Quantum homomorphic encryption for polynomial-sized circuits
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 [BJ15] and recent results in the area of
instantaneous non-local quantum computation [Spe15], 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.
joint work with Yfke Dulek and Florian Speelman
appeared at CRYPTO 2016 and QIP 2017
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