Quantum Homomorphic Encryption for Circuits of Low T-gate Complexity

Broadbent, Anne; Jeffery, Stacey

doi:10.1007/978-3-662-48000-7_30

Cited by 104 publications

(169 citation statements)

References 44 publications

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“…Following the definition in Ref. [33], Ref. [16] defines IND, IND-CPA and IND-CCA with an incremental way instead of interactive game.…”

Section: Quantum Block Encryptionmentioning

confidence: 99%

Block encryption of quantum messages

Liang¹,

Yang

2020

Quantum Inf Process

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In modern cryptography, block encryption is a fundamental cryptographic primitive. However, it is impossible for block encryption to achieve the same security as one-time pad. Quantum mechanics has changed the modern cryptography, and lots of researches have shown that quantum cryptography can outperform the limitation of traditional cryptography.This article proposes a new constructive mode for private quantum encryption, named E HE, which is a very simple method to construct quantum encryption from classical primitive. Based on E HE mode, we construct a quantum block encryption (QBE) scheme from pseudorandom functions. If the pseudorandom functions are standard secure, our scheme is indistinguishable encryption under chosen plaintext attack. If the pseudorandom functions are permutation on the key space, our scheme can achieve perfect security. In our scheme, the key can be reused and the randomness cannot, so a 2n-bit key can be used in an exponential number of encryptions, where the randomness will be refreshed in each time of encryption. Thus 2n-bit key can perfectly encrypt O(n2 n ) qubits, and the perfect secrecy would not be broken if the 2n-bit key is reused for only exponential times.Comparing with quantum one-time pad (QOTP), our scheme can be the same secure as QOTP, and the secret key can be reused (no matter whether the eavesdropping exists or not). Thus, the limitation of perfectly secure encryption (Shannon's theory) is broken in the quantum setting. Moreover, our scheme can be viewed as a positive answer to the open problem in quantum cryptography "how to unconditionally reuse or recycle the whole key of private-key quantum encryption". In order to physically implement the QBE scheme, we only need to implement two kinds of single-qubit gates (Pauli X gate and Hadamard gate), so it is within reach of current quantum technology. Index TermsQuantum cryptography, quantum encryption, block encryption, quantum pseudorandom functions, perfect security. I. INTRODUCTIONT HE combination of quantum mechanics and information science forms a new science -quantum information science, in which the information extends to quantum information. The requirement of processing quantum information occurs, and we have to develop quantum cryptographic technology for quantum information, e.g. encryption of quantum information. Since the quantum information can be seen as an extension of classical information in complex Hilbert space, the cryptographic schemes for quantum information are suitable for classical information, but not vice versa.Quantum information encryption is a kind of basic quantum cryptographic primitive, especially the quantum one-time pad (QOTP), which has been applied in various quantum cryptographic schemes. For example, the quantum message authentication (QMA) is applied in the constructions of secure multiparty quantum computation [1] and quantum interactive proof [2], and the authenticity of QMA can be guaranteed by quantum encryption [3].QOTP (or private quantum channel) [4]-[7] is the first kind ...

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“…Following the definition in Ref. [33], Ref. [16] defines IND, IND-CPA and IND-CCA with an incremental way instead of interactive game.…”

Section: Quantum Block Encryptionmentioning

confidence: 99%

Block encryption of quantum messages

Liang¹,

Yang

2020

Quantum Inf Process

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“…This includes topics such as the encryption of quantum messages in the information-theoretic [9,41,134,153], entropic [95,96] and computational [52] settings, quantum secret sharing [77], multi-party quantum computation [22], authentication of quantum messages [15], two-party secure function evaluation [98,99], quantum anonymous transmission [49,74], quantum one-time programs [54] and quantum homomorphic encryption [52,239].…”

Section: Further Topicsmentioning

confidence: 99%

Quantum cryptography beyond quantum key distribution

Broadbent

Schaffner

2015

Des. Codes Cryptogr.

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169

109

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Quantum cryptography is the art and science of exploiting quantum mechanical effects in order to perform cryptographic tasks. While the most well-known example of this discipline is quantum key distribution (QKD), there exist many other applications such as quantum money, randomness generation, secure two-and multi-party computation and delegated quantum computation. Quantum cryptography also studies the limitations and challenges resulting from quantum adversaries-including the impossibility of quantum bit commitment, the difficulty of quantum rewinding and the definition of quantum security models for classical primitives. In this review article, aimed primarily at cryptographers unfamiliar with the quantum world, we survey the area of theoretical quantum cryptography, with an emphasis on the constructions and limitations beyond the realm of QKD.

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“…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%

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

Liang¹

2019

Quantum Inf Process

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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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Quantum Homomorphic Encryption for Circuits of Low T-gate Complexity

Cited by 104 publications

References 44 publications

Block encryption of quantum messages

Block encryption of quantum messages

Quantum cryptography beyond quantum key distribution

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

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