Florian Speelman

Andreas Bluhm, Matthias Christandl, Florian Speelman

The position of a device or agent is an important security credential in today's society, both online and in the real world. Unless in direct proximity, however, the secure verification of a position is impossible without further assumptions. This is true classically, but also in any future quantum-equipped communications infrastructure. We show in this work that minimal quantum resources, in the form of a single qubit, combined with classical communication are sufficient to thwart quantum adversaries that pretend to be at a specific position and have the ability to coordinate their action with entanglement. More precisely, we show that the adversaries using an increasing amount of entanglement can be combatted solely by increasing the number of classical bits used in the protocol. The presented protocols are noise-robust and within reach of current quantum technology.

Yfke Dulek, Florian Speelman

We investigate quantum authentication schemes constructed from quantum error-correcting codes. We show that if the code has a property called purity testing, then the resulting authentication scheme guarantees the integrity of ciphertexts, not just plaintexts. On top of that, if the code is strong purity testing, the authentication scheme also allows the encryption key to be recycled, partially even if the authentication rejects. Such a strong notion of authentication is useful in a setting where multiple ciphertexts can be present simultaneously, such as in interactive or delegated quantum computation. With these settings in mind, we give an explicit code (based on the trap code) that is strong purity testing but, contrary to other known strong-purity-testing codes, allows for natural computation on ciphertexts.

Yfke Dulek, Christian Schaffner, Florian Speelman

We present a new scheme for quantum homomorphic encryption which is compact and allows for efficient evaluation of arbitrary polynomial-sized quantum circuits. Building on the framework of Broadbent and Jeffery and recent results in the area of instantaneous non-local quantum computation, we show how to construct quantum gadgets that allow perfect correction of the errors which occur during the homomorphic evaluation of T gates on encrypted quantum data. Our scheme can be based on any classical (leveled) fully homomorphic encryption (FHE) scheme and requires no computational assumptions besides those already used by the classical scheme. The size of our quantum gadget depends on the space complexity of the classical decryption function -- which aligns well with the current efforts to minimize the complexity of the decryption function. Our scheme (or slight variants of it) offers a number of additional advantages such as ideal compactness, the ability to supply gadgets "on demand", circuit privacy for the evaluator against passive adversaries, and a three-round scheme for blind delegated quantum computation which puts only very limited demands on the quantum abilities of the client.

Florian Speelman

We study position-based cryptography in the quantum setting. We examine a class of protocols that only require the communication of a single qubit and 2n bits of classical information. To this end, we define a new model of communication complexity, the garden-hose model, which enables us to prove upper bounds on the number of EPR pairs needed to attack such schemes. This model furthermore opens up a way to link the security of position-based quantum cryptography to traditional complexity theory.