<p>Due to the operational efficiency and lower computational costs of the Chebyshev polynomial compared to ECC, this chaotic system has attracted widespread attention in public key cryptography. However, the single recurrence coefficient limitation and inherent short-period flaw, often render the Chebyshev polynomials cryptosystem ineffective against various attacks, such as Exhaustive Attacks and Ciphertext-Only Attacks. To address these vulnerabilities, the Multi-Dimensional General Chebyshev Polynomials (MDGCP) is developed in this study by parameterizing the coefficient of the Chebyshev polynomial over finite fields and converting its variable from one dimension to multiple dimensions. The MDGCP preserves the semigroup property and significantly reduces the likelihood of short periods by imposing a simple and explicit restriction on the initial state matrix. This enhancement improves the complexity and pluralism of the Chebyshev polynomial, thereby increasing its applicability in the design of public key cryptosystems. Consequently, a novel public key encryption algorithm based on MDGCP is proposed. Theoretical analyses and experimental results reveal that the proposed algorithm possesses better abilities than existing public key encryption algorithms based on Chebyshev polynomial in resisting exhaustive attacks and Ciphertext-only attacks.</p>