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ASIACRYPT
2008
Springer

Speeding Up the Pollard Rho Method on Prime Fields

14 years 1 months ago
Speeding Up the Pollard Rho Method on Prime Fields
Abstract. We propose a method to speed up the r-adding walk on multiplicative subgroups of the prime field. The r-adding walk is an iterating function used with the Pollard rho algorithm and is known to require less iterations than Pollard's original iterating function in reaching a collision. Our main idea is to follow through the r-adding walk with only partial information about the nodes reached. The trail traveled by the proposed method is a normal r-adding walk, but with significantly reduced execution time for each iteration. While a single iteration of most r-adding walks on Fp require a multiplication of two integers of log p size, the proposed method requires an operation of complexity only linear in log p, using a pre-computed table of size O((log p)r+1
Jung Hee Cheon, Jin Hong, Minkyu Kim
Added 12 Oct 2010
Updated 12 Oct 2010
Type Conference
Year 2008
Where ASIACRYPT
Authors Jung Hee Cheon, Jin Hong, Minkyu Kim
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