Abstract

We use the specific structure of the inputs to the cofactorization step in the general number field sieve (GNFS) in order to optimize the runtime for the cofactorization step on a hardware cluster. An optimal distribution of bitlength-specific ECM modules is proposed and compared to existing ones. With our optimizations we obtain a speedup between 17% and 33% of the cofactorization step of the GNFS when compared to the runtime of an unoptimized cluster.KeywordsGeneral Number Field Sieve (GNFS)Elliptic Curve Method (ECM)hardware clustercofactorization step

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