CWI Cryptology Group

Abstract: The connection between secret sharing and matroid theory is known since the early 90s. In this talk we survey the results on this topic with special emphasis on the most recent ones. In particular, we discuss some recent results that have been obtained by applying, for the first time in secret sharing, the so-called non-Shannon information inequalities.

Abstract: Network coding offers increased throughput and improved robustness to random faults in completely decentralized networks. Since it does not require centralized control, network coding has been suggested for routing packets in ad-hoc networks, for content distribution in peer-to-peer file systems, and for improving the efficiency of large-scale data dissemination over the Internet.
In contrast to traditional routing schemes, however, network coding requires intermediate nodes to modify data packets en route. For this reason, standard signature schemes are inapplicable and it is a challenge to provide resilience to tampering by malicious nodes.
After reviewing the basics of network coding, we will describe a secure, efficient signature scheme that can be used in conjunction with network coding to prevent malicious modification of data. Our scheme can be viewed as signing linear subspaces in the sense that a signature $\sigma$ on a subspace $V$ authenticates exactly those vectors in $V$.
This research is joint work with Dan Boneh (Stanford), Jonathan Katz (Maryland), and Brent Waters (Austin).

Abstract: It has been known for a long time that the class of self-dual codes over a finite field is asymptotically good and that it attains the Gilbert-Varshamov bound. Stichtenoth showed that over fields with quadratic cardinality self-dual codes even attain the Tsfasman-Vladut-Zink bound. In this talk I will explain this construction and show how one can obtain an analogous result for self-dual codes over cubic finite fields using some well-known facts about quadratic forms and a new tower of function fields.