Attack of Many Eavesdroppers via Optimal Strategy in Quantum Cryptography

TL;DR

This paper analyzes the impact of multiple eavesdroppers employing optimal strategies on the Bennett-Brassard quantum cryptography protocol, revealing how their interactions affect information gain and error rates.

Contribution

It provides explicit formulas for information gain and error rates when multiple eavesdroppers attack simultaneously, highlighting the limitations of subsequent eavesdroppers.

Findings

First eavesdropper gains mutual information without disturbance.

Subsequent eavesdroppers increase the receiver's error rate.

Later eavesdroppers gain less information than optimal ones.

Abstract

We examine a situation that $n$ eavesdroppers attack the Bennett-Brassard cryptographic protocol via their own optimal and symmetric strategies. Information gain and mutual information with sender for each eavesdropper are explicitly derived. The receiver's error rate for the case of arbitrary $n$ eavesdroppers can be derived using a recursive relation. Although first eavesdropper can get mutual information without disturbance arising due to other eavesdroppers, subsequent eavesdropping generally increases the receiver's error rate. Other eavesdroppers cannot gain information on the input signal sufficiently. As a result, the information each eavesdropper gains becomes less than optimal one.