Mosaics of combinatorial designs for information-theoretic security

TL;DR

This paper introduces security functions based on mosaics of combinatorial designs, optimizing seed length and message/key rate for information-theoretic security applications like wiretap channels and secret key generation.

Contribution

It proposes a novel approach using mosaics of combinatorial designs for security functions, providing explicit examples and bounds for seed length and security performance.

Findings

Explicit examples with optimal seed length and message/key rate

Bounds on security performance of design-based security functions

Trade-offs between seed length and message/key rate

Abstract

We study security functions which can serve to establish semantic security for the two central problems of information-theoretic security: the wiretap channel, and privacy amplification for secret key generation. The security functions are functional forms of mosaics of combinatorial designs, more precisely, of group divisible designs and balanced incomplete block designs. Every member of a mosaic is associated with a unique color, and each color corresponds to a unique message or key value. Every block index of the mosaic corresponds to a public seed shared between the two trusted communicating parties. The seed set should be as small as possible. We give explicit examples which have an optimal or nearly optimal trade-off of seed length versus color (i.e., message or key) rate. We also derive bounds for the security performance of security functions given by functional forms of mosaics of designs.