Anne Müller

Quantum cryptography allows to achieve security goals that are unobtainable using classical cryptography alone, it offers the promise of everlasting privacy. That is, an adversary trying to attack a protocol must succeed during the run of the protocol, after the protocol has terminated security holds unconditionally. In this work we initiate the study of a new model which we call the quantum decoherence model (QDM). In a nutshell, this model requires that the adversary is computationally bounded during the run of a protocol (and some time after), but becomes computationally unbounded long after the protocol terminates. Importantly, once the adversary becomes computationally unbounded, he can only remember a bounded number of qubits from before the bound was lifted. As our main contribution, we construct a non-interactive commitment scheme achieving unconditional security against malicious senders and everlasting security against malicious receivers in the UC model. Additionally, we show that it gives rise to everlasting public key encryption and OT in the QDM. Finally, we also consider the weaker notion of incompressible encryption in the setting of quantum decoherence, and show that post-quantum IND-CPA secure public key encryption is sufficient to realize this notion without resorting to random oracles.

Functional encryption is a powerful cryptographic primitive that enables fine- grained access to encrypted data and underlies numerous applications. Although the ideal security notion for FE—simulation security—has been shown to be impossible in the classical setting, those impossibility results rely on inherently classical arguments. This leaves open the question of whether simulation-secure functional encryption can be achieved in the quantum regime. In this work, we rule out this possibility by showing that the classical impossibility results largely extend to the quantum world. In particular, when the adversary can issue an un- bounded number of challenge messages, we prove an unconditional impossibility, matching the classical barrier. In the case where the adversary may obtain many functional keys, clas- sical arguments only yield impossibility under the assumption of pseudorandom functions; we strengthen this by proving impossibility under the potentially weaker assumption of pseudo- random quantum states. In the same setting, we also establish an alternative impossibility based on public-key encryption. Since public-key encryption is not known to imply pseudo- random quantum states, this provides independent evidence of the barrier. As part of our proofs, we show a novel incompressibility property for pseudorandom states, which may be of independent interest.