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Johann Bernoulli Colloquium, Prof.dr. Ronald Cramer

23 maart 2011

Date:         Wednesday, March 23rd 2011

Speaker:   Prof. dr. Ronald Cramer (CWI en Mathematical Institute,
                 Leiden University)

Room:       5161.0267 (Bernoulliborg)

Time:        16.15

Title: The Arithmetic Codex


Abstract:

We define the notion of an arithmetic codex (or codex, for short). This notion encompasses as well as generalizes, in a single mathematical framework,  all known types of specialized secret sharing schemes from the area of secure multi-party computation, i.e., the so-called (strongly) multiplicative linear secret sharing schemes. Our notion is not merely a unification for its own sake. First, it casts these schemes in terms of a dedicated  ``representation'' of K-algebras, thereby bringing the relevant mathematical structure to the surface. Second,  it identifies novel types of special secret sharing schemes. And, third, there are novel cryptographic applications. Besides presenting some elementary examples and giving an overview of the basic theory and the main applications, we discuss a construction of arithmetic secret sharing schemes based on a novel algebraic-geometric paradigm that we also introduce.

This talk is mainly based on several recent joint works with Nacho Cascudo (CWI) and Chaoping Xing (NTU). But in part it is also based on recent joint work with Ivan Damgaard (Aarhus University) and Valerio Pastro ( AarhusUniversity).

Colloquium coordinators Mathematics are Prof.dr. A.C.D. van Enter (e-mail : A.C.D.van.Enter@rug.nl) and Dr. M.E. Dür (e-mail: M.E.Dur@rug.nl)

Colloquium coordinators Computer Science are Prof.dr. M. Aiello (e-mail: M.Aiello@rug.nl ) and Prof.dr. M. Biehl (e-mail: M.Biehl@rug.nl )

Laatst gewijzigd:04 juli 2014 21:24

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