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UID:8141@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20150312T143000
DTEND;TZID=Europe/Paris:20150312T153000
DTSTAMP:20241120T210042Z
URL:https://www.i2m.univ-amu.fr/evenements/secret-sharing-schemes-with-a-l
 arge-number-of-players-from-toric-varieties/
SUMMARY:Johan P. Hansen (...): Secret Sharing Schemes with a large number o
 f players from Toric Varieties
DESCRIPTION:Johan P. Hansen: A general theory for constructing linear secre
 t sharing schemes over a finite field $\\Fq$ from toric varieties is intro
 duced. The number of players can be as large as $(q-1)^r-1$ for $r\\geq 1$
 .\nWe present general methods to obtain the reconstruction and privacy thr
 esholds as well as conditions for multiplication on the associated secret 
 sharing schemes.\nIn particular we apply the method on certain toric surfa
 ces. The main results are ideal linear secret sharing schemes where the nu
 mber of players can be as large as $(q-1)^2-1$\, we determine bounds for t
 he reconstruction and privacy thresholds and conditions for strong multipl
 ication using the cohomology and the intersection theory on toric surfaces
 .\nJohan P. Hansen\, Aarhus University\n\n
CATEGORIES:Séminaire,Arithmétique et Théorie de l’Information
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