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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]

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]