# Quantum Authentication Evolution: Novel Approaches for Securing Quantum Key Distribution
## 6 Outcomes of QKD Mono-Authentication
It is noteworthy that these results were derived after conducting a comprehensive analysis of the time taken by each algorithm to authenticate a range of bits, approximately from 0 to 2000, prior to averaging them to obtain the presented outcomes. In Table 4, we determine the rate at which each algorithm can generate signatures per second relative to a given key rate. Since none of the algorithms complete an exchange of more than 2000 bits within the specified time intervals, continuous authentication remains feasible within those periods. Notably, CRYSTALS-DILITHIUM displays the highest throughput, while RAINBOW exhibits the slowest performance. For example, considering a key rate of 100 kbps, the minimal duration required to authenticate the transmitted data within the designated timeframe is 0.0011 s.  
The mono-authentication approach significantly enhances authentication efficiency by delivering results swiftly. Noise serves as a critical factor amplifying the divergence in performance between verification and signature methods, as well as in overhead authentication. It is noteworthy that in noisy channel environments, mono-authentication emerges as the optimal implementation, as it remains unaffected by any QKD parameter. In contexts where the quantum channel incurs substantial costs, meticulous error scrutiny takes precedence. Conversely, in scenarios with exceptionally economical quantum channels, the preferred strategy often involves discarding keys and initiating fresh exchanges. Figure 5: The varying security bits led to the key’s rejection, correlating with the number of bits selected for correction. In our evaluation of post-quantum algorithms, CRYSTALS-DILITHIUM has consistently demonstrated outstanding performance in total authentication time, encompassing both signature and verification phases. Remarkably, CRYSTALS-DILITHIUM exhibits minimal overhead, consistently below 0.5% for both BB84 and SARG04 protocols. Further exploration across various security levels reveals a discernible trend: as authentication costs rise, processing durations extend. Consequently, transactions with lower security bit levels tend to feature shorter authentication times. To conclude, the analysis of recommendations across different key rates consistently highlights CRYSTALS-DILITHIUM's superior performance over the RAINBOW post-quantum scheme. In the final phase, we successfully applied the PQC CRYSTALS-DILITHIUM algorithm within the context of a QKD point-to-point link, spanning fiber distances ranging from 1 to 1000 km. As depicted in Figure 7, the key rates exhibit a characteristic decline with increasing fiber length, aligning closely with theoretical predictions. To gain further insights, we conducted a comparative analysis of key rates across varying fiber lengths, employing both the QKD-BB84 and QKD-SARG04 protocols. Notably, the disparity in average key rates between the two protocols was found to be less than 0.5 standard deviations, indicating a high degree of consistency in their performance. In contrast, we conducted a comparison between our theoretical QKD system, utilizing the PQC mono-authentication CRYSTALS-DILITHIUM algorithm, and an experimental PQC authentication method employing the Shor algorithm [23]. Our algorithm demonstrates a superior key rate of up to 10,000 kb/s and supports longer fiber lengths of up to 1000 km. However, it requires experimental validation, which constitutes a primary objective of our future research endeavors. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{3}{c}{**Post-Quantum Algorithms**} \\ \hline \multirow{2}{*}{**Security Bits**} & \multirow{2}{*}{**Key Rate (kb/s)**} & **CRYSTALS-DILITHIUM** & **RAINBOW** \\  & & **Time (s)** & **Time (s)** \\ \hline
128 & 100 & 0.0011 & 0.11 \\
192 & 1000 & 0.0024 & 0.14 \\
256 & 10,000 & 0.0088 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The minimum duration required by each post-quantum signature algorithm for mono-authentication, expressed in terms of key rate.