# A Finite State Machine-Based Improved Cryptographic Technique
## 3 Proposed Methodology
### Finite State Machine with Reverse Data Hiding
The security of the cryptosystem may be ensured by choosing the value of p that will be a large prime integer. This will produce an elliptic curve of high order that contains many points, which will satisfy the requirements for safety. The creation of a top-secret lookup table is the first step in the implementation of the MCTC that has been suggested. This step is subsequently followed by the development of interleaving locations. Let us assume that the point G on the elliptic curve of prime order Ep is a concealed generator (\(a\), \(b\)). The most top-secret lookup table is created using computational techniques  
\[P_{s}=(x_{s},y_{s})=(s\times G),\,s=0,\,1,\,2,\,3,\ldots,\,N, \tag{16}\]  
where \(P_{s}\) is a point on the elliptic curve. \[Q_{d}=(k_{m}\times P_{d}),\,d=0,\,1,\,2,\,3,\ldots,\,N, \tag{17}\]  
where \(Q_{d}\) is the collection of elliptic points that are concealed inside the index t of the lookup table. The key \(k_{m}\) may have a single bit altered, which will cause a whole new lookup table to be generated, as shown in Table 3. This protects the private lookup table from being read by a third party who is not authorized to examine it in any capacity. Both the transmitter and the receiver make use of two hidden parameters that they refer to as \(G\) and \(k_{m}\). These parameters are only known to the transmitter and the receiver. These parameters are accountable for ensuring that the confidential lookup table's privacy is always preserved. In addition, even if the adversary is successful in learning one of the secret parameters, \(G\) or \(k_{m}\), the ECDLP that is used in elliptic curve arithmetic makes it exceedingly difficult for them to uncover the other secret parameter. The MCTC oversees creating the interleaved bit locations v for each input bit location u that it receives, and it is accountable for doing so. The MCTC is the one responsible for producing the interleaved bit location v, which serves as the index of the secret lookup table. This index is associated with the elliptic point \(P_{u}\), which can be determined using the formula  
\[ \begin{array}{c}P_{u}=(u\times Q),\,u=1,\,2,\ldots,\,N-1\\ \text{and}\,\,Q=(k_{s}\times P),\end{array}  \tag{18}\]  
where \(k_{s}\) is the secret key and \(P\) is a secret elliptic curve point given to MCTC. Table 3 provides an illustration of the case that may be used to explain the production of an interleaved bit location for the mask key \(k_{m}\) = 2,853,234. Case 1 and case 2 demonstrate the positions of the interleaved bits for the same secret key \(k_{s}\) but for different secret points, P. Even if the keys \(k_{m}\) and \(k_{s}\) are the same, the interleaving sequence is completely different because of a change in P, as can be seen in the results for cases 1 and 2. Cases 2 and 3 demonstrate that even though P remains unchanged, the generation of a totally new interleaving sequence is brought about by a single bit shift in the secret key, \(k_{s}\). According to the findings, the user must be in possession of practically all the secret key parameters to successfully recover the right interleaving pattern. An entirely new sequence is generated if there is a modification to even one of the parameters. Every FSM has a matching de-FSM that works on the interleaved sequence to construct the sequence in its natural order. This order is maintained throughout the process. To de-interleave the sequence that has been interleaved, the receiver will need to construct an interleaving sequence that is awfully close to the one that was sent. It is possible for the receiver to produce a comparable interleaving sequence by secretly broadcasting the keys \"\(k_{m}\), \(k_{s}\), G, P.\" Because of this, there is no longer a need for additional bandwidth, which was necessary to share the whole table between the sender and the receiver. While using a secure system, an adversary is rendered incapable, or at best exceedingly improbable, of regaining access to the original data.