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arXiv:0806.1231

Quantum Authentication of Classical Messages with Perfect Security

Francisco de Assis, Paulo Mateus, Yasser Omar

Published Jun 6, 2008• 1 citation
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Abstract

In this work we have investigated how quantum resources can improve the security of protocol for authentication of classical messages, introduced by Brassard in 1983. In that protocol, the shared key is the seed of a pseudo-random generator (PRG) and a hash function is used to create the authentication tag of a public message. We have started by showing that a BB84-type encoding of secret bits offers more security than the classicalXOR function introduced by Brassard. Furthermore, we established the conditions a general PRG must satisfy for our quantum-enhanced protocol to yield informationtheoretical security. Altogether, our proposal represents a twofold improvement: first it offers proven information-theoretical security under some assumptions on the PRG; secondly, these assumptions are weaker than the requirements for the PRG in Brassard’s protocol. Additionally, our proposal is also more practical in the sense that it requires a shorter key than the classical scheme by using the pseudorandom bits to choose the tag’s hash function. 1

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In this work we have investigated how quantum resources can improve the security of protocol for authentication of classical messages, introduced by Brassard in 1983. In that protocol, the shared key is the seed of a pseudo-random generator (PRG) and a hash function is used to create the authentication tag of a public message. We have started by showing that a BB84-type encoding of secret bits offers more security than the classicalXOR function introduced by Brassard. Furthermore, we established the conditions a general PRG must satisfy for our quantum-enhanced protocol to yield informationtheoretical security. Altogether, our proposal represents a twofold improvement: first it offers proven information-theoretical security under some assumptions on the PRG; secondly, these assumptions are weaker than the requirements for the PRG in Brassard’s protocol. Additionally, our proposal is also more practical in the sense that it requires a shorter key than the classical scheme by using the pseudorandom bits to choose the tag’s hash function. 1
We propose a quantum protocol to authenticate classical messages that can be used to replace Wegman–Carter’s classical authentication scheme in quantum key distribution (QKD) protocols. We show that the proposed scheme achieves greater conditional entropy of the seed for the intruder given her (quantum) observation than the classical case. The proposed scheme is suitable for situations where the shared symmetric key used in authentication becomes dangerously short (due to noise or eavesdropping), and there is a threat that it might be completely consumed without being replaced. Our protocol is an improvement over a classical scheme by Brassard and takes advantage of quantum channel properties. It is motivated by information-theoretical results. We stress that the proposed authentication protocol can also be used as an independent authentication protocol that is not a part of a QKD. However by adopting it, QKD becomes a fully quantum protocol. We prove that quantum resources can improve both the secrecy of the key generated by the PRG and the secrecy of the tag obtained with a hidden hash function. We conclude that the proposed quantum encoding offers more security than the classical scheme and, by applying a classical result, we show that it can be used under noisy quantum channels.
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.
Quantum authentication protocol can be used to authenticate classical messages in a secure manner. In this paper, by using the cryptographic hash function and non-orthogonal qubits, a quantum authentication protocol of classical messages is proposed. In our protocol, the classical messages and their corresponding tags are encoded as nonorthogonal qubits. The message receiver decodes the classical messages and their corresponding tags from the received qubits by using the authentication key. To verify the validity of the received classical messages, the message receiver verifies whether the hash values of the decoded classical messages are equal to the corresponding tags. Our scheme can be proved to be secure against forgery attack and measurement attack. On the other hand, the authentication key is a binary string, which can be securely obtained and easily saved. What is more, because the authentication key remains secure after executing the authentication protocol, it provides the possibility of reusing the authentication key.
Classical messages can be authenticated by traditional authentication protocols based on hash functions.The security of these protocols depends on long authentication keys, the selection of appropriate hash functions and some assumptions concerning the computational complexity of some algorithms.In this paper, by encoding the classical binary messages and binary keys as nonorthogonal quantum messages and nonorthogonal sets of states, respectively, and using quantum encrypting scheme, a new quantum authentication protocol is proposed.In our protocol, instead of entangled quantum states, the traditional binary bits, which can be easily saved, are encoded as quantum keys.Because the quantum messages are nonorthogonal, any forgery or measurement on the quantum messages will be detected with a certain probability.Our protocol allows the authentication of binary classical messages in a secure manner.
Authentication is a well-studied area of classical cryptography: a sender A and a receiver B sharing a classical secret key want to exchange a classical message with the guarantee that the message has not been modified or replaced by a dishonest party with control of the communication line. In this paper we study the authentication of messages composed of quantum states. We give a formal definition of authentication in the quantum setting. Assuming A and B have access to an insecure quantum channel and share a secret, classical random key, we provide a non-interactive scheme that enables A to both encrypt and authenticate an m qubit message by encoding it into m+s qubits, where the error probability decreases exponentially in the security parameter s. The scheme requires a secret key of size 2m+O(s). To achieve this, we give a highly efficient protocol for testing the purity of shared EPR pairs. It has long been known that learning information about a general quantum state will necessarily disturb it. We refine this result to show that such a disturbance can be done with few side effects, allowing it to circumvent cryptographic protections. Consequently, any scheme to authenticate quantum messages must also encrypt them. In contrast, no such constraint exists classically. This reasoning has two important consequences: It allows us to give a lower bound of 2m key bits for authenticating m qubits, which makes our protocol asymptotically optimal. Moreover, we use it to show that digitally signing quantum states is impossible.