1,025 research outputs found
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
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
Delegating Quantum Computation in the Quantum Random Oracle Model
A delegation scheme allows a computationally weak client to use a server's
resources to help it evaluate a complex circuit without leaking any information
about the input (other than its length) to the server. In this paper, we
consider delegation schemes for quantum circuits, where we try to minimize the
quantum operations needed by the client. We construct a new scheme for
delegating a large circuit family, which we call "C+P circuits". "C+P" circuits
are the circuits composed of Toffoli gates and diagonal gates. Our scheme is
non-interactive, requires very little quantum computation from the client
(proportional to input length but independent of the circuit size), and can be
proved secure in the quantum random oracle model, without relying on additional
assumptions, such as the existence of fully homomorphic encryption. In practice
the random oracle can be replaced by an appropriate hash function or block
cipher, for example, SHA-3, AES.
This protocol allows a client to delegate the most expensive part of some
quantum algorithms, for example, Shor's algorithm. The previous protocols that
are powerful enough to delegate Shor's algorithm require either many rounds of
interactions or the existence of FHE. The protocol requires asymptotically
fewer quantum gates on the client side compared to running Shor's algorithm
locally.
To hide the inputs, our scheme uses an encoding that maps one input qubit to
multiple qubits. We then provide a novel generalization of classical garbled
circuits ("reversible garbled circuits") to allow the computation of Toffoli
circuits on this encoding. We also give a technique that can support the
computation of phase gates on this encoding.
To prove the security of this protocol, we study key dependent message(KDM)
security in the quantum random oracle model. KDM security was not previously
studied in quantum settings.Comment: 41 pages, 1 figures. Update to be consistent with the proceeding
versio
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
Ring Learning With Errors: A crossroads between postquantum cryptography, machine learning and number theory
The present survey reports on the state of the art of the different
cryptographic functionalities built upon the ring learning with errors problem
and its interplay with several classical problems in algebraic number theory.
The survey is based to a certain extent on an invited course given by the
author at the Basque Center for Applied Mathematics in September 2018.Comment: arXiv admin note: text overlap with arXiv:1508.01375 by other
authors/ comment of the author: quotation has been added to Theorem 5.
Lattice-Based proof of a shuffle
In this paper we present the first fully post-quantum proof of a shuffle for RLWE encryption schemes. Shuffles are commonly used to construct mixing networks (mix-nets), a key element to ensure anonymity in many applications such as electronic voting systems. They should preserve anonymity even against an attack using quantum computers in order to guarantee long-term privacy. The proof presented in this paper is built over RLWE commitments which are perfectly binding and computationally hiding under the RLWE assumption, thus achieving security in a post-quantum scenario. Furthermore we provide a new definition for a secure mixing node (mix-node) and prove that our construction satisfies this definition.Peer ReviewedPostprint (author's final draft
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