# Adaptive Authentication Protocol Based on Zero-Knowledge Proof
## 6 Analysis of the Results of the Conducted Research
The total execution time of the authentication protocol with a minimal level of confidentiality was \(T_{\mathrm{min}}^{(32)}=185.780\)\(\upmu\)s.  
The figure shows the dependence of the volume of information traffic on the intensity of road traffic when using a 32-bit authentication protocol. The analysis of Figure 1 allows us to draw the following conclusions. If the \(OBU\) density per 1 km is 30, then, for the authentication protocol with a maximal level of confidentiality, the volume of information traffic was 126,012.3 bytes. A reduction in the level of confidentiality to a minimal level allowed us to increase information traffic by 1.015 times, bringing its volume to the value of 127,816.3 bytes. If we increase the \(OBU\) density per 1 km three times, then the volume of information traffic is 115,892.8 bytes, with a maximal level of confidentiality. A reduction in the level of confidentiality to a minimal one allows us to increase information traffic by almost 5%, bringing its volume to 121,305 bytes. Figure 1: Dependence of the volume of information traffic on road traffic intensity with a 32-bit protocol. Figure 2 shows the dependence of the average number of packets per \(OBU\) when using a 32-bit authentication protocol with a maximal level of confidentiality. The analysis of Figure 2 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 84. When increasing a packet size to 150 bytes, the average number of packets per \(OBU\) is 27. We receive 16 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 25 with a packet size of 50 bytes. The average number of packets per \(OBU\) is seven, with a packet size of 150 bytes. We receive four packets with a packet size of 250 bytes. The average number of packets per \(OBU\) will be greater when a minimal level of confidentiality is used in the authentication protocol. Figure 3 shows the dependence of the average number of packets per \(OBU\) when using a 32-bit authentication protocol with a minimal level of confidentiality. If the density of an \(OBU\) does not exceed 30 per 1 km, then the average number of 50-byte packets per \(OBU\) is 85. When the packet size is increased to 150 bytes, the average number of packets per \(OBU\) is 28. We obtain 17 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 27, with a packet size of 50 bytes. The average number of packets per  
Figure 3: Dependence of the average number of packets per \(OBU\) on road traffic intensity with minimal level of confidentiality and a 32-bit protocol. Figure 2: Dependence of the average number of packets per \(OBU\) on road traffic intensity with maximal level of confidentiality and a 32-bit protocol. _OBU_ is eight, with a packet size of 150 bytes. We obtain five packets with a packet size of 250 bytes. The experimental results shown in Figures 2 and 3, obtained using a 32-bit protocol, differ slightly from each other. This is because this protocol has a low computational complexity. Therefore, changing the protocol parameters (reducing modular exponentiation operations, the number of answers to the question and the bit depth of the prover's signal) has a negligible effect on the authentication time in the case of a transition from a maximal confidentiality level to a minimal one. Therefore, the experimental results presented in Figures 2 and 3 do not allow us to fully assess the effectiveness of the developed authentication protocol. However, a 32-bit modulus cannot be used because it has low resistance to brute force attacks. At the same time, the implementation time of such an attack is very short. Let us increase the bit depth of the modulus used in the developed zero-knowledge authentication protocol.