## 3 Proposed Scheme
### Encryption Algorithm  
Our algorithm comprises three primary stages. The first stage involves encoding the plaintext using ASCII characters and inducing diffusion in its representation. In the second stage, we compute points on an elliptic curve and apply a mapping method to create randomness in the data. Finally, in the third stage, we decompose the output using a max-plus algebra-based wavelet transform and generate a ciphertext. We provide a comprehensive explanation of these stages as follows. In the first stage, the plaintext is encoded using ASCII characters, and then a process of diffusion is applied to the ASCII representation of the plaintext. Suppose the plaintext contains \(n\) characters. Convert each character into its corresponding ASCII code and denote them as \(a_{1},a_{2},\ldots,a_{n}\). Compute the sum of these ASCII codes, take the result modulo 94, as there are a total of 94 printable ASCII characters, and let \(s\) be the remainder. Then, add \(s\) to each ASCII code of the plaintext to obtain the diffused ASCII values \(k_{1},k_{2},\ldots,k_{n}\), where for \(1\leq i\leq n\), \(k_{i}=a_{i}+s\). Figure 1: Flowchart of our proposed text encryption scheme. During the second stage, we first generate points over an elliptic curve. To do so, we use a MEC, denoted by \(E_{p,b}\), which satisfies the equation \(y^{2}\equiv x^{3}+b\pmod{p}\) where \(p\equiv 2\pmod{3}\). We assume that the value of \(p\) is at least \(221\) because the standard ASCII table shows that ASCII character codes range from \(0\) to \(127\), and since the maximum value for \(s\) is \(93\), the biggest possible diffused value is \(220\). Select any point \(G\) on the \(E_{p,b}\) whose order is greater than \(220\). Let the order of point \(G\) be \(m\). To generate a sequence of points \(2G,3G,\ldots,220G\) over an elliptic curve \(E_{p,b}\), we start with a point \(G=(x,y)\). We use the group law [35] operations to compute the subsequent points \(1G,2G,\ldots,220G\). We consider each diffused ASCII value \(k_{i}\) and map it to a specific point \(k_{i}G\) on the curve \(E_{p,b}\), where \(k_{i}\leq 220\), and \(1\leq i\leq n\). In the third stage, we apply Type IVa MP wavelet for improving the security and robustness of our designed text encryption process. For \(1\leq i\leq n\), let \(k_{i}G=(x_{k_{i}},y_{k_{i}})\), then compute the original signal as \(u_{0}(i)=y_{k_{i}}\). If the total number of characters \(n\) is even, then we set \(u_{0}(i)=y_{k_{i}}\). On the other hand, if \(n\) is odd, we set \(u_{0}(i)=y_{k_{i}}\) and add an extra signal \(u_{0}(i+1)=-\infty\). We add this extra signal because the Type IVa MP-wavelet synthesis process requires an even number of signals. This is because the synthesis process involves dividing the input signals into two parts: approximation and detail signals. We use Equations (1) and (2) to compute the approximation and detail signal, respectively [14]:  
\[u_{\ell+1}(i)=u_{\ell}(c_{\ell+1}i)\oplus u_{\ell}(c_{\ell+1}i+1), \tag{1}\]  
\[v_{\ell+1,j}(i)=u_{\ell}(c_{\ell+1}i+j)-u_{\ell}(c_{\ell+1}i+j-1), \tag{2}\]  
where \(\ell\geq 0\), \(c_{\ell}\) represents the channel of a signal at level \(\ell\), \(i=1,2,\ldots,\lceil\frac{n}{2}\rceil\), \(j=1,2,\ldots,c_{\ell+1}-1\), and \(\oplus\) represents max-plus addition. Next, we create a binary representation of the detail signals \(v_{\ell+1,j}\) by assigning \(1\) to negative values and \(0\) to positive values. This binary encoding denoted by \(B\) is used in the decryption process. Finally, the ASCII code for the encrypted message is obtained by transforming both the approximation signals and the absolute value of detail signals into the form of \(94q+r\). The quotient \(q\) is used in the decryption process. To ensure that all ASCII codes are printable, we increase \(r\) by \(32\). Note that any ASCII code with a value of \(32\) or more is considered printable. The ciphertext \(C\) is generated by the obtained ASCII codes into a text. Figure 2 illustrates an example of the encryption process of our designed text encryption scheme.