**Block encryption of quantum messages**

*Min Liang and Li Yang*

**Abstract: **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 $\mathcal{EHE}$, which is a very simple method to construct quantum encryption from classical primitive. Based on $\mathcal{EHE}$ mode, we construct a quantum block encryption (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 exponential times of encryption, 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 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 an 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.

**Category / Keywords: **secret-key cryptography / Quantum cryptography, quantum encryption, block encryption, quantum pseudorandom functions, perfect security

**Date: **received 26 Dec 2017, last revised 31 May 2018

**Contact author: **liangmin07 at mails ucas ac cn

**Available format(s): **PDF | BibTeX Citation

**Note: **23 pages, 1 figure

**Version: **20180531:141053 (All versions of this report)

**Short URL: **ia.cr/2017/1247

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