## Parallel Solution of Sparse Linear Systems Defined over GF(p)

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### BibTeX

@MISC{Page_parallelsolution,

author = {D. Page},

title = {Parallel Solution of Sparse Linear Systems Defined over GF(p)},

year = {}

}

### OpenURL

### Abstract

Introduction The security of modern public-key cryptography is usually based on the presumed hardness of problems such as factoring integers or computing discrete logarithms. The Number Field Sieve [19] (NFS) and Function Field Sieve [1] (FFS) oer two examples of algorithms that can attack these problems. Such algorithms are generally speci ed in two phases. The rst phase, sometimes called the sieving step, aims to collect many relations that represent small items of information about the problem one is trying to solve. This phase is easy to parallelise since one can generate the relations independently. It is therefore attractive for distributed, Internet based collaborative computation [26]. The second phase of processing, sometimes called the matrix step, aims to collect the relations and combine them into a single linear system which, when solved, allows one to eciently compute answers to the original problem. Ecient implementation of the matrix step is challenging since the li