Block encryption of quantum messages

Abstract

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 $\mathcal {EHE}$, which is a very simple method to construct quantum encryption from classical primitive. Based on $\mathcal {EHE}$ 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.”