Yfke Dulek

Abstract Device-independent protocols use untrusted quantum devices to achieve a cryptographic task. Such protocols are typically based on Bell inequalities and require the assumption that the quantum device is composed of separated non-communicating components. In this submission, we present protocols for self-testing and device-independent quantum key distribution (DIQKD) that are secure even if the components of the quantum device can exchange arbitrary quantum communication. Instead, we assume that the device cannot break a standard post-quantum cryptographic assumption. Importantly, the computational assumption only needs to hold during the protocol execution and only applies to the (adversarially prepared) device in possession of the (classical) user, while the adversary herself remains unbounded. The output of the protocol, e.g. secret keys in the case of DIQKD, is information-theoretically secure. For our self-testing protocol, we build on a recently introduced cryptographic tool (Brakerski et al., FOCS 2018; Mahadev, FOCS 2018) to show that a classical user can enforce a bipartite structure on the Hilbert space of a black-box quantum device, and certify that the device has prepared and measured a state that is entangled with respect to this bipartite structure. Using our self-testing protocol as a building block, we construct a protocol for DIQKD that leverages the computational assumption to produce information-theoretically secure keys. The security proof of our DIQKD protocol uses the self-testing theorem in a black-box way. Our self-testing theorem thus also serves as a first step towards a more general translation procedure for standard device-independent protocols to the setting of computationally bounded (but freely communicating) devices.

Abstract In quantum copy-protection, an adversary who is given a quantum state computing a function f cannot produce two (possibly entangled) quantum states that each individually compute f. No constructions for copy-protection are known in the plain model. We consider a weaker notion, secure software leasing (SSL), where it is only impossible to produce two copies that can both compute f using the honest evaluation algorithm. We show the following: (1) SSL is possible for a subclass of evasive functions, assuming the existence of post-quantum indistinguishability obfuscators and hardness of LWE; (2) SSL is impossible in general, assuming hardness of LWE. The second statement has important implications for existing quantum-cryptographic notions: in particular, it implies the impossibility of quantum copy-protection for arbitrary unlearnable functions, and impossibility of quantum virtual-black-box obfuscation of classical circuits.