On the Shannon cipher system with a capacity-limited key-distribution channel

TL;DR

This paper analyzes a secure communication system where the secret key is transmitted over a limited-capacity channel, establishing optimal strategies for security, compression, and distortion, akin to source-channel separation principles.

Contribution

It characterizes the achievable trade-offs among security, compression, and distortion in a Shannon cipher system with a capacity-limited key channel, highlighting the optimality of key matching and source coding.

Findings

Optimal key matching via reliable channel coding

Trade-offs between security, compression, and distortion

Extension of classical source-channel separation to secure communication

Abstract

We consider the Shannon cipher system in a setting where the secret key is delivered to the legitimate receiver via a channel with limited capacity. For this setting, we characterize the achievable region in the space of three figures of merit: the security (measured in terms of the equivocation), the compressibility of the cryptogram, and the distortion associated with the reconstruction of the plaintext source. Although lossy reconstruction of the plaintext does not rule out the option that the (noisy) decryption key would differ, to a certain extent, from the encryption key, we show, nevertheless, that the best strategy is to strive for perfect match between the two keys, by applying reliable channel coding to the key bits, and to control the distortion solely via rate-distortion coding of the plaintext source before the encryption. In this sense, our result has a flavor similar to that of the classical source-channel separation theorem. Some variations and extensions of this model are discussed as well.