# Monte Carlo methods for index computation ()

@article{Pollard1978MonteCM, title={Monte Carlo methods for index computation ()}, author={John M. Pollard}, journal={Mathematics of Computation}, year={1978}, volume={32}, pages={918-924} }

We describe some novel methods to compute the index of any integer relative to a given primitive root of a prime p. Our flrst method avoids the use of stored tables and apparently requires O(p 1/2) operations. Our second algorithm, which may be regarded as a method of catching kangaroos, is applicable when the index is known to lie in a certain interval; it requires O(w/2) operations for an interval of width w, but does not have complete certainty of success. It has several possible areas of…

## 796 Citations

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This paper uses an iterating function whose image size is much smaller than its domain and hence reaches a collision faster than the original Iterating function, and shows time complexity advantage over the original Pollard rho method on multiplicative subgroups of Fpm.

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New iterating functions for computing discrete logarithms with the rho method are defined and compared and it is shown that one of these functions is expected to reduce the number of steps by a factor of approximately 0.8, in comparison with Pollard's originally used function.

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Two new low-storage algorithms for the discrete logarithm problem in an interval of size N, based on the Pollard kangaroo method and the Gaudry-Schost algorithm, are presented and experimental results show that the methods do work close to that predicted by the theoretical analysis.

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A method for determining the expected time until the first collision of pseudo-random implementations of Markov chains, using Pollard's Kangaroo, Pollard’s Rho, and a few versions of Gaudry-Schost as examples.

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