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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum message authentication based on algebraic coding theory

Li Yang, Lei Hu, Dengguo Feng

Published Jan 11, 2005• 1 citation
Publisher

Abstract

We present a new type of authentication scheme for quantum message based on algebraic coding theory and quantum computation operations between different quantum registers. The results are that 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. The advantage of this scheme is that the public and secret keys are merely some classical data.

DOI
10.1117/12.576777

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We present a new type of authentication scheme for quantum message based on algebraic coding theory and quantum computation operations between different quantum registers. The results are that 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. The advantage of this scheme is that the public and secret keys are merely some classical data.
This paper presents a simple, but efficient class of non-interactive protocols for quantum authentication of mmm-length clas sical messages. The message is encoded using a classical linear algebraic code C[n,m,t]C[n,m,t]C[n,m,t]. We assume that Alice and Bob share a classical secret key, xABx_{AB}xAB​, of nnn bits. Alice creates nnn qubits based on the code word and the key, that indicates the bases used to create each qubit. The quantum states are sent to Bob through a noiseless quantum channel. We calculate the failure probability of the protocol considering several types of attacks.
A quantum cryptosystem based on algebraic codes, which uses single photons as quantum message carriers, is given. The cryptosystem is equipped with authentication, data integrity, and non-repudiation. There is no need for a parallel classical channel since public conversation is omitted. Indeed by using a suitable algebraic error-correcting code, Alice and Bob do not need to share a string of common bases. Therefore, they already share only one secret key for encryption. The secret key can be reused many times also in a noisy environment. The encryption and the decryption are similar, so the cryptosystem can be thought symmetric. Analysis shows that the cryptosystem is secure, low cost, and more practical compared with the previous ones.
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.
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.