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 F p require a multiplication of two integers of logp size, the proposed method requires an operation of complexity only linear in logp, using a pre-computed table of size O((logp) r + 1•loglogp). In practice, our rudimentary implementation of the proposed method increased the speed of Pollard rho with r-adding walks by a factor of more than 10 for 1024-bit random primes p. © 2008 Springer Berlin Heidelberg.
CITATION STYLE
Cheon, J. H., Hong, J., & Kim, M. (2008). Speeding up the pollard rho method on prime fields. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5350 LNCS, pp. 471–488). https://doi.org/10.1007/978-3-540-89255-7_29
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