On statistically-secure quantum homomorphic encryption

Homomorphic encryption is an encryption scheme that allows computations to be evaluated on encrypted inputs without knowledge of their raw messages. Recently Ouyang et al. constructed a quantum homomorphic encryption (QHE) scheme for Clifford circuits with statistical security (or information-theoretic security (IT-security)). It is desired to see whether an information-theoretically-secure (ITS) quantum FHE exists. If not, what other nontrivial class of quantum circuits can be homomorphically evaluated with IT-security? We provide a limitation for the first question that an ITS quantum FHE necessarily incurs exponential overhead. As for the second one, we propose a QHE scheme for the instantaneous quantum polynomial-time (IQP) circuits. Our QHE scheme for IQP circuits follows from the one-time pad.

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Physical-layer encryption on the public internet: A stochastic approach to the Kish-Sethuraman cipher

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194514603615 ◽

2014 ◽

Vol 33 ◽

pp. 1460361 ◽

Cited By ~ 1

Author(s):

Lachlan J. Gunn ◽

James M. Chappell ◽

Andrew Allison ◽

Derek Abbott

Keyword(s):

Quantum Key Distribution ◽

Secure Communication ◽

Key Distribution ◽

Stochastic Approach ◽

Physical Layer ◽

Information Theoretic ◽

The Public ◽

Information Theoretic Security ◽

Transit Times ◽

The One

While information-theoretic security is often associated with the one-time pad and quantum key distribution, noisy transport media leave room for classical techniques and even covert operation. Transit times across the public internet exhibit a degree of randomness, and cannot be determined noiselessly by an eavesdropper. We demonstrate the use of these measurements for information-theoretically secure communication over the public internet.

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Merlin-Arthur with efficient quantum Merlin and quantum supremacy for the second level of the Fourier hierarchy

Quantum ◽

10.22331/q-2018-11-15-106 ◽

2018 ◽

Vol 2 ◽

pp. 106 ◽

Cited By ~ 5

Author(s):

Tomoyuki Morimae ◽

Yuki Takeuchi ◽

Harumichi Nishimura

Keyword(s):

Quantum Computing ◽

Polynomial Time ◽

Probability Distributions ◽

Quantum Circuits ◽

Universal Models ◽

Reversible Circuit ◽

Universal Quantum ◽

Quantum Polynomial ◽

Output Probability ◽

Probabilistic Polynomial Time

We introduce a simple sub-universal quantum computing model, which we call the Hadamard-classical circuit with one-qubit (HC1Q) model. It consists of a classical reversible circuit sandwiched by two layers of Hadamard gates, and therefore it is in the second level of the Fourier hierarchy. We show that output probability distributions of the HC1Q model cannot be classically efficiently sampled within a multiplicative error unless the polynomial-time hierarchy collapses to the second level. The proof technique is different from those used for previous sub-universal models, such as IQP, Boson Sampling, and DQC1, and therefore the technique itself might be useful for finding other sub-universal models that are hard to classically simulate. We also study the classical verification of quantum computing in the second level of the Fourier hierarchy. To this end, we define a promise problem, which we call the probability distribution distinguishability with maximum norm (PDD-Max). It is a promise problem to decide whether output probability distributions of two quantum circuits are far apart or close. We show that PDD-Max is BQP-complete, but if the two circuits are restricted to some types in the second level of the Fourier hierarchy, such as the HC1Q model or the IQP model, PDD-Max has a Merlin-Arthur system with quantum polynomial-time Merlin and classical probabilistic polynomial-time Arthur.

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Impossibility of blind quantum sampling for classical client

Quantum Information and Computation ◽

10.26421/qic19.9-10-3 ◽

2019 ◽

Vol 19 (9&10) ◽

pp. 793-806

Author(s):

Tomoyuki Morimae ◽

Harumichi Nishimura ◽

Yuki Takeuch ◽

Seiichiro Tani

Keyword(s):

Quantum Computing ◽

Polynomial Time ◽

Open Problem ◽

Input Output ◽

Information Theoretic ◽

Single Qubit ◽

The Third ◽

The One ◽

Qubit States ◽

Polynomial Time Hierarchy

Blind quantum computing enables a client, who can only generate or measure single-qubit states, to delegate quantum computing to a remote quantum server in such a way that the input, output, and program are hidden from the server. It is an open problem whether a completely classical client can delegate quantum computing blindly (in the information theoretic sense). In this paper, we show that if a completely classical client can blindly delegate sampling of subuniversal models, such as the DQC1 model and the IQP model, then the polynomial-time hierarchy collapses to the third level. Our delegation protocol is the one where the client first sends a polynomial-length bit string to the server and then the server returns a single bit to the client. Generalizing the no-go result to more general setups is an open problem.

