Measuring Secrecy by the Probability of a Successful Guess

TL;DR

This paper introduces a new secrecy metric based on the probability exponent of successful eavesdropper guesses within acceptable distortion, analyzing both keyless and keyed communication systems.

Contribution

It provides a single-letter characterization of the maximum achievable secrecy exponent and demonstrates optimal strategies for both legitimate users and eavesdroppers.

Findings

Derived the secrecy exponent for keyless systems without rate constraints.

Extended the analysis to systems with shared keys and rate constraints.

Identified asymptotically optimal strategies for secure communication and eavesdropping.

Abstract

The secrecy of a communication system in which both the legitimate receiver and an eavesdropper are allowed some distortion is investigated. The secrecy metric considered is the exponent of the probability that the eavesdropper estimates the source sequence successfully within an acceptable distortion level. The problem is first studied when the transmitter and the legitimate receiver do not share any key and the transmitter is not subject to a rate constraint, which corresponds to a stylized model of a side channel and reveals connections to source coding with side information. The setting is then generalized to include a shared secret key between the transmitter and the legitimate receiver and a rate constraint on the transmitter, which corresponds to the Shannon cipher system. A single-letter characterization of the highest achievable exponent is provided, and asymptotically-optimal strategies for both the primary user and the eavesdropper are demonstrated.