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UID:6042@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20220519T110000
DTEND;TZID=Europe/Paris:20220519T120000
DTSTAMP:20241120T200724Z
URL:https://www.i2m.univ-amu.fr/evenements/a-modular-approach-to-osidh/
SUMMARY:Leonardo Colò (I2M\, Aix-Marseille Université): A modular approac
 h to OSIDH
DESCRIPTION:Leonardo Colò: We recently defined an OSIDH protocol — for o
 riented supersingular isogeny Diffie-Hellman — by imposing the data of 
 an orientation by an imaginary quadratic ring O on the category of sup
 ersingular elliptic curves. Starting with an elliptic curve E_0 oriented
  by a CM order O_K of class number one\, we push forward the class grou
 p action along an l-isogeny chains\, on which the class group of an ord
 er O of large index l^n in O_K acts. The map from l-isogeny chains 
 to its terminus forgets the structure of the orientation\, and the origi
 nal base curve E_0. For a sufficiently long random l-isogeny chain\, th
 e terminal curve represents a generic supersingular elliptic curve.One of
  the advantages of working in this general framework is that the group act
 ion by Cl(O) can be carried out effectively solely on the sequence of m
 oduli points (such as j-invariants) on a modular curve\, thereby avoidin
 g expensive generic isogeny computations or the requirement of rational 
 torsion points. The goal of this talk is to describe how to realize this g
 roup action as an effective algorithm\, make it efficient\, and introduc
 e the use of level structures\, replacing the j-line X(1) with a modula
 r curve X(Γ) of higher level. This is joint work with David Kohel.\n\n
 \n\nReferences [1]  W. Castryck\, T. Lange\, C. Martindale\, L. Panny\, 
 and J. Renes. CSIDH: an efficient post- quantum commutative group action. 
 Cryptology ePrint Archive\, 2018/383\, https://eprint. iacr.org/2018/383\
 n [2]  D. Charles\, E. Goren\, and C. Lauter. Cryptographic hash functio
 ns from expander graphs. J. Cryptography bf 22 (1)\, 93–113\, 2009.\n [
 3]  L. Colò and D. Kohel\, Orienting supersingular isogeny graphs. In 
 Journal of Mathemati- cal Cryptology\, vol. 14.1\, Walter de Gruyter\, 
 414–437\, 2020. http://dx.doi.org/10.1515/ jmc-2019-0034.\n [4]  D. 
 Jao and L. De Feo. Towards quantum-resistant cryptosystems from supersingu
 lar curve iso- genies. In Post-Quantum Cryptography\, LNCS 7071\, 19–
 34\, Springer\, 2011. https://eprint. iacr.org/2011/506. \n\n \n\n\nSi
 te : \nhttps://sites.google.com/view/samuele-anni/home/s%C3%A9minaire-at
 i?authuser=0\n\n[su_spacer size="10"]\n\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Leonardo_Colo-.jpg
CATEGORIES:Séminaire,Arithmétique et Théorie de l’Information
LOCATION:I2M Luminy - Ancienne BU\, Salle Séminaire CIELL (1er étage)\, 1
 63 Avenue de Luminy\, 13009 Marseille\, France\, Salle 216\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, 1300
 9 Marseille\, France\, Salle 216\, France;X-APPLE-RADIUS=100;X-TITLE=I2M L
 uminy - Ancienne BU\, Salle Séminaire CIELL (1er étage):geo:0,0
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