A Comprehensive Review of Algebraic Structures for Threshold Cryptography for Cloud Storage: Security Models, Optimization Techniques, and Emerging Computing Applications

Abstract

The rapid adoption of cloud storage systems has transformed data management by offering scalable, flexible, and cost-effective solutions, but it has also introduced significant security challenges related to data confidentiality, integrity, and access control. Traditional cryptographic techniques often depend on centralized key management, making them susceptible to single points of failure and insider threats. To overcome these limitations, threshold cryptography, based on advanced algebraic structures such as finite fields, elliptic curves, and lattice-based systems, has emerged as a robust approach for distributed trust and secure data handling. By dividing cryptographic keys into multiple shares and requiring a threshold number of participants for reconstruction, this method enhances fault tolerance and supports decentralized security models. This review provides a comprehensive analysis of algebraic approaches to threshold cryptography in cloud environments, focusing on security models, optimization techniques, and emerging applications such as blockchain-integrated storage and post-quantum cryptography. Techniques including polynomial interpolation, linear secret sharing, and ring-based constructions enable secure multi-party computation and distributed key generation. Despite