(Quantum) MinEntropy Resources
Abstract
We model (interactive) resources that provide Alice with a string $X$ and a guarantee that any Eve interacting with her interface of the resource obtains a (quantum) system $E$ such that the conditional (smooth) minentropy of $X$ given $E$ is lower bounded by some $k$. This (abstract) resource specification encompasses any setting that results in the honest players holding such a string (or aborting). For example, it could be constructed from, e.g., noisy channels, quantum key distribution (QKD), or a violation of Bell inequalities, which all may be used to derive bounds on the minentropy of $X$. As a first application, we use this minentropy resource to modularize key distribution (KD) schemes by dividing them in two parts, which may be analyzed separately. In the first part, a KD protocol constructs a minentropy resource given the (physical) resources available in the specific setting considered. In the second, it distills secret key from the minentropy resourcei.e., it constructs a secret key resource. We prove security for a generic key distillation protocol that may use any minentropy resource. Since the notion of resource construction is composablesecurity of a composed protocol follows from the security of its parts this reduces proving security of a KD protocol (e.g., QKD) to proving that it constructs a minentropy resource. As a second application, we provide a composable security proof for the recent FehrSalvail protocol [EUROCRYPT 2017] that authenticates classical messages with a quantum message authentication code (QMAC), and recycles all the key upon successfully verifying the authenticity of the message. This protocol uses (and recycles) a nonuniform key, which we model as consuming and constructing a minentropy resource.
 Publication:

arXiv eprints
 Pub Date:
 May 2017
 arXiv:
 arXiv:1705.10595
 Bibcode:
 2017arXiv170510595P
 Keywords:

 Quantum Physics;
 Computer Science  Cryptography and Security;
 Computer Science  Information Theory
 EPrint:
 39+18 pages, 11 figures