As the Internet expands rapidly worldwide, authentication has become a more critical issue, consuming significant research efforts. Integrating Blockchain technology into authentication systems has emerged as a promising approach, leveraging its advantages to enhance security and reliability. However, Blockchain has inherent limitations, such as high storage costs and restricted data capacity. This paper presents an approach that incorporates the RSA Accumulator into Blockchain-based authentication systems. The proposed approach aims to reduce costs while maintaining the ability to validate users effectively with minimal on-chain data storage.