The special algorithm based on RSA cryptography for signing and verifying digital signature.

This aim of this research is to present the improved equations to enhance RSA cryptography for signing and verifying processes. The primary benefit is in signing procedure, where it could decrease computing resources by introducing a new integer to be utilized as exponents instead of the private key. In fact, this integer is always smaller than the private key. However, authenticating the digital signature will require additional processing resources. The result obtained from validating the signature with the original equation must be multiplied by a single integer. However, while evaluating the entire process of signing and validating digital signatures, the proposed method presents a chance to significantly reduce the computing resources. Furthermore, two new techniques for generating all necessary parameters are introduced, Algorithm 3.1 and Algorithm 3.2. Although the long duration of these procedures is required, they will be executed only once. The experimental results demonstrate that Algorithm 3.2, which has a longer execution time than Algorithm 3.1, demands an average period of 70 s to generate a 1024-bit modulus and all associated parameters. Furthermore, the experimental results on the process of signing digital signatures indicate that the proposed method may reduce the average time about 30 %.