An All-But-One Entropic Uncertainty Relation, and Application to Password-based Identification

TL;DR

This paper introduces a novel entropic uncertainty relation that bounds measurement uncertainty for all but one measurement choice using min-entropy, and applies it to enhance quantum identification security.

Contribution

It presents the first uncertainty relation with this specific 'all-but-one' property using min-entropy, and applies it to develop a more robust quantum identification scheme.

Findings

New uncertainty relation with 'all-but-one' property

Security of the identification scheme against unbounded adversaries with limited operations

Scheme remains secure even if the bounded quantum storage assumption fails

Abstract

Entropic uncertainty relations are quantitative characterizations of Heisenberg's uncertainty principle, which make use of an entropy measure to quantify uncertainty. In quantum cryptography, they are often used as convenient tools in security proofs. We propose a new entropic uncertainty relation. It is the first such uncertainty relation that lower bounds the uncertainty in the measurement outcome for all but one choice for the measurement from an arbitrarily large (but specifically chosen) set of possible measurements, and, at the same time, uses the min-entropy as entropy measure, rather than the Shannon entropy. This makes it especially suited for quantum cryptography. As application, we propose a new quantum identification scheme in the bounded quantum storage model. It makes use of our new uncertainty relation at the core of its security proof. In contrast to the original quantum identification scheme proposed by Damg{\aa}rd et al., our new scheme also offers some security in case the bounded quantum storage assumption fails hold. Specifically, our scheme remains secure against an adversary that has unbounded storage capabilities but is restricted to non-adaptive single-qubit operations. The scheme by Damg{\aa}rd et al., on the other hand, completely breaks down under such an attack.