Parallel hash collision search by Rho method with distinguished points

In this paper, we realized a memory efficient general parallel Pollard's rho method for collision search on hash functions introduced by Van Oorschot and Wiener in 1996. This utilizes the principles of the birthday paradox to greatly increase the probability of a finding a collision, while using significantly less memory than the classic birthday attack, and allowing a larger portion of the subject hash function to be searched before running out of memory by saving only a few select digests called distinguished points. Using our implementation, we are able to find an average of 50 MD5 half collisions in the first hour of searching using a distributed memory high performance computing system called Penzias (one of CUNY HPC systems) on 32 processors. We then extend the technique with Cyrillic character replacement to search for meaningful MD5 half collisions. Next we analyze and measure how the performance of our implementation scales with different processor counts. Finally, we experiment with how the rarity of distinguished points affects the rate at which collisions are found at varying numbers of processors.