Speeding Up Pollard's Rho Method For Computing Discrete Logarithms

Speeding Up Pollard's Rho Method For Computing Discrete Logarithms (1998)

by Edlyn Teske

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Datum	Value	Source
TITLE	Speeding Up Pollard's Rho Method For Computing Discrete Logarithms	user correction - Legacy Corrections
AUTHOR NAME	Edlyn Teske	SVM HeaderParse 0.1
ABSTRACT	. In Pollard's rho method, an iterating function f is used to define a sequence (y i ) by y i+1 = f(y i ) for i = 0; 1; 2; : : : , with some starting value y 0 . In this paper, we define and discuss new iterating functions for computing discrete logarithms with the rho method. We compare their performances in experiments with elliptic curve groups. Our experiments show that one of our newly defined functions is expected to reduce the number of steps by a factor of approximately 0:8, in comparison with Pollard's originally used function, and we show that this holds independently of the size of the group order. For group orders large enough such that the run time for precomputation can be neglected, this means a real-time speed-up of more than 1:2. 1. Introduction Let G be a finite cyclic group, written multiplicatively, and generated by the group element g. Given an element h in G, we wish to find the least non-negative number x such that g x = h. This problem is the discre...	user correction - Legacy Corrections
YEAR	1998	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	541--554	INFERENCE
VOLUME	1423	INFERENCE
CITATIONS	18 found	ParsCit 1.0