This study aims to enhance the efficiency of the Schnorr and Elgamal cryptographic schemes by leveraging the randomness of chaotic maps. After evaluating 45 different types of chaotic maps, a novel one-dimensional chaotic system derived from the logistic map is introduced. As the dissipation parameter increases, a period-doubling phenomenon is observed, leading to classical behavior, along with intriguing characteristics at intermediate parameter settings. This chaotic system is then integrated into the Schnorr and Elgamal schemes. Comprehensive randomness assessments confirm the algorithm’s outstanding performance. Following rigorous testing and evaluation, the algorithm achieves impressive signing and verification times of approximately 0.000080486 seconds and 0.0000402130 seconds for the Schnorr scheme, and 0.00001671199 seconds and 0.00005969873 seconds for the Elgamal scheme, respectively—significantly faster than other proposed algorithms. Additionally, the private key space is expanded from 2^160 to 2^256, further enhancing security. Testing with 100,000 messages of varying lengths validates the algorithm’s robustness, establishing it as a promising candidate for modern cryptosystems in multimedia data exchange. |
