# A Finite State Machine-Based Improved Cryptographic Technique
## 4 Results and Analysis of Proposed Work
### Periodicity Analysis of Elliptic Curve Cryptographic FSM  
The MCTC makes use of a cryptographic FSM that, all the way along its length, randomly permutes and distributes the data that it gets as an input to provide the highest possible level of security. This was performed so that the MCTC could give the largest possible degree of protection. After an interleaving period of that length, the MCTC will then proceed to repeat the permutation sequence N times in each of its subsequent cycles. This will continue until the sequence is exhausted. The passage of time results in an increase not just in the number of feasible combinations but also in the degree of unpredictability in the bits that are created, which ultimately leads to an increase in the total number of combinations that are conceivable. The number of bits encoded by CTC is equal to the frame length, which is denoted by the letter L in the frame length notation. This is the case because the number of bits encoded by CTC is equal to the frame length. If you want each frame to be long enough to interleave the input bits, the bits themselves need to be at least as long as the period of the FSM. The bits that are interleaved are sufficiently random when N is big enough to accommodate them. Because of this, there is less correlation between the code words and, as a result, error-correction performance in CTC is enhanced. Nevertheless, when N is quite low, the interleaved bits are not nearly as random as they should be. This occurs because the interleaved bits are determined by N. Interleaved bits make use of the higher statistical properties offered by huge periods of time, which makes it much more difficult for an adversary to determine the specific interleaving pattern. A certain amount of time must pass before an interleaving sequence may begin repeating itself; this minimum amount of time is referred to as the sequence's period. The period of an interleaving sequence is the same as the sequence's period. If each of the criteria that are given below is met, then we may say that the series of numbers has a period \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Statistical Test** & **Required** & **Case 1** & **Case 2** & **Case 3** \\  & **Interval** & & & \\ \hline Mono bit test & Input 1 & 9998 & 10,001 & 10,019 \\ Poker test & Input 2 & 10.9696 & 11.4560 & 15.4880 \\ Example 1 & Input 3 & 1785 & 1720 & 1470 \\ Example 2 & Input 4 & 1789 & 1789 & 1247 \\ Long run test & Input 5 & 1 & 2 & 3 \\ Final Result & success & success & success \\ \hline \hline \end{tabular}
\end{table} 
Table 7: FIPS-140-2 statistical test results. of N, where N is an integer that is greater than zero. If all these conditions are met, then the sequence of numbers has a period of N  
\[\
u_{i}=\
u_{i+N},for\ i\geq 0, \tag{21}\]  
where the letter \"i\" denotes a particular location inside the integer v. The periodicity of the proposed MCTC is largely governed by several different parameters, the most significant of which is the number of points on an elliptic curve that are created by the generator point G. The suggested MCTC is mostly determined by these factors. It is possible to define a cyclic group using an elliptic curve of prime order. The building of a cyclic group results in the production of all the points on an elliptic curve. This is accomplished by selecting a single point from the cyclic group to serve as the beginning point in the process. One point from the collection may be chosen at random to serve as an example of this. An example of a cyclic group is shown in each of the Figure 6a-c. These groups were generated by an elliptic curve with the order 19 and the generator points (10,11), (7,6), and (16,4), respectively. Each of these figures is shown in its own separate figure. An elliptic curve served as the basis for the construction of each of these groups. In the field of mathematics, an example of an elliptic curve can be found denoted by the notation E17(2,2), which corresponds to this cyclic group.