How long does it take to catch a wild kangaroo?

Authors:
Ravi Montenegro;Prasad Tetali
Affiliations:
University of Massachusetts Lowell, Lowell, MA, USA;Georgia Institute of Technology, Atlanta, GA, USA
Venue:
Proceedings of the forty-first annual ACM symposium on Theory of computing
Year:
2009

Citing 2
Cited 1

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ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory

Using equivalence classes to accelerate solving the discrete logarithm problem in a short interval

PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography

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Abstract

The discrete logarithm problem asks to solve for the exponent x, given the generator g of a cyclic group G and an element h∈ G such that gx=h. We give the first rigorous proof that Pollard's Kangaroo method finds the discrete logarithm in expected time (3+o(1))√{b-a} for the worst value of x∈[a,b], and (2+o(1))√b-a when x∈uar[a,b]. This matches the conjectured time complexity and, rare among the analysis of algorithms based on Markov chains, even the lead constants 2 and 3 are correct.