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Rate-1 Quantum Fully Homomorphic Encryption

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Theory of Cryptography (TCC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13042))

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Abstract

Secure function evaluation (SFE) allows Alice to publish an encrypted version of her input m such that Bob (holding a circuit C) can send a single message that reveals C(m) to Alice, and nothing more. Security is required to hold against malicious parties, that may behave arbitrarily. In this work we study the notion of SFE in the quantum setting, where Alice outputs an encrypted quantum state \(\left|\psi \right>\) and learns \(C(\left|\psi \right>)\) after receiving Bob’s message.

We show that, assuming the quantum hardness of the learning with errors problem (LWE), there exists an SFE protocol for quantum computation with communication complexity

$$ (|\left|\psi \right>| + |C(\left|\psi \right>)|) \cdot (1 + o(1)) $$

which is nearly optimal. This result is obtained by two main technical steps, which might be of independent interest. Specifically, we show (i) a construction of a rate-1 quantum fully-homomorphic encryption and (ii) a generic transformation to achieve malicious circuit privacy in the quantum setting.

O. Chardouvelis—Work done while the author was an intern at the Max Planck Institute for Security and Privacy.

N. Döttling—This work is partially funded by the Helmholtz Association within the project "Trustworthy Federated Data Analytics” (TFDA) (funding number ZT-I-OO1 4).

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Notes

  1. 1.

    Clearly, this notion only makes sense when the circuit C is public and the resources needed by Alice to check Bob’s proof are less than those required to evaluate C.

  2. 2.

    The name is inspired by a similar phenomenon happening in multi-key FHE schemes [DHRW16].

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Author information

Authors and Affiliations

  1. National Technical University of Athens, Athens, Greece

    Orestis Chardouvelis

  2. CISPA Helmholtz Center for Information Security, Saarbrücken, Germany

    Nico Döttling

  3. Max Planck Institute for Security and Privacy, Bochum, Germany

    Giulio Malavolta

Authors
  1. Orestis Chardouvelis
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  2. Nico Döttling
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  3. Giulio Malavolta
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Editor information

Editors and Affiliations

  1. Georgetown University, Washington, WA, USA

    Kobbi Nissim

  2. The University of Texas at Austin, Austin, TX, USA

    Brent Waters

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Chardouvelis, O., Döttling, N., Malavolta, G. (2021). Rate-1 Quantum Fully Homomorphic Encryption. In: Nissim, K., Waters, B. (eds) Theory of Cryptography. TCC 2021. Lecture Notes in Computer Science(), vol 13042. Springer, Cham. https://doi.org/10.1007/978-3-030-90459-3_6

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  • DOI: https://doi.org/10.1007/978-3-030-90459-3_6

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