MoL-2016-05: Quantum Homomorphic Encryption for Polynomial-Sized Circuits

MoL-2016-05: Dulek, Yfke (2016) Quantum Homomorphic Encryption for Polynomial-Sized Circuits. [Report]

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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.

Item Type: Report
Report Nr: MoL-2016-05
Series Name: Master of Logic Thesis (MoL) Series
Year: 2016
Uncontrolled Keywords: Homomorphic encryption, quantum cryptography, quantum teleportation, gardenhose model, Barrington's theorem, Clifford group
Date Deposited: 12 Oct 2016 14:39
Last Modified: 12 Oct 2016 14:39

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