## 4 Descriptors of the Second Criteria and Experimental Results  
### Transaction Costs  
This section analyzes the transaction costs charged by the Ethereum blockchain consortium to launch the solution. First, the cost of a single smart contract, as described in the previous sections, was estimated. The next step was to estimate the costs of launching our solution in the Republic of Kazakhstan, namely the amount of gas that our solution consumes per year based on the number of students in all universities of the Republic of Kazakhstan. The fee required for the Progress smart contract to be executed on the Ethereum network consortium is shown in Table 3. More precisely, the table shows how much gas was spent to launch the smart contract. To calculate these data from the smart contract code, we used Remix IDE. Alternatively, the Solidity compiler can be used. The data in Table 3 indicate that the smart contract constructor is the most expensive function. The reason for this is that the input data for these constructors are larger than the input data for the other functions. Moreover, our designers initiate internal variables in non-volatile memory, which depends on expensive instructions of the Ethereum virtual machine. However, constructors are executed only once when deploying a smart contract. Thus, its cost is paid only once. Let us turn to an assessment of how much gas is needed to use our solution in the Republic of Kazakhstan. Our estimate requires some approximate values, which are presented in Table 4.  
According to the Review of the Higher Education System, in 2022, the number of higher education institutions amounted to 122. In most universities, students study at three levels: the levels of a bachelor's degree, master's degree and doctoral degree. Annually, more than 150,000 people begin their studies at the universities of the Republic of Kazakhstan. \begin{table}
\begin{tabular}{c c} \hline \hline
**Description** & **Approximate Value** \\ \hline Active Kazakhstan HELs & 122 \\ Average stages offered by an HEI & 3 \\ Average number of bachelors students entering HEIs per year & 144,139 \\ Average number of masters students entering HEIs per year & 17,308 \\ Average number of PhD students entering HEIs per year & 2304 \\ Average bachelor stage duration in years & 4 \\ Average master stage duration in years & 2 \\ Average PhD stage duration in years & 3 \\ Average bachelor stage courses required per semester & 6 \\ Average master stage courses required per semester & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Approximate parameters for calculating cost. \begin{table}
\begin{tabular}{c c} \hline \hline
**Function** & **Gas Used** \\ \hline Constructor & 651,687 \\ addStudData & 550,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Prototype’s gas cost. We estimated approximately how many courses students would take and how long they would take to earn a degree. Note that this strongly depends on the degree that a student is pursuing. According to the order of the Minister of Education and Science of the Republic of Kazakhstan dated 20 April 2011, No. 152, 240 ECTS credits are required for a bachelor's degree; for a master's degree, it is 120; and for a doctoral degree, it is 180. The average durations of bachelors, masters and PhD studies are 4, 2 and 3 years, respectively. Based on the above approximations, we could estimate the operating costs of our prototype in terms of gas for the entire higher education system of the Republic of Kazakhstan. Figure 7 shows the costs during the first 4 years of deployment. We assumed a gradual increase, starting only with newly enrolled students. One transaction per semester is performed per student by a one-time calculation of the addStudData function. Depending on the student's degree, the function call is made from four to eight times per student.