Perfect Secrecy Systems Immune to Spoofing Attacks
This addresses security vulnerabilities in cryptographic systems for applications requiring robust authentication, though it is incremental in building on existing theoretical frameworks.
The paper tackles the problem of designing perfect secrecy systems immune to spoofing attacks, presenting novel constructions that achieve arbitrary high security levels and efficient optimal systems with up to 7-fold security against spoofing.
We present novel perfect secrecy systems that provide immunity to spoofing attacks under equiprobable source probability distributions. On the theoretical side, relying on an existence result for $t$-designs by Teirlinck, our construction method constructively generates systems that can reach an arbitrary high level of security. On the practical side, we obtain, via cyclic difference families, very efficient constructions of new optimal systems that are onefold secure against spoofing. Moreover, we construct, by means of $t$-designs for large values of $t$, the first near-optimal systems that are 5- and 6-fold secure as well as further systems with a feasible number of keys that are 7-fold secure against spoofing. We apply our results furthermore to a recently extended authentication model, where the opponent has access to a verification oracle. We obtain this way novel perfect secrecy systems with immunity to spoofing in the verification oracle model.