Abstract

This study aims to propose the improvement of RSA to secure the digital signature. This algorithm, which is called FE-RSA, focuses on two primary challenges: security and computing efficiency. A secret key and a fake public key are selected for the implementation to provide an additional security layer. In fact, FE-RSA attempts to protect against digital signature forgery. Moreover, the other main point of FE-RSA is that although an attacker can factor the modulus, FE-RSA is still secure. In addition, 512-bit, 1024-bit, and 2048-bit key sizes across four cryptography algorithms, including RSA, Multi-Prime RSA, the application of RSA and ElGamal (RSA-ElGamal), and FE-RSA, are selected for the experiment. Performance evaluations focused on processing time for the generation and validation processes. The experimental results demonstrate that FE-RSA regularly outperforms Multi-Prime RSA and RSA-ElGamal in terms of signing and verifying speed. In the signing process, FE-RSA is approximately 92.47%, 64.50%, and 3.82% faster than RSA-ElGamal for key sizes of 512-bit, 1024-bit, and 2048-bit, respectively. However, in the verification process, this method reduces processing time by about 97.12%, 87.53%, and 34.33% for identical key sizes. Then, it implies that FE-RSA provides the most significant performance benefit in the verification process. Although the processing time required in FE-RSA is slower than that of RSA, the security is higher than that of RSA. The reason is that RSA is based on only the Integer Factorization Problem (IFP). On the other hand, FE-RSA is based on both the Discrete Logarithm Problem (DLP) and IFP. However, FE-RSA is effectively applied in situations when a specific and reliable verifier has the secret key. In fact, FE-RSA integrates enhanced computing efficiency with multi-layered security. Therefore, the proposed method is established as a viable and resilient option for digital signature systems.