# Adaptive Authentication Protocol Based on Zero-Knowledge Proof
## 6 Analysis of the Results of the Conducted Research
The time spent checking the status of the _OBU_ and _RSU_ increased with the transition to a 64-bit authentication protocol. For a minimal level of confidentiality, the calculation time of the true digest was \(T_{1}\) = 54,000 ns, and the calculation time of the noisy digest was \(T_{2}\) = 55,600 ns. The transmission time of the question was \(T_{3}\) = 64,000 ns. The calculation time of the answer to the question was \(T_{4}\) = 800 ns. The transmission time of the answer to the question was \(T_{5}\) = 132,000 ns. The answer check time was \(T_{6}\) = 108,180 ns. The total execution time of the authentication protocol with a minimal level of confidentiality is \(T_{\min}^{(64)}=414.580\)\(\mu\)s.  
When the level of confidentiality is switched to a maximal one, the time spent on protocol execution increases by 1.95 times, reaching the value of \(T_{\min}^{(64)}=808.070\)\(\mu\)s. Figure 4 shows the volume of information traffic's dependence on the road traffic intensity when executing a 64-bit protocol. The analysis of Figure 4 allows us to draw the following conclusions. If the _OBU_ density per 1 km is 30, then, for the authentication protocol with maximal level of confidentiality, the volume of information traffic is 124,702.9 bytes. A reduction in the level of confidentiality to a minimal one allows us to increase information traffic by 1.025 times, bringing its volume to the value of 127,811.6 bytes. If we increase the _OBU_ density per 1 km by three times, then the volume of information traffic is 11,1964.8 bytes, with a maximal level of confidentiality. A reduction in the confidentiality level to a minimal one allows us to increase information traffic by 1.09 times, bringing its volume to 121,290 bytes. Figure 5 shows the dependence of the average number of packets per _OBU_ when using a 64-bit authentication protocol with a maximal level of confidentiality. Figure 4: Dependence of the volume of information traffic on road traffic intensity with a 64-bit protocol. The analysis of Figure 5 allows us to draw the following conclusions. If the density of an \(OBU\) per 1 km does not exceed 30, then the average number of packets of 50 bytes per \(OBU\) is 81. When the packet size is increased to 150 bytes, the average number of packets per \(OBU\) is 25. We obtain 11 packets with a packet size of 250 bytes. If the density of \(OBU\) per 1 km increases by three times, then the average number of packets per \(OBU\) will be 22, with a packet size of 50 bytes. The average number of packets per \(OBU\) is five, with a packet size of 150 bytes. We obtain two packets, with a packet size of 250 bytes. When a minimal confidentiality level is used for the authentication protocol, the average number of packets per \(OBU\) will be greater. Figure 6 shows the dependence of the average number of packets per \(OBU\) when using a 64-bit authentication protocol with a minimal level of confidentiality. If the density of an \(OBU\) per 1 km does not exceed 30, then the average number of packets of 50 bytes per \(OBU\) is 83. When the packet size is increased to 150 bytes, the average number of packets per \(OBU\) is 27. We obtain 14 packets, with a packet size of  
Figure 5: Dependence of the average number of packets per \(OBU\) on road traffic intensity with maximal level of confidentiality and a 64-bit protocol. Figure 6: Dependence of the average number of packets per \(OBU\) on road traffic intensity with a minimal level of confidentiality and a 64-bit protocol. 250 bytes. If the density of \(OBUI\) per 1 km increases by three times, then the average number of packets per \(OBUI\) will be 26, with a packet size of 50 bytes. The average number of packets per \(OBUI\) is seven, with a packet size of 150 bytes. We obtain four packets, with a packet size of 250 bytes. Analysis of the results showed that the time spent increases 1.048 times when switching from a 32-bit protocol to a 64-bit protocol.