Information-theoretic bounds for authentication schemes
Journal of Cryptology
Cartesian authentication schemes
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Essentially ℓ -fold secure authentication systems
EUROCRYPT '90 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
Veronese varieties over fields with non-zero characteristic: a survey
Discrete Mathematics - Special issue: Combinatorics 2000
| Hi-index | 0.00 |
In this paper we deal with authentication systems in which one keyis used to authenticate many source states. We answer a related question onthe cardinalities of the intersections of quadrics in PG (d,q). We firstgeneralize a class of geometric authentication systems, which has beenintroduced by Beutelspacher, Tallini and Zanella4. The source states are thelines through a special point N of PG (d,q) (the d-dimensional projectivespace over GF (q)). The keys are some hypersurfaces which have N as anucleus ( N is a nucleus of Σ if every line through N meets Σ inexactly one point). The message belonging to a source state ℓ and a keyΣ is the unique point of intersection of the line ℓ with thehypersurface Σ. We give the values of s for which the constructedauthentication systems have a security which is comparable to the bestallowed by a theoretical bound. In case the hypersurfaces are quadrics, wegive further results on the security. To this end, we determine the greatestcardinality for the intersections of the finite Veronese varieties with theprojective subspaces of any given dimension. Finally, we discuss a possibleimplementation.