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Aix-Marseille Université
Institut de Mathématiques de Marseille (I2M) - UMR 7373
Site Saint-Charles : 3 place Victor Hugo, Case 19, 13331 Marseille Cedex 3
Site Luminy : Campus de Luminy - Case 907 - 13288 Marseille Cedex 9

Séminaire

Secret Sharing Schemes with a large number of players from Toric Varieties

Johan P. Hansen


Date(s) : 12/03/2015   iCal
14h30 - 15h30

A general theory for constructing linear secret sharing schemes over a finite field $\Fq$ from toric varieties is introduced. The number of players can be as large as $(q-1)^r-1$ for $r\geq 1$.
We present general methods to obtain the reconstruction and privacy thresholds as well as conditions for multiplication on the associated secret sharing schemes.

In particular we apply the method on certain toric surfaces. The main results are ideal linear secret sharing schemes where the number of players can be as large as $(q-1)^2-1$, we determine bounds for the reconstruction and privacy thresholds and conditions for strong multiplication using the cohomology and the intersection theory on toric surfaces.

Johan P. Hansen, Aarhus University

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