Chebyshev Polynomial based ElGamal Encryption with Chaotic Greater Cane Algorithm for Secure Communication

Recently, the practice of Chebyshev polynomials in public-key system design has been recommended. In fact, they have certain satisfying chaotic features that make them appropriate for usage in cryptography. Thereby, various public-key cryptosystem employing Chebyshev polynomials has been focused however, the successive analysis has revealed its insecurity. In this paper, a novel Chebyshev polynomial based ElGamal Encryption with Diffie- Hellman Key Exchange (CPEE-CFGC) is proposed for guaranteeing security in various applications. The various steps involve in CPEE-CFGC algorithm are key generation, encryption and decryption with secure key exchange process. In the key generation process, the private keys are generated using Fuzzy Logistic Tent Membership Function (FLMF) for each party engaging in the communication. Then, the optimal keys are selected using Greater Cane Rat Algorithm (GCRA). The Diffie Hellman key exchange mechanism is exchange the keys in an unsecure channel. Further, the encryption and decryption process are carried out using chebyshev polynomial based ElGamal encryption (CPEE) algorithm. The simulation of CPEE-CFGC algorithm is carried out using python programming language, and the performance is evaluated with dissimilar performance indicators. As a result, the CPEE-CFGC has obtained a better key generation time of 10256.25 ms, encryption time of 5160.78 ms, decryption time of 230.45 ms and total execution time of 12100.57ms by varying the bit size to 2048 bits than the existing algorithms.