Eve's forgery probability from her false acceptance probability: interactive authentication, Holevo information and the min-entropy

TL;DR

This paper derives bounds on Eve's forgery probability in quantum communication, linking it to false acceptance probabilities and Holevo information, ensuring security and composability in noisy quantum channels.

Contribution

It introduces a unified security threshold for quantum authentication protocols over noisy channels, improving security analysis by relating forgery probability to Holevo information.

Findings

Eve's forgery probability can be tightly bounded using Holevo-type quantities.

The protocol achieves epsilon-security and composability against forgery and key leakage.

A new method relates false acceptance probability to security thresholds in quantum protocols.

Abstract

We obtain estimates for Eve's forgery probability, namely the probability that she is able to forge a message which Alice or Bob mistakenly accept over a noisy Quantum channel for generating a shared Quantum secret key. This probability is related to Eve's success probability obtained in a previous work due to Renner and Wolf, which was obtained from assumptions on the min-entropy for characterizing asymmetric security. To demonstrate that protocols over noisy Quantum channels are dependent upon a single, unified security threshold in comparison to multiple security parameters in the Renner-Wolf interactive authentication protocol framework we upper bound Eve's forgery probability with a Holevo-type quantity that can be made negligibly small. By leveraging estimates for Eve's false acceptance probability that have previously been obtained by the author, we obtain the desired security threshold by bounding the false acceptance probability with a suitably chosen two-universal function which serves as a counterpart to two-universal hashing functions that have previously been examined for cryptographic protocols in Quantum key distribution. As a result the protocol is not only $\epsilon$-secure, for some $\epsilon>0$, but also composable against forgery and key leakage.