Pollard's kangaroo algorithm: Difference between revisions

Revision as of 15:26, 28 June 2010

Revision as of 06:46, 24 August 2010

Line 37:

The algorithm is well known by two names.

The first is "Pollard's kangaroo algorithm". This name is a reference to an analogy used in the paper presenting the algorithm, where the algorithm is explained in terms of using a ''tame'' [[kangaroo]] to trap a ''wild'' kangaroo. Pollard has explained<ref>J. M. Pollard, ''Kangaroos, Monopoly and Discrete Logarithms'', Journal of Cryptology, Volume 13, pp 437-447, 2000</ref> that this analogy was inspired by a "fascinating " article published in the same issue of ''[[Scientific American]]'' as an exposition of the [[RSA]] [[public key cryptosystem]]. The article<ref>T. J. Dawson, ''Kangaroos'', Scientific American, August 1977, pp. 78-89</ref> described an experiment in which a kangaroo's "energetic cost of locomotion, measured in terms of oxygen consumption at various speeds, was determined by placing kangaroos on a [[treadmill]]".

The second is "Pollard's lambda algorithm". Much like the name of another of Pollard's discrete logarithm algorithms, [[Pollard's rho algorithm for logarithms|Pollard's rho algorithm]], this name refers to the similarity between a visualisation of the algorithm and the [[Greek letter]] [[lambda]] (<math>\lambda</math>). The shorter stroke of the letter lambda corresponds to the sequence <math>\{x_i\}</math>, since it starts from the position b to the right of x. Accordingly, the longer stroke corresponds to the sequence <math>\{y_i\}</math>, which "collides with" the first sequence (just like the strokes of a lambda intersect) and then follows it subsequently.