Rigorous Analysis of a Randomised Number Field Sieve

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• Jonathan Lee (University of Cambridge)
• Thursday 26 February 2015, 16:00-17:00
• MR12.

If you have a question about this talk, please contact Andrew Thomason.

The Number Field Sieve is the current practical and theoretical state of the art algorithm for factoring. Unfortunately, there has been no rigorous analysis of this type of algorithm.

By suitably randomising key aspects of the number theory, we prove that an NFS -type algorithm produces congruences of squares in expected time L(1/3, 2.88). These results are tightly coupled to recent progress on the distribution of smooth numbers, and we provide additional tools to turn progress on these problems into improved bounds.

This talk is part of the Combinatorics Seminar series.

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