Quantum fully homomorphic encryption scheme based on universal quantum circuit

Liang, Min

doi:10.1007/s11128-015-1034-9

Cited by 54 publications

(35 citation statements)

References 35 publications

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“…Our two protocols are based on perfectly secure QHE (or secure delegated QC); 6,8,9 they can retain security if extra steps they take and extra data they reveal with respect to the basic QHE do not cause any damage.…”

Section: Security and Performancementioning

confidence: 99%

Quantum Search on Encrypted Data Based on Quantum Homomorphic Encryption

Zhou

Cui

et al. 2020

Sci Rep

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We propose a blind quantum search protocol based on quantum homomorphic encryption, in which a client Alice with limited quantum ability can give her encrypted data to a powerful but untrusted quantum server and let the server search for her without decryption. By outsourcing the interactive key update process to a trusted key center, Alice only needs to encrypt her original data and decrypt the ciphered search result in linear time, and perfectly conceals the underlying plaintext from the search server as well. Besides, we also present a compact and secure quantum homomorphic evaluation protocol for Clifford circuits, where all possible keys are updated in parallel by the evaluator, and another server who would not contact the evaluator then searches out the true decryption key. In contrast with the CL scheme proposed by Broadbent, such protocol does not need any help from classical homomorphic encryption to achieve compactness.Please note: Abbreviations should be introduced at the first mention in the main text -no abbreviations lists. Suggested structure of main text (not enforced) is provided below. arXiv:1711.10066v2 [quant-ph] 25 Nov 2018 1. Randomly generate a four-bit encryption key ek = (x 0 , z 0 ) for |ψ . 6/15 15/15

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Section: Security and Performancementioning

confidence: 99%

Quantum Search on Encrypted Data Based on Quantum Homomorphic Encryption

Zhou

Cui

et al. 2020

Sci Rep

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“…The QHE scheme in Ref. [9] realizes T -gate homomorphically, however an interaction are used to remove P -error that occurs in the homomorphic evaluation of T -gate: whenever Server performs a T -gate on a qubit, he sends the qubit to Client; Then Client performs a quantum operator P x (x is a secret bit which is known only by Client) 2 on the qubit and returns it to Server.…”

Section: Homomorphic Evaluation Of T -Gatementioning

confidence: 99%

“…For example, the scheme in Ref. [9] uses a few interactions, and its total number is the same as that of T -gates. Because the interactions necessarily decrease the efficiency of the protocol, this article focuses on interactive QHE scheme.…”

Section: Introductionmentioning

confidence: 99%

“…Later, the researchers study QHE schemes with certain loosen condition. For example, the interactivity is allowed in the schemes [9,14], the expected security level is computational security [15,16], the client accommodates the server with enough copies of encrypted ancillary states [17,18]. The scheme in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…Refs. [17,18] associate homomorphic encryption with transversal computation, and propose non-interactive QFHE schemes based on quantum codes. In their schemes, Client must provide Server with sufficient copies of certain encrypted ancillary state; Too many copies of the ancillary states would leak some information about the secret key, so this kind of construction cannot achieve perfect security.…”

Section: Introductionmentioning

confidence: 99%

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Teleportation-based quantum homomorphic encryption scheme with quasi-compactness and perfect security

Liang¹

2019

Quantum Inf Process

Self Cite

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Quantum homomorphic encryption (QHE) is an important cryptographic technology for delegated quantum computation. It enables remote Server performing quantum computation on encrypted quantum data, and the specific algorithm performed by Server is unnecessarily known by Client. Quantum fully homomorphic encryption (QFHE) is a QHE that satisfies both compactness and F-homomorphism, which is homomorphic for any quantum circuits. However, Yu et al.[Phys. Rev. A 90, 050303(2014)] proved a negative result: assume interaction is not allowed, it is impossible to construct perfectly secure QFHE scheme. So this article focuses on non-interactive and perfectly secure QHE scheme with loosen requirement, specifically quasi-compactness. This article defines encrypted gate, which is denoted by EG[U ] : |α → ((a, b), Enc a,b (U |α )). We present a gate-teleportation-based two-party computation scheme for EG[U ], where one party gives arbitrary quantum state |α as input and obtains the encrypted U -computing result Enc a,b (U |α ), and the other party obtains the random bits a, b. Based on EG[P x ](x ∈ {0, 1}), we propose a method to remove the P -error generated in the homomorphic evaluation of T /T † -gate. Using this method, we design two non-interactive and perfectly secure QHE schemes named GT and VGT. Both of them are F-homomorphic and quasi-compact (the decryption complexity depends on the T /T † -gate complexity). Assume F-homomorphism, non-interaction and perfect security are necessary property, the quasi-compactness is proved to be bounded by O(M ), where M is the total number of T /T † -gates in the evaluated circuit. VGT is proved to be optimal and has M -quasi-compactness. According to our QHE schemes, the decryption would be inefficient if the evaluated circuit contains exponential number of T /T † -gates. Thus our schemes are suitable for homomorphic evaluation of any quantum circuit with low T /T † -gate complexity, such as any polynomial-size quantum circuit or any quantum circuit with polynomial number of T /T † -gates.

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QFactory: Classically-Instructed Remote Secret Qubits Preparation

Cojocaru

Colisson

Kashefi

et al. 2019

Lecture Notes in Computer Science

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The functionality of classically-instructed remotely prepared random secret qubits was introduced in (Cojocaru et al 2018) as a way to enable classical parties to participate in secure quantum computation and communications protocols. The idea is that a classical party (client) instructs a quantum party (server) to generate a qubit to the server's side that is random, unknown to the server but known to the client. Such task is only possible under computational assumptions. In this contribution we define a simpler (basic) primitive consisting of only BB84 states, and give a protocol that realizes this primitive and that is secure against the strongest possible adversary (an arbitrarily deviating malicious server). The specific functions used, were constructed based on known trapdoor one-way functions, resulting to the security of our basic primitive being reduced to the hardness of the Learning With Errors problem. We then give a number of extensions, building on this basic module: extension to larger set of states (that includes non-Clifford states); proper consideration of the abort case; and verifiablity on the module level. The latter is based on "blind self-testing", a notion we introduced, proved in a limited setting and conjectured its validity for the most general case.

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Quantum fully homomorphic encryption scheme based on universal quantum circuit

Cited by 54 publications

References 35 publications

Quantum Search on Encrypted Data Based on Quantum Homomorphic Encryption

Quantum Search on Encrypted Data Based on Quantum Homomorphic Encryption

Teleportation-based quantum homomorphic encryption scheme with quasi-compactness and perfect security

QFactory: Classically-Instructed Remote Secret Qubits Preparation

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