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UID:6835@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20200130T110000
DTEND;TZID=Europe/Paris:20200130T120000
DTSTAMP:20241120T202024Z
URL:https://www.i2m.univ-amu.fr/evenements/the-generalized-quaternion-isog
 eny-path-problem/
SUMMARY:Antonin Leroux (LIX\, École Polytechnique\, Palaiseau): The genera
 lized quaternion isogeny path problem
DESCRIPTION:Antonin Leroux: The correspondence between maximal orders in a 
 quaternion algebra and supersingular elliptic curves has uncovered new per
 spectives in the field of isogeny-based cryptography. The KLPT algorithm o
 f Kohel et al. in 2014 introduces an algorithm solving the quaternion isog
 eny path problem in polynomial time. Studying this problem has application
 s both constructive and destructive. It has allowed to reduce the problem 
 of computing isogenies between two curves to the one of endomorphism ring 
 computation. The GPS signature scheme from Galbraith et al. in 2017 was bu
 ilt on this algorithm.\nThe main algorithm of KLPT solves the problem when
  the maximal order is special extremal. The paper also proposes a generali
 zed version\, but it produces an output that has some very characteristic 
 property that prevent from using it in some applications\, like a generali
 zation of the GPS signature. In this work\, we propose a new method to gen
 eralize the algorithm. It produces a shorter solution with the same time c
 omplexity and without the problematic property mentioned earlier.
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Antonin_Leroux.jpg
CATEGORIES:Séminaire,Arithmétique et Théorie de l’Information
LOCATION:I2M Luminy - TPR2\, Amphithéâtre Herbrand 130-134 (1er étage)\,
  163 Avenue de Luminy\, Marseille\, 13009\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, Mars
 eille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=I2M Luminy - TPR2\, Amph
 ithéâtre Herbrand 130-134 (1er étage):geo:0,0
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DTSTART:20191027T020000
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