Perfect Secrecy Systems Immune to Spoofing Attacks

TL;DR

This paper introduces new perfect secrecy systems that are highly secure against spoofing attacks, combining theoretical existence proofs with practical constructions for various levels of security, including systems with immunity in extended authentication models.

Contribution

It provides the first constructions of perfect secrecy systems that are 5- and 6-fold secure against spoofing, and introduces methods for systems with high security levels using combinatorial designs.

Findings

Constructed systems with 5- and 6-fold security against spoofing.

Developed efficient, optimal systems using cyclic difference families.

Extended the model to include immunity in verification oracle scenarios.

Abstract

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.