Paper 2017/1247

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.

Note: 23 pages, 1 figure

Metadata
Available format(s)
PDF
Category
Secret-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
Quantum cryptographyquantum encryptionblock encryptionquantum pseudorandom functionsperfect security
Contact author(s)
liangmin07 @ mails ucas ac cn
History
2018-05-31: revised
2017-12-30: received
See all versions
Short URL
https://ia.cr/2017/1247
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2017/1247,
      author = {Min Liang and Li Yang},
      title = {Block encryption of quantum messages},
      howpublished = {Cryptology ePrint Archive, Paper 2017/1247},
      year = {2017},
      note = {\url{https://eprint.iacr.org/2017/1247}},
      url = {https://eprint.iacr.org/2017/1247}
}
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