CWI Cryptology Group

Abstract: We take a closer look at the strongly multiplicative algebraic geometric ramp schemes introduced by Chen and Cramer in 2006, and discuss some situations where, by carefully selecting the parameters of the scheme, the difference between the privacy and reconstruction thresholds can be made smaller (joint work with H. Chen, R. Cramer and C. Xing).

Abstract: Chen and Cramer proposed a new family of linear secret sharing schemes (LSSS), constructed from algebraic geometric Goppa codes, that provide multiparty computation (MPC) protocols over small fields. In this talk, we analyze how these algebraic geometric LSSS can be used to obtain secure MPC protocols. Specifically, we study the (strong) multiplication property of these schemes and we give a characterization of the access structure of the schemes defined by hyperelliptic curves. Combining these results, we present non-threshold adversary structures for which is not possible to build secure MPC protocol by composing threshold schemes, but it is possible by using algebraic LSSS. Joint work with Carles Padro' and Iwan Duursma.

Abstract: A survey of the parameters and the construction of algebraic geometry codes will be given. The q-th power algorithm for the computation of the integral closure of a ring in finite characteristic will be explained in some detail.

Abstract: After a short introduction to towers of algebraic function fields, I will introduce a new explicit tower over cubic finite fields, whose limit attains Zink's lower bound. Many features of this tower are very similar to those of an optimal tower of Garcia-Stichtenoth over quadratic finite fields, whose modularity was shown by Elkies. This is joint work with A. Garcia and H. Stichtenoth.