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

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 of all but one measurement outcome with respect to an arbitrary (and in particular an arbitrarily large) set of possible measurements, and, at the same time, uses the minentropy 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 Damg̊ard 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 single-qubit operations. The scheme by Damg̊ard et al., on the other hand, completely breaks down under such an attack.