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

Niek J. Bouman (CWI Amsterdam), Serge Fehr (CWI Amsterdam), Carlos Gonzalez-Guillen (Universidad Politecnica de Madrid and IMI) and Christian Schaffner (CWI Amsterdam and University of Amsterdam)

 

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 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 Damgård 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 Damgård et al., on the other hand, completely breaks down under such an attack.