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Root Optimization of Polynomials in the Number Field Sieve

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Executive Summary

The general number field sieve is the most efficient algorithm known for factoring large integers. It consists of several stages including polynomial selection, sieving, filtering, linear algebra and finding square roots. The General Number Field Sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages; one of them is, being polynomial selection. The quality of the chosen polynomials in polynomial selection can be modelled in terms of size and root properties. In this paper, the authors describe some algorithms for selecting polynomials with very good root properties.

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