A Quantum-Corrected Chaotic System for Strengthening Schnorr and Elgamal Signatures to Optimize Key Generation and Performance

This paper aims to improve the performance of Schnorr and Elgamal schemes using the random property of the chaotic maps. After analyzing different chaotic map types, this paper generates a new 1D chaotic system based on sin and logistic maps. After that, we derived a new map with quantum corrections by coupling a kicked quantum system with a harmonic oscillator bath. As the dissipation parameter increases, we observe a period-doubling progression towards classical behavior, along with other intriguing characteristics at intermediate parameter values. Then, this new chaotic system is applied to the Schnorr and Elgamal schemes. Extensive randomness tests were conducted, and the algorithm demonstrated exceptional performance. Following rigorous testing and analysis, the algorithm exhibited impressive signing and verification times of approximately 0.0000799212 (s) and 0.0000100223 (s) for the Schnorr scheme, and 0.000029932 (s) and 0.0000399298 (s) for the Elgamal scheme, respectively. These times are notably lower compared to other proposed algorithms. The private key space was expanded to from , further strengthening security. Testing with 100,000 messages of varying lengths confirmed the algorithm's robust performance, making it a viable option for contemporary cryptosystems used in multimedia data exchange.