On random walks for Pollard's rho method

DOI10.1090/S0025-5718-00-01213-8zbMath1029.11071OpenAlexW1985265065MaRDI QIDQ2701566

Edlyn Teske

Publication date: 19 February 2001

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-00-01213-8

zbMATH Keywords

discrete logarithmPollard's rho methodrandom walks in groups

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Cryptography (94A60) Number-theoretic algorithms; complexity (11Y16)

Related Items (17)

Improving ECDLP Computation in Characteristic 2 ⋮ On improvements of ther-adding walk in a finite field of characteristic 2 ⋮ Improved algorithm for the isogeny problem for ordinary elliptic curves ⋮ A variant of the Galbraith-Ruprai algorithm for discrete logarithms with improved complexity ⋮ An efficient collision detection method for computing discrete logarithms with Pollard's rho ⋮ Speeding up elliptic curve discrete logarithm computations with point halving ⋮ Computing discrete logarithms with the parallelized kangaroo method. ⋮ Accelerating Pollard's rho algorithm on finite fields ⋮ Computing elliptic curve discrete logarithms with the negation map ⋮ Computational hardness of IFP and ECDLP ⋮ Cycle detection algorithms and their applications ⋮ The parallelized Pollard kangaroo method in real quadratic function fields ⋮ Speeding Up the Pollard Rho Method on Prime Fields ⋮ Cryptographic implications of Hess' generalized GHS attack ⋮ Boneh-Boyen Signatures and the Strong Diffie-Hellman Problem ⋮ On the heuristic of approximating polynomials over finite fields by random mappings ⋮ Solving discrete logarithm problems faster with the aid of pre-computation

Uses Software

• LiDIA

Cites Work

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• Random mappings with constraints on coalescence and number of origins
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• Random random walks on the integers mod \(n\)
• A Monte Carlo Factoring Algorithm With Linear Storage
• Factorization of the Eighth Fermat Number
• The Complexity of Finding Cycles in Periodic Functions
• A monte carlo method for factorization
• An improved algorithm for computing logarithms over<tex>GF(p)</tex>and its cryptographic significance (Corresp.)
• A space efficient algorithm for group structure computation
• Improving the parallelized Pollard lambda search on anomalous binary curves
• Probability Distributions Related to Random Mappings

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