Uncloneable Cryptographic Primitives with Interaction

Much of the strength of quantum cryptography may be attributed to the no-cloning property of quantum information. We construct three new cryptographic primitives whose security is based on uncloneability, and that have in common that their security can be established via a novel monogamy-of-entanglement (MoE) property: - We define interactive uncloneable encryption, a version of the uncloneable encryption defined by Broadbent and Lord [TQC 2020] where the receiver must partake in an interaction with the sender in order to decrypt the ciphertext. We provide a one-round construction that is secure in the information-theoretic setting, in the sense that no other receiver may learn the message even if she eavesdrops on all the interactions. - We provide a way to make a bit string commitment scheme uncloneable. The scheme is augmented with a check step chronologically in between the commit and open steps, where an honest sender verifies that the commitment may not be opened by an eavesdropper, even if the receiver is malicious. - We construct a receiver-independent quantum key distribution (QKD) scheme, which strengthens the notion of one-sided device independent QKD of Tomamichel, Fehr, Kaniewski, and Wehner (TFKW) [NJP 2013] by also permitting the receiver's classical device to be untrusted. Explicitly, the sender remains fully trusted while only the receiver's communication is trusted. To show security, we prove an extension of the MoE property of coset states introduced by Coladangelo, Liu, Liu, and Zhandry [Crypto 2021]. In our stronger version, the player Charlie also receives Bob's answer prior to making his guess, simulating a party who eavesdrops on an interaction. To use this property, we express it as a new type of entropic uncertainty relation which arises naturally from the structure of the underlying MoE game.