finite fields

ANTS-I Proceedings of the First International Symposium on Algorithmic Number Theory
Speeding Up Pollard's Rho Method for Computing Discrete Logarithms

ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Lower bounds for discrete logarithms and related problems

EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques

Curve25519: new diffie-hellman speed records

PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper extends the analysis of Pollard's rho algorithm for solving a single instance of the discrete logarithm problem in a finite cyclic group G to the case of solving more than one instance of the discrete logarithm problem in the same group G. We analyze Pollard's rho algorithm when used to iteratively solve all the instances. We also analyze the situation when the goal is to solve any one of the multiple instances using any DLP algorithm.