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EXACT NON-IDENTITY CHECK IS NQP-COMPLETE

International Journal of Quantum Information ◽

10.1142/s0219749910006599 ◽

2010 ◽

Vol 08 (05) ◽

pp. 807-819

Author(s):

YU TANAKA

Keyword(s):

Computational Complexity ◽

Polynomial Time ◽

Decision Problem ◽

Quantum Circuit ◽

Quantum Circuits ◽

Quantum Gates ◽

Unitary Operation ◽

Classical Description ◽

Quantum Polynomial ◽

Equivalence Check

To understand quantum gate array complexity, we define a problem named exact non-identity check, which is a decision problem to determine whether a given classical description of a quantum circuit is strictly equivalent to the identity or not. We show that the computational complexity of this problem is non-deterministic quantum polynomial-time (NQP)-complete. As corollaries, it is derived that exact non-equivalence check of two given classical descriptions of quantum circuits is also NQP-complete and that minimizing the number of quantum gates for a given quantum circuit without changing the implemented unitary operation is NQP-hard.

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Achieving quantum supremacy with sparse and noisy commuting quantum computations

Quantum ◽

10.22331/q-2017-04-25-8 ◽

2017 ◽

Vol 1 ◽

pp. 8 ◽

Cited By ~ 53

Author(s):

Michael J. Bremner ◽

Ashley Montanaro ◽

Dan J. Shepherd

Keyword(s):

Probability Distribution ◽

Error Correction ◽

Polynomial Time ◽

Quantum Circuits ◽

Square Lattice ◽

Constant Amount ◽

Small Constant ◽

Variation Distance ◽

Quantum Polynomial ◽

Output Probability

The class of commuting quantum circuits known as IQP (instantaneous quantum polynomial-time) has been shown to be hard to simulate classically, assuming certain complexity-theoretic conjectures. Here we study the power of IQP circuits in the presence of physically motivated constraints. First, we show that there is a family of sparse IQP circuits that can be implemented on a square lattice of n qubits in depth O(sqrt(n) log n), and which is likely hard to simulate classically. Next, we show that, if an arbitrarily small constant amount of noise is applied to each qubit at the end of any IQP circuit whose output probability distribution is sufficiently anticoncentrated, there is a polynomial-time classical algorithm that simulates sampling from the resulting distribution, up to constant accuracy in total variation distance. However, we show that purely classical error-correction techniques can be used to design IQP circuits which remain hard to simulate classically, even in the presence of arbitrary amounts of noise of this form. These results demonstrate the challenges faced by experiments designed to demonstrate quantum supremacy over classical computation, and how these challenges can be overcome.

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Low Size Cipher Text Homomorphic Encryption Scheme for Cloud Data

International Journal of Private Cloud Computing Environment and Management ◽

10.21742/ijpccem.2017.4.1.02 ◽

2017 ◽

Vol 4 (1) ◽

pp. 13-20

Author(s):

Manish M. Potey ◽

◽

C. A. Dhote ◽

Deepak H. Sharma ◽

◽

...

Keyword(s):

Homomorphic Encryption ◽

Encryption Scheme ◽

Cloud Data ◽

Cipher Text

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Device-independent quantum key distribution with random key basis

Nature Communications ◽

10.1038/s41467-021-23147-3 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

René Schwonnek ◽

Koon Tong Goh ◽

Ignatius W. Primaatmaja ◽

Ernest Y.-Z. Tan ◽

Ramona Wolf ◽

...

Keyword(s):

Quantum Key Distribution ◽

Bell Inequality ◽

Key Distribution ◽

Theory And Practice ◽

Information Theoretic ◽

Information Theoretic Security ◽

Experimental Parameters ◽

Secret Keys ◽

Simple Variant ◽

First Time

AbstractDevice-independent quantum key distribution (DIQKD) is the art of using untrusted devices to distribute secret keys in an insecure network. It thus represents the ultimate form of cryptography, offering not only information-theoretic security against channel attacks, but also against attacks exploiting implementation loopholes. In recent years, much progress has been made towards realising the first DIQKD experiments, but current proposals are just out of reach of today’s loophole-free Bell experiments. Here, we significantly narrow the gap between the theory and practice of DIQKD with a simple variant of the original protocol based on the celebrated Clauser-Horne-Shimony-Holt (CHSH) Bell inequality. By using two randomly chosen key generating bases instead of one, we show that our protocol significantly improves over the original DIQKD protocol, enabling positive keys in the high noise regime for the first time. We also compute the finite-key security of the protocol for general attacks, showing that approximately 108–1010 measurement rounds are needed to achieve positive rates using state-of-the-art experimental parameters. Our proposed DIQKD protocol thus represents a highly promising path towards the first realisation of DIQKD in practice.

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