State of the art network security is based on end-to-end encryption and link encryption. Many operations on networks are however broadcast ( or multicast or flooding) oriented. This implies that the straightforward application of link or end-to-end oriented authentication techniques to network integrity implies either that the required bandwidth increases dramatically or that a terrible key management problem is created. A geometry-based non-interactive unconditional authentication scheme for a single- sender-multiple-receiver environment has been co-authored by the principal investigator. The solution is based on secret sharing (threshold) schemes. This gives rise to the following open problems to be investigated in this research: (1) can unconditionally and conditionally secure multi-sender and multi- receiver authentication and privacy schemes which are (partially) non-interactive be achieved (2) is there a duality between sharing and authentication (3) what are the most optimal schemes and what other enhancements can be obtained? Geometry could continue to play an important role in solving the above problems.
