# The Conditional Information Leakage Given Eavesdropper's Received Signals in Wiretap Channels

## TL;DR

This paper introduces a new measure called conditional information leakage in wiretap channels, enabling efficient computation and providing a new security criterion for eavesdropper's information gain.

## Contribution

It defines the conditional information leakage, develops a linear-complexity algorithm for its computation, and validates its effectiveness as a security measure in specific channel models.

## Key findings

- Efficient linear-time algorithm for computing conditional information leakage.
- Validation of the measure as a security criterion in binary symmetric and erasure channels.
- Demonstration of the measure's advantage over traditional exponential-complexity calculations.

## Abstract

Information leakage in Wyner's wiretap channel model is usually defined as the mutual information between the secret message and the eavesdropper's received signal. We define a new quantity called "conditional information leakage given the eavesdropper's received signals," which expresses the amount of information that eavesdropper gains from his/her received signal. A benefit of introducing this quantity is that we can develop a fast algorithm for computing the conditional information leakage, which has linear complexity in the code length $n$, while the complexity for computing the usual information leakage is exponential in $n$. Validity of such a conditional information leakage as a security criterion is confirmed by studying the cases of binary symmetric channels and binary erasure channels.