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Lecture notes in computer science

Quantum-Secure Message Authentication Codes

Dan Boneh, Mark Zhandry

Published Jan 1, 2013• 130 citations
Publisher
DOI
10.1007/978-3-642-38348-9_35

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The rise of quantum computing poses significant challenges to security systems, with traditional message authentication codes (MACs) at unprecedented risk of compromise. This paper proposes a quantum message authentication code (QMAC) leveraging quantum mechanics to achieve robust security. The QMAC uses quantum one-way functions (QOWFs) to convert encrypted classical bits into qubits. This approach fundamentally differs from the computational hardness assumptions of conventional MACs. The QMAC's security is computationally difficulty-independent based on the inherent properties of quantum mechanics, making it impervious to exhaustive search attacks. Additionally, the protocol integrates authentication directly into the secure communication framework, obviating the need for extra particles and reducing computational complexity compared to stabilizer code-based or controlled unitary operations. Through a rigorous security analysis, we demonstrate the resilience of the proposed QMAC protocol against a wide range of adversarial strategies, including interception-resend attacks, identity impersonation, and entanglement-based attacks, among others.
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 this paper, we investigate multi-message authentication to combat adversaries with infinite computational capacity. An authentication framework over a wiretap channel (W1,W2)(W_1,W_2)(W1​,W2​) is proposed to achieve information-theoretic security with the same key. The proposed framework bridges the two research areas in physical (PHY) layer security: secure transmission and message authentication. Specifically, the sender Alice first transmits message MMM to the receiver Bob over (W1,W2)(W_1,W_2)(W1​,W2​) with an error correction code; then Alice employs a hash function (i.e., ε\varepsilonε-AWU2_22​ hash functions) to generate a message tag SSS of message MMM using key KKK, and encodes SSS to a codeword XnX^nXn by leveraging an existing strongly secure channel coding with exponentially small (in code length nnn) average probability of error; finally, Alice sends XnX^nXn over (W1,W2)(W_1,W_2)(W1​,W2​) to Bob who authenticates the received messages. We develop a theorem regarding the requirements/conditions for the authentication framework to be information-theoretic secure for authenticating a polynomial number of messages in terms of nnn. Based on this theorem, we propose an authentication protocol that can guarantee the security requirements, and prove its authentication rate can approach infinity when nnn goes to infinity. Furthermore, we design and implement an efficient and feasible authentication protocol over binary symmetric wiretap channel (BSWC) by using \emph{Linear Feedback Shifting Register} based (LFSR-based) hash functions and strong secure polar code. Through extensive experiments, it is demonstrated that the proposed protocol can achieve low time cost, high authentication rate, and low authentication error rate.