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SUMMARY:Rigorous Analysis of a Randomised Number Field Sieve - Jonathan Le
 e (University of Cambridge)
DTSTART:20150226T160000Z
DTEND:20150226T170000Z
UID:TALK57193@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:The Number Field Sieve is the current practical and theoretica
 l state of the art algorithm for factoring. Unfortunately\, there has been
  no rigorous analysis of this type of algorithm.\n\nBy suitably randomisin
 g key aspects of the number theory\, we prove that an NFS-type algorithm p
 roduces congruences of squares in expected time L(1/3\, 2.88). These resul
 ts are tightly coupled to recent progress on the distribution of smooth nu
 mbers\, and we provide additional tools to turn progress on these problems
  into improved bounds.\n
LOCATION:MR12
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