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DTSTART:20260308T070000
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DTSTART:20251102T060000
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DTSTART;TZID=America/Toronto:20260320T153000
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DTEND;TZID=America/Toronto:20260320T163000
URL:https://uwaterloo.ca/combinatorics-and-optimization/events/tutte-colloq
 uium-bruno-sterner-large-smooth-twins-short
SUMMARY:Tutte Colloquium -Bruno Sterner-Large smooth twins from short latti
 ce\nvectors
CLASS:PUBLIC
DESCRIPTION:SPEAKER:\n Bruno Sterner\n\nAFFILIATION:\n University of Waterl
 oo\n\nLOCATION:\n MC 5501\n\nABSTRACT: We discuss the challenging problem
  of finding pairs of\nconsecutive smooth integers\, which we refer to as a
  smooth twin. In\nother words the largest prime factor in the twin is rela
 tively small.\nThis computational number theoretic problem has appeared in
  the\ncontext of isogeny-based cryptography whereby a select number of\ncr
 yptosystems use such twins as part of their parameter setup. The\nchalleng
 ing part to the problem is finding smooth twins whose largest\nprime facto
 r is as small as possible. Prior to this work\, twins of\nthis nature have
  at most 74-bits which is much too small for\ncryptographic relevance. We 
 bridge this gap by presenting a new method\nthat finds significantly large
 r smooth twins with as small as possible\nsmoothness bound. The idea of ou
 r algorithm is based on the well known\nand studied problem of finding sho
 rt vectors in a well constructed\nlattice. We report a 196-bit smooth twin
  which falls in this regime as\nwell as a few larger twins that have small
  (but not the smallest)\nsmoothness bounds.
DTSTAMP:20260402T164431Z
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