A Novel RSA Cryptosystem Variant Using Chaotic Exponent Selection and Ciphertext Blinding

This paper presents an enhanced variant of the RSA cryptosystem that integrates chaotic exponent selection and ciphertext blinding to address security limitations inherent in classical RSA. Traditional RSA relies on a fixed public exponent, which generates predictable encryption patterns and increases exposure to exponent-based attacks. In the proposed scheme, the encryption exponent is dynamically derived from a logistic-map–based chaotic sequence, introducing high sensitivity to initial conditions and producing session-dependent exponent values. This chaotic exponentiation increases unpredictability without modifying the established RSA framework. Additionally, a ciphertext blinding factor is incorporated to prevent deterministic outputs and strengthen resistance against chosen-ciphertext and side-channel attacks. The paper outlines the mathematical background of the logistic map, details the complete encryption and decryption procedures, and demonstrates the correctness of the method through a numerical example using small primes. A theoretical security analysis shows that the combined effects of chaotic exponent selection and blinding significantly improve resistance to key-related attacks while maintaining compatibility with the original RSA structure. These enhancements offer a lightweight and practical improvement to RSA for environments requiring increased confidentiality and unpredictability in exponent selection.