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Abstract: The best algorithms to compute discrete logarithms in arbitrary groups (of prime order) are the baby-step giant-step method, the rho method and the kangaroo method. The first two have (expected) running time O( p n) group operations (n denoting the group order), thereby matching Shoup's lower bounds. While the baby-step giant-step method is deterministic but with large memory requirements, the rho and the kangaroo method are probabilistic but can be implemented very space efficiently, and they... (Update)
Context of citations to this paper: More
...of generic algorithms when the unknown discrete logarithm is restricted to a subset (of a group) having speci ed cardinality. Teske [10] is survey of discrete logarithm algorithms having complexity O( p n) We will restrict our attention to instances of the Discrete...
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0.8: On Random Walks For Pollard's Rho Method - Teske (2000) (Correct)
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2: Lower bounds for discrete logarithms and related problems - Shoup - 1997
2: A subexponential algorithm for discrete logarithms over the rational subgroup of.. (context) - Adleman, DeMarrais et al. - 1994
BibTeX entry: (Update)
E. Teske. Square-root algorithms for the discrete logarithm problem (a survey). In Public Key Cryptography and Computational Number Theory, Walter de Gruyter, 2001, pp. 283-301. 12 http://citeseer.ist.psu.edu/teske01squareroot.html More
@misc{ teske01squareroot,
author = "E. Teske",
title = "Square-root algorithms for the discrete logarithm problem",
booktitle = "Public Key Cryptography and Computational Number Theory",
publisher = "Walter de Gruyter",
pages = "283--301",
year = "2001",
url = "citeseer.ist.psu.edu/teske01squareroot.html" }
Citations (may not include all citations):168 An improved algorithm for computing logarithms over GF (context) - Pohlig, Hellman - 1978
124 Lower bounds for discrete logarithms and related problems - Shoup - 1997
63 Monte Carlo methods for index computation (context) - Pollard - 1978
52 Parallel collision search with cryptanalytic applications - van Oorschot, Wiener - 1999
42 An improved Monte Carlo factorization algorithm (context) - Brent - 1980
29 Improving the parallelized Pollard lambda search on binary a.. - Gallant, Lambert et al. - 2000
27 Speeding up Pollard's rho method for computing discrete loga.. - Teske - 1998
24 a theory of factorization and genera (context) - Shanks - 1971
20 Handbook of Applied Cryptography (context) - Menezes, van Oorschot et al. - 1996
20 Probability distributions related to random mappings (context) - Harris - 1960
13 A Monte Carlo factoring algorithm with linear storage (context) - Schnorr, Lenstra - 1984
9 Speeding up the discrete log computation on curves with auto.. - Duursma, Gaudry et al. - 1999
9 Random walks supported on the random points of Z=nZ (context) - Hildebrand - 1994
8 On random walks for Pollard's rho method - Teske - 2000
7 Some baby-step giant-step algorithms for the low Hamming wei.. - Stinson
6 Discrete logarithms: The past and the future - Odlyzko - 2000
6 Combinatorial Algorithms (context) - Kreher, Stinson - 1999
4 Attacking elliptic curve cryptosystems using the parallel Po.. (context) - Escott, Sager et al. - 1998
3 Generating random walks in groups (context) - Sattler, Schnorr - 1985
3 Parallel algorithms for integer factorization (context) - Brent - 1990
3 On some computational problems in nite abelian groups (context) - Buchmann, Jacobson et al. - 1997
2 Random cayley graphs and the discrete log (context) - Horwitz, Venkatesan - 2000
2 A modication of Shanks' baby-step giant-step algorithm (context) - Terr - 2000
1 SQUARE-ROOT ALGORITHMS FOR THE DISCRETE LOGARITHM PROBLEM (context) - Pollard, Monopoly et al. - 2000
1 Computing discrete logarithms with the parallelized kangaroo.. - Teske - 2001
1 Baby-step giant-step algorithms for non-uniform distribution.. - Blackburn, Teske - 2000
1 A space ecient algorithm for group structure computation (context) - Teske - 1998
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