Here effort, we offer a novel or efficient digital signature system built on the rank properties of circulant matrices. Digital signature schemes are crucial for ensuring authenticity and integrity in digital communications, yet existing methods often face challenges in balancing security, efficiency, and resource consumption. Our proposed scheme leverages the unique algebraic structure of circulant matrices, which allows for the rapid computation of signatures and verification while maintaining high levels of security against contemporary cryptographic attacks. By utilizing the rank characteristics of circulant matrices, we achieve a signature scheme that not only enhances computational efficiency but also provides resistance to linear algebra-based attacks. We demonstrate that our approach offers a significant improvement in performance compared to traditional signature schemes, such as RSA and ECC, particularly in environments where computational resources are constrained. The proposed scheme is appropriate for a variety of uses, including as large-scale data authentication in cloud computing and secure communication in Internet of Things devices. Our experimental results validate the practicality and robustness of the scheme, confirming its potential as a highly efficient alternative regarding digital cryptography.