# Quantum Authentication Evolution: Novel Approaches for Securing Quantum Key Distribution
## 6 Outcomes of QKD Mono-Authentication  
Findings are presented by concerning two transmission scenarios: block-based and continuous photon wave, which can be generated through a tunable laser, spontaneous parametric down conversion (SPDC), an optical parametric generator (OPG), or an optical parametric oscillator (OPO). Our analysis comprises 100 iterations for the mono-authentication algorithm based on the BB84 and SARG04 protocols. We evaluate the efficacy of various post-quantum algorithms in the mono-authentication method across different parameters. Initially, we analyze how the outcomes are influenced by the level of noise present in the quantum channel and then in continuous photon stream. Regarding the mono-authentication method, we observe in the plot that the SARG04 signature times are always slower than the BB84 signature ones as shown in Figure 2. For example, in the RAINBOW, we can observe that the SARG04 signature time is 0.08 s, while it is 0.5 s for the BB84 signature time. An intriguing finding is the consistent overhead of authentication in the mono-authentication configuration with CRISTALS-DILITHIUM, as depicted in Figure 3. For the BB84 protocol, this overhead remains at approximately 0.5%, while for the SARG04 protocol, it stands at 0.4%. However, there is a notable decrease in overhead for RAINBOW mono-authentication, dropping from 70 to 50% for the BB84 protocol and from 60 to 39% for the SARG04 one. It is worth noting that the security bits are 128 in this simulation. The following observations are made with the QBER fixed at 11%, representing the worst-case scenario observed experimentally. Figure 2: The signature time of mono-authentication as a function of the QBER for the two distinct protocols. We investigated the optimal threshold for maximum corrected errors within the mono-authentication algorithm. As depicted in Figure 4, we observed a notable increase in the total authentication time for the SARG04 protocol as the error correction bits escalated as well as with the security bits. Additionally, we computed the duration required to rectify a specific number of errors relative to the key size and noted a corresponding increase with the number of maximum corrected bits. The maximum durations for correcting between 0 and 3 errors across each security level are documented in Table 3.  
Examining Figure 5 sheds light on why authentication becomes more financially burdensome in cases where no corrections are made. The trend becomes evident: as the security level escalates, the number of rejected keys surge  
Figure 4: The graph illustrates the total authentication time, encompassing both signature and verification durations, alongside the time required for error correction, across varying maximum corrected bits given in Table 3. These data points are presented for three distinct security levels, all under a constant QBER of 11%. Figure 3: The overhead of the mono-authentication as a function of the QBER for two different protocols. rectification. This surge in rejections is primarily attributed to the introduction of a QBER of 0.011. Moreover, longer keys inherently harbor a heightened likelihood of containing errors, amplifying the rejection frequency. In this section, our inquiry delves into elucidating the minimum intervals essential for recommencing QKD authentication, contingent upon the bit rate of photons transmitted through the quantum channel. Nonetheless, prior to embarking on this investigation, it is imperative to ascertain the duration required by each algorithm to authenticate a designated quantity of bits. Figure 6 illustrates that CRYSTALS-DILITHIUM for mono-authentication for two different security bits 128 and 256 for the SARG04 protocol at the key rate of 50 kb/s exhibits the highest authentication rate, while RAINBOW performs the least efficiently. Interestingly, in most scenarios, the authentication performance appears to be largely unaffected by the number of bits being signed, particularly when signing up to 2000 bits.