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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 y0 . 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... (Update)
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BibTeX entry: (Update)
E. Teske, "Speeding up Pollard's rho method for computing discrete logarithms, " Technical Report No. TI-1/98, Technische Hochschule Darmstadt, Darmstadt, Germany, (1998). http://citeseer.ist.psu.edu/teske98speeding.html More
@article{ teske98speeding,
author = "Edlyn Teske",
title = "Speeding Up {Pollard}'s Rho Method for Computing Discrete Logarithms",
journal = "Lecture Notes in Computer Science",
volume = "1423",
pages = "541--554",
year = "1998",
url = "citeseer.ist.psu.edu/teske98speeding.html" }
Citations (may not include all citations):257 Elliptic curve cryptosystems (context) - Koblitz - 1987
249 Volume 3: Sorting and searching (context) - Knuth, of - 1973
237 The arithmetic of elliptic curves (context) - Silverman - 1986
228 Uses of elliptic curves in cryptography (context) - Miller - 1986
168 An improved algorithm for computing logarithms over GF (context) - Pohlig, Hellman - 1978
77 A Course in Number Theory and Cryptography (context) - Koblitz - 1987
63 Monte Carlo methods for index computation (context) - Pollard - 1978
52 The number of points on an elliptic curve modulo a prime (context) - Atkin
52 Parallel collision search with cryptanalytic applications - van Oorschot, Wiener
42 An improved Monte Carlo factorization algorithm (context) - Brent - 1980
24 a theory of factorization and genera (context) - Shanks - 1971
13 A Monte Carlo factoring algorithm with linear storage (context) - Schnorr, Lenstra - 1984
8 Random walks on groups with subgroup invariance properties (context) - Greenhalgh - 1989
7 New algorithms for finite abelian groups (context) - Teske - 1998
6 A space efficient algorithm for group structure computation - Teske - 1998
3 eco - a tool for elliptic curve group order computations (context) - Lehmann, Maurer et al. - 1997
1 Random walks supported on the random points of ZZ=nZZ (context) - Hildebrand - 1994
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