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Block encryption is a fundamental cryptographic primitive in modern cryptography. 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 EHE , which is a very simple method to construct quantum encryption from classical primitive. Based on EHE mode, we construct a quantum block encryption 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 the same security as quantum one-time pad, and the secret key can be securely reused for exponential times if the receiver sends a confirmation after every round of "encryption–decryption." Thus, 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." [ABSTRACT FROM AUTHOR]

Quantum homomorphic encryption (QHE) is an important cryptographic technology for delegated quantum computation. It enables remote server to perform quantum computation on encrypted 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 (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 loose requirement, e.g., quasi-compactness. This article defines encrypted gate, which is denoted by E G [ U ] : | α ⟩ → (a , b) , E n c 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 E n c a , b (U | α ⟩) , and the other party obtains the random bits a, b. Based on E G [ 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 properties, the quasi-compactness is proved to be bounded by Ω (M) , where M is the total number of T / T † -gates in the evaluated circuit. We prove VGT is M-quasi-compact and reaches the optimal bound. According to our QHE schemes, the decryption would be inefficient when 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. [ABSTRACT FROM AUTHOR]

Fully homomorphic encryption enables arbitrary computation on encrypted data without decrypting the data. Here it is studied in the context of quantum information processing. Based on universal quantum circuit, we present a quantum fully homomorphic encryption (QFHE) scheme, which permits arbitrary quantum transformation on any encrypted data. The QFHE scheme is proved to be perfectly secure. In the scheme, the decryption key is different from the encryption key; however, the encryption key cannot be revealed. Moreover, the evaluation algorithm of the scheme is independent of the encryption key, so it is suitable for delegated quantum computing between two parties. [ABSTRACT FROM AUTHOR]

Suppose some data have been encrypted, can you compute with the data without decrypting them? This problem has been studied as homomorphic encryption and blind computing. We consider this problem in the context of quantum information processing, and present the definitions of quantum homomorphic encryption (QHE) and quantum fully homomorphic encryption (QFHE). Then, based on quantum one-time pad (QOTP), we construct a symmetric QFHE scheme, where the evaluate algorithm depends on the secret key. This scheme permits any unitary transformation on any $$n$$ -qubit state that has been encrypted. Compared with classical homomorphic encryption, the QFHE scheme has perfect security. Finally, we also construct a QOTP-based symmetric QHE scheme, where the evaluate algorithm is independent of the secret key. [ABSTRACT FROM AUTHOR]