[Paper Review] Quantum authentication scheme based on algebraic coding

Rex A. C. Medeiros, Francisco de Assis+2 more|ArXiv.org|Jul 14, 2003

Quantum Computing Algorithms and Architecture4 references4 citations

TL;DR

This paper proposes a non-interactive quantum authentication protocol for classical messages of length $m$ using classical linear algebraic codes $C[n,m,t]$ and a shared $n$-bit secret key. The scheme encodes the message into a codeword, prepares $n$ qubits in bases determined by the key, and transmits them over a noiseless quantum channel; Bob verifies authenticity via a parity check on measurement outcomes. The protocol achieves information-theoretic security with failure probabilities that can be made exponentially small by choosing appropriate code parameters.

ABSTRACT

This paper presents a simple, but efficient class of non-interactive protocols for quantum authentication of $m$-length clas sical messages. The message is encoded using a classical linear algebraic code $C[n,m,t]$. We assume that Alice and Bob share a classical secret key, $x_{AB}$, of $n$ bits. Alice creates $n$ 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.

Motivation & Objective

• To develop a simple, non-interactive quantum authentication protocol for classical messages of length $m$.
• To ensure information-theoretic security by leveraging classical linear codes and quantum state preparation.
• To minimize the failure probability of message forgery under various attack models.
• To enable key reuse when the quantum channel is free of eavesdropping, enhancing protocol efficiency.
• To provide a practical alternative to existing quantum authentication schemes that rely on complex quantum operations or entangled states.

Proposed method

• A classical linear code $C[n,m,t]$ is used to encode each $m$-bit message into an $n$-bit codeword.
• Alice and Bob share an $n$-bit classical secret key $x_{AB}$, which determines the basis for preparing and measuring $n$ qubits.
• For each bit of the key, Alice prepares a qubit in the computational or Hadamard basis, encoding the codeword into a quantum state.
• The $n$-qubit state is transmitted via a noiseless quantum channel to Bob, who measures each qubit in the basis specified by the key.
• Bob performs a parity check using the parity-check matrix $H$ of the code; if $m_B H^T = 0$, the message is accepted as authentic.
• The protocol detects eavesdropping through measurement outcomes that fail the parity check, ensuring integrity.

Experimental results

Research questions

• RQ1 Can a non-interactive quantum authentication protocol be designed using only single-qubit state preparation and measurement, without requiring entanglement or complex quantum operations?
• RQ2 How does the choice of classical linear code $C[n,m,t]$ affect the failure probability of message forgery?
• RQ3 What is the relationship between the code parameters $n$ and $t$ and the security level of the protocol?
• RQ4 Can the protocol achieve information-theoretic security without relying on computational assumptions?
• RQ5 Under what conditions can the secret key be safely reused after a successful transmission?

Key findings

• For binary BCH codes of length $n=63$, the failure probability $P_f$ is $1.3 \times 10^{-8}$, and for $n=127$, it drops to $1.4 \times 10^{-16}$, demonstrating exponential security scaling.
• The probability of successful forgery under intercept-resend attacks, $P'_{f}$, is as low as $2.4 \times 10^{-26}$ for $C[127,120,1]$, showing high resilience.
• The decoding failure probability $P_{Dec}$ is extremely low, reaching $3.0 \times 10^{-32}$ for $C[127,120,1]$, indicating high reliability.
• The protocol achieves information-theoretic security, independent of computational assumptions, unlike classical MAC schemes.
• Key reuse is possible when no eavesdropping is detected, as the integrity of the quantum state ensures no key compromise.
• The scheme outperforms prior protocols in simplicity and resource efficiency, avoiding the need for quantum tag generation or entangled pairs.