How long does it take to catch a wild kangaroo?

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 when the logarithm 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.

• Type: Conference
• Year: 2009
• Where: STOC
• Authors: Ravi Montenegro, Prasad Tetali
• Keywords: Algorithms, Discrete Logarithm, Discrete Logarithm Problem, STOC 2009, first Rigorous Proof