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SUMMARY:Cryptography\, quantum computers and analytic number theory - Céd
 ric Pilatte (University of Oxford)
DTSTART:20250205T133000Z
DTEND:20250205T150000Z
UID:TALK225112@talks.cam.ac.uk
CONTACT:Julia Wolf
DESCRIPTION:The security of many widely used communication systems hinges 
 on the presumed difficulty of factoring integers or computing discrete log
 arithms. However\, Shor's celebrated algorithm from 1994 demonstrated that
  quantum computers can perform these tasks in polynomial time. In 2023\, R
 egev proposed an even faster quantum algorithm for factoring integers. Unf
 ortunately\, the correctness of his new method is conditional on an ad hoc
  number-theoretic conjecture. Using tools from analytic number theory\, we
  establish a result in the direction of Regev's conjecture. This enables u
 s to design a provably correct quantum algorithm for factoring and solving
  the discrete logarithm problem\, whose efficiency is comparable to Regev'
 s approach.\n\nIn the first part of this talk\, we will provide an accessi
 ble overview of these developments and their place within the broader cont
 ext of cryptography. The discussion will require no prior background as we
  will cover the necessary concepts\, including a brief introduction to qua
 ntum computing from a mathematician's perspective.\n\nThe second part of t
 he talk will focus on the number-theoretic aspects of this work. We will o
 utline the proof of a variant of Regev's conjecture\, using lattice techni
 ques\, character sums and zero-density estimates for Dirichlet L-functions
 .
LOCATION:MR4\, CMS
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