(Quantum) Min-Entropy Resources

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) min-entropy of X given E is lower bounded by some k, H min(X |E) ≥ 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 min-entropy of X . As a first application, we use this min-entropy 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 min-entropy resource given the (physical) resources available in the specific setting considered. In the second, it distills secret key from the min-entropy resource—i.e., it constructs a secret key resource. We prove security for a generic key distillation protocol that may use any min-entropy resource. Since the notion of resource construction is composable— security 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 min-entropy resource. As a second application, we provide a composable security proof for the recent Fehr-Salvail protocol [EUROCRYPT 2017] that authenticates classical messages with a quantum message authentication code (Q-MAC), 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.