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arXiv:quant-ph/0310078

Quantum message authentication based on classical NP-complete problem

Li Yang, Lei Hu, Dengguo Feng

Published Oct 12, 2003• 4 citations
arXivHTMLPDF

Abstract

This note presents a method to authenticate a quantum message based on classical SN-S authentication code and the computations between different quantum registers. If the pre-coding generator matrix in SN-S code is public, the quantum scheme is a public-key data integrity scheme; if it is secret, the quantum scheme is a hybrid data origin authentication scheme.

DOI
10.48550/arxiv.quant-ph/0310078

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This note presents a method to authenticate a quantum message based on classical SN-S authentication code and the computations between different quantum registers. If the pre-coding generator matrix in SN-S code is public, the quantum scheme is a public-key data integrity scheme; if it is secret, the quantum scheme is a hybrid data origin authentication scheme.
Public-key cryptosystems for quantum messages are considered from two aspects: public-key encryption and public-key authentication. Firstly, we propose a general construction of quantum public-key encryption scheme, and then construct an information-theoretic secure instance. Then, we propose a quantum public-key authentication scheme, which can protect the integrity of quantum messages. This scheme can both encrypt and authenticate quantum messages. It is information-theoretic secure with regard to encryption, and the success probability of tampering decreases exponentially with the security parameter with regard to authentication. Compared with classical public-key cryptosystems, one private-key in our schemes corresponds to an exponential number of public-keys, and every quantum public-key used by the sender is an unknown quantum state to the sender.
We present a quantum public-key cryptography protocol for quantum message transmission. The private key of this protocol includes three classical matrices: a generator matrix of a Goppa code, an invertible matrix and a permutation matrix. The public key is product of these three matrices. The encryption and decryption algorithms are merely quantum computations related with the transformations between bases of the quantum registers. The security of this protocol is based on the hypothesis that there is no effective algorithm of NP-complete problem.
Abstract We propose a quantum message authentication scheme that provides integrity and origin authentication using a remote state preparation. Authentication is one of the security services that must be provided in secure communication. Quantum message authentication is the base scheme for realizing quantum authentication that is known to be a secure technique even in a forthcoming quantum computer environment. The proposed scheme creates a quantum message authentication code (QMAC) with only a single qubit measurement. It is therefore easy to implement and operate compared to existing technology that normally generates a QMAC with a Bell measurement or controlled unitary operation. For security analysis, we design a quantum random oracle model based on the random oracle model and demonstrate the quantum collision resistance with it. From the analysis, the probability of the quantum collision is 0.69 N per qubit, where N is the size of the message sequence. Since the probability of quantum collision in the case of N ≥ 13 becomes extremely low of under 0.8%, we confirm that the proposed scheme guarantees the integrity and origin authentication of the message.
In conventional cryptography, information-theoretically secure message authentication can be achieved by means of universal hash functions, and requires that the two legitimate users share a random secret key, which is at least twice as long as the tag. We address the question of whether quantum resources can offer any advantage over classical unconditionally secure message authentication codes. It is shown that a broad class of symmetric prepare-and-measure quantum message-authentication schemes cannot do better than their classical counterparts.
In conventional cryptography, information-theoretically secure message authentication can be achieved by means of universal hash functions, and requires that the two legitimate users share a random secret key, which is at least twice as long as the tag. We address the question of whether quantum resources can offer any advantage over classical unconditionally secure message authentication codes. It is shown that a broad class of symmetric prepare-and-measure quantum message-authentication schemes cannot do better than their classical counterparts.