# Quantum Authentication Evolution: Novel Approaches for Securing Quantum Key Distribution
## 5 QKD Authentication Model Setup and Details
### Mono-Authentication
A comparison between \(F^{\prime}\) and \(F^{\prime\prime}\) is then made, and any disparity (\(F^{\prime}\
eq F^{\prime\prime}\)) indicates errors within the key. To rectify these errors, [PERSON] systematically tests bit flips in his key until the computed hashes match. This meticulous process ensures alignment between the keys of [PERSON] and [PERSON]. Importantly, for potential eavesdroppers attempting to compromise the key, the task of brute-forcing a pre-image of the hash is impractical and computationally daunting. This robust approach underscores the security of the key exchange, instilling confidence in the unassailable integrity of the shared secret key. To mitigate the computational burden associated with lengthy calculations, the implementation strategically limits the acceptable number of errors in the used key, a crucial parameter known as the maximum corrected errors. [PERSON] systematically explores various combinations, initially attempting to flip one bit of his key at a time and comparing each potential option's hash to \(F^{\prime}\). If this initial search fails, he repeats the process with two errors, continuing until conducting a brute force search capped at a predetermined maximum number of errors. If [PERSON] exhausts all combinations without finding a hash match, he discards the key, triggering a restart of the QKD process--an abortive measure. Conversely, upon discovering matching hashes, he corrects these errors, resulting in the refined secret key denoted as \(\Psi_{kAB^{\prime}}^{B}\). Subsequently, [PERSON] proceeds with privacy amplification, culminating in the generation of the shared secret key \(\Psi_{skAB}^{B}=F\ \big{(}P\big{(}\Psi_{kAB^{\prime}}^{B}\big{)}\big{)}\), where \(\Psi_{skAB}^{B}=\Psi_{kAB}^{A}\), indicating the successful exchange of a secret key utilizing quantum states. A detailed schematic of this process is depicted in Figure 1, illustrating the sequential steps involved in this mono-authentication style. Within the mono-authentication approach, only two signatures are executed at the conclusion of the communication. An important consideration in this process is the error correction applied to the exchanged bit string. In scenarios where the key undergoes correction and the process is restarted, certain signatures may be discarded. In the context of mono-signature, emphasis is placed on the non-aborted instances, ensuring that only successfully completed signatures contribute to the authentication process. First and foremost, the process begins with the invocation of \(PQAlg.KeyGen()\), a function that generates both secret keys (SK) and public keys (PK) for users [PERSON] and [PERSON]. PQAlg specifically represents the chosen post-quantum algorithm implemented for authentication purposes. Integral to the authentication process are the signatures (\(\sigma\)), produced as outputs of the \(PQAlg.Sign_{SK}()\) functions. These signatures play a crucial role and are transmitted through the classical channel. The subsequent verification step is pivotal. Utilizing \(PQAlg.Verify_{PK}()\), the received signatures undergo scrutiny to determine their authenticity. The success of this authentication process dictates the seamless continuation of subsequent steps within the protocol. This comprehensive overview sheds light on the intricacies of the BB84 protocol's signature style, encompassing key generation, communication modalities, signature generation, and the critical verification step that ensures the integrity of the authentication process. Our authentication protocol incorporates a PK infrastructure enhanced with PQC algorithms, including CRYSTALS-DILITHUM, SPHINCS+, and RAINBOW. Both the transmitter and receiver exchange certificates and sign the message with their private keys, subsequently verifying the signatures using public keys. To mitigate replay attacks, our mono-authentication protocol integrates the use of a nonce.