This article introduces a novel approach that integrates the ElGamal and RSA algorithms to advance the security and efficiency of public-key cryptosystems. By combining these two established asymmetric-key algorithms, our method leverages their individual strengths and addresses the limitations of traditional systems, particularly in relation to the integer factorization and discrete logarithm problems. The application of Gaussian integers enhances the robustness of both encryption and digital signature processes, offering a more secure cryptographic framework. Our study involves a comprehensive analysis of the integrated algorithms, including practical implementations and extensive cryptanalytic evaluations focused on the integer factorization and discrete logarithm challenges. Quantitative assessments are provided to evaluate the effectiveness and computational efficiency of the proposed system. While key generation is slightly slower compared to using RSA or ElGamal individually, our approach delivers comparable performance in encryption and decryption, with notable improvements in robustness and versatility. In contrast to existing research predominantly focused on optical image processing, our work extends the scope to a broader range of applications, enhancing both theoretical insights and practical implementations of cryptographic schemes. Future research will focus on optimizing key generation, exploring integration with existing security frameworks, and evaluating performance in diverse real-world scenarios to further refine and validate the proposed approach.
Key words: Combined RSA-ElGamal public-key cryptosystem, RSA, ElGamal, Digital Signature, Gaussian integers.
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