# A Novel Digital Signature Scheme for Advanced Asymmetric Encryption Techniques
## 3 The Proposed Signature Scheme  
In asymmetric encryption techniques, the receiver needs to authenticate the author of sent data and guarantee its non-repudiation, which is ensured by digital signature. In fact, there are many algorithms that are used to create signatures, and these algorithms use smaller keys, for example Elliptic-Curve-Cryptography (ECC)-based signature algorithms, but to use ECC, both the private and public keys must be created over an elliptic curve. In this paper, we studied the creation of an accompanying signature for cryptographic algorithms that have a linear and very special public key generated independently of ECC, where \(pk=k+r\times p\), with \(p\) a prime number and \(k\) and \(r\) random numbers. To the best of our knowledge, there is still no corresponding signature for this form of keys. We focused on this type of public key for its ease of creation and also for its resistance to attacks so the secret parameters (\(k\), \(r\), and \(p\)) cannot be extracted from it. To provide a suitable scenario describing the new signature scheme's functional mode, we need certain details about the planned architectural model to use. Figure 1 shows the proposed architectural model. Most modern cryptographic architectures follow a layered approach, with each layer providing a specific security function. The proposed architecture layers include the following components: the sender, the encryption operation, the signing module, the Internet, the receiver, the decryption operation, the verifying module, and the comparing module:  
1. Sender: This plays the role of the signer and transforms the plain text into a cipher text that will be used later for data validity. 2. Key generation: This component is responsible for providing all keys required for the signing and verifying processes, including private keys, split public keys, and whole public keys. 3. Signing module: By applying the newly proposed signing formulas, this component creates a digital signature of the original message that is sent by the signer. It uses private keys for extracting the two parts of the signature. The created digital signature will be sent along with the encrypted message to the Internet for further processing
4. Internet: Its role is to transport information to the receiver directly or to the cloud for storing, allowing the authorized user to access the stored data. 5. Receiver: This obtains the authorization for accessing the specific data, which are transported by the Internet and stored in an encrypted format with a signature. The encrypted message will be accessed by the receiver and decrypted using the decryption operation. The receiver then has the original data and a digital signature created by the sender using the sender's private key. The authorized receiver can then verify the originality of the message with the help of the sender's public key. 6. Decryption operation: This transforms the cipher text into plain text. 7. Verifying module: The verification module verifies the sent digital signature of the original message that is created by the sender. New values will be created by applying the verification formula. 8. Comparing module: The created values using the signature, which is available along with the original message, will be compared to each other. If both values are the same, then the integrity of the data is validated; otherwise, the accessed data are a modified message or a fake message. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Scheme** & **Enc** & **Dec** \\ \hline
[38] & \(c=m\times pk\) & \(m=(c-c\mod\alpha)\mod(\alpha-1)\) \\ \hline
[39] & \(c=d_{0}\times pk_{0}+d_{1}\times pk_{1}+..d_{i}\times pk_{i}\) & \(m=\sum_{j=i}^{0}\frac{c}{k_{j}}\times 10^{j}\), \(c\gets c-\frac{c}{k_{j}}\times k^{j}\) \\ \hline
[40] & \(c=(m+r\times(pk-1))\mod n\) & \(m=(c\mod p)\mod(k-1)\) \\ \hline
[36] & \(c=(m+k)\mod p\) & \(m=(c-k)\mod p\) \\ \hline
[37] & \(c=(m+r\times k)\mod k\times p\) & \(m=c\mod p\) \\ \hline \hline \end{tabular}
\end{table}