379 research outputs found
Limitations on information-theoretically-secure quantum homomorphic encryption
Homomorphic encryption is a form of encryption which allows computation to be carried out on the encrypted data without the need for decryption. The success of quantum approaches to related tasks in a delegated computation setting has raised the question of whether quantum mechanics may be used to achieve information-theoretically-secure fully homomorphic encryption. Here we show, via an information localization argument, that deterministic fully homomorphic encryption necessarily incurs exponential overhead if perfect security is required
Experimental Demonstration of Quantum Fully Homomorphic Encryption with Application in a Two-Party Secure Protocol
A fully homomorphic encryption system hides data from unauthorized parties,
while still allowing them to perform computations on the encrypted data. Aside
from the straightforward benefit of allowing users to delegate computations to
a more powerful server without revealing their inputs, a fully homomorphic
cryptosystem can be used as a building block in the construction of a number of
cryptographic functionalities. Designing such a scheme remained an open problem
until 2009, decades after the idea was first conceived, and the past few years
have seen the generalization of this functionality to the world of quantum
machines. Quantum schemes prior to the one implemented here were able to
replicate some features in particular use-cases often associated with
homomorphic encryption but lacked other crucial properties, for example,
relying on continual interaction to perform a computation or leaking
information about the encrypted data. We present the first experimental
realisation of a quantum fully homomorphic encryption scheme. We further
present a toy two-party secure computation task enabled by our scheme. Finally,
as part of our implementation, we also demonstrate a post-selective two-qubit
linear optical controlled-phase gate with a much higher post-selection success
probability (1/2) when compared to alternate implementations, e.g. with
post-selective controlled- or controlled- gates (1/9).Comment: 11 pages, 16 figures, 2 table
Classical Homomorphic Encryption for Quantum Circuits
We present the first leveled fully homomorphic encryption scheme for quantum
circuits with classical keys. The scheme allows a classical client to blindly
delegate a quantum computation to a quantum server: an honest server is able to
run the computation while a malicious server is unable to learn any information
about the computation. We show that it is possible to construct such a scheme
directly from a quantum secure classical homomorphic encryption scheme with
certain properties. Finally, we show that a classical homomorphic encryption
scheme with the required properties can be constructed from the learning with
errors problem
Quantum Fully Homomorphic Encryption With Verification
Fully-homomorphic encryption (FHE) enables computation on encrypted data
while maintaining secrecy. Recent research has shown that such schemes exist
even for quantum computation. Given the numerous applications of classical FHE
(zero-knowledge proofs, secure two-party computation, obfuscation, etc.) it is
reasonable to hope that quantum FHE (or QFHE) will lead to many new results in
the quantum setting. However, a crucial ingredient in almost all applications
of FHE is circuit verification. Classically, verification is performed by
checking a transcript of the homomorphic computation. Quantumly, this strategy
is impossible due to no-cloning. This leads to an important open question: can
quantum computations be delegated and verified in a non-interactive manner? In
this work, we answer this question in the affirmative, by constructing a scheme
for QFHE with verification (vQFHE). Our scheme provides authenticated
encryption, and enables arbitrary polynomial-time quantum computations without
the need of interaction between client and server. Verification is almost
entirely classical; for computations that start and end with classical states,
it is completely classical. As a first application, we show how to construct
quantum one-time programs from classical one-time programs and vQFHE.Comment: 30 page
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