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Quantum Homomorphic Encryption for Polynomial-Sized Circuits

  • Yfke Dulek
  • Christian Schaffner
  • Florian Speelman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9816)

Abstract

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”, and circuit privacy for the evaluator against passive adversaries.

Keywords

Homomorphic encryption Quantum cryptography Quantum teleportation Garden-hose model 

Notes

Acknowledgements

We acknowledge useful discussions with Anne Broadbent, Harry Buhrman, and Leo Ducas. We thank Stacey Jeffery for providing the inspiration for a crucial step in the security proof, and Gorjan Alagic and Anne Broadbent for helpful comments on a draft of this article. This work was supported by the 7th framework EU SIQS and QALGO, and a NWO VIDI grant.

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Copyright information

© International Association for Cryptologic Research 2016

Authors and Affiliations

  1. 1.University of AmsterdamAmsterdamThe Netherlands
  2. 2.CWIAmsterdamThe Netherlands
  3. 3.QuSoftAmsterdamThe Netherlands

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