Mosaics of combinatorial designs for information-theoretic security

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.

References in corpus (6)

• Rényi Divergence and Kullback-Leibler Divergence
• Exponential decreasing rate of leaked information in universal random privacy amplification
• Upper bounds of eavesdropper's performances in finite-length code with decoy method
• Secure Multiplex Coding with Dependent and Non-Uniform Multiple Messages
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Cited by in corpus (2)

• Semantic Security for Quantum Wiretap Channels
• Small examples of mosaics of combinatorial designs