# Wiretap channel capacity: Secrecy criteria, strong converse, and phase change

## TL;DR

This paper analyzes the capacity of the discrete memoryless wiretap channel under four secrecy criteria using equal-image-size source partitioning, revealing differences in capacity and phase change phenomena depending on the criteria and tolerances.

## Contribution

It introduces a unified approach to derive capacities under various secrecy criteria and uncovers phase change phenomena and conditions for the strong converse property.

## Key findings

- Capacities differ under various secrecy criteria with non-zero error and secrecy tolerances.
- Strong converse property holds only under tail probability-based criteria.
- Phase change phenomenon occurs as secrecy tolerances vary.

## Abstract

This paper employs equal-image-size source partitioning techniques to derive the capacities of the general discrete memoryless wiretap channel (DM-WTC) under four different secrecy criteria. These criteria respectively specify requirements on the expected values and tail probabilities of the differences, in absolute value and in exponent, between the joint probability of the secret message and the eavesdropper's observation and the corresponding probability if they were independent. Some of these criteria reduce back to the standard leakage and variation distance constraints that have been previously considered in the literature. The capacities under these secrecy criteria are found to be different when non-vanishing error and secrecy tolerances are allowed. Based on these new results, we are able to conclude that the strong converse property generally holds for the DM-WTC only under the two secrecy criteria based on constraining the tail probabilities. Under the secrecy criteria based on the expected values, an interesting phase change phenomenon is observed as the tolerance values vary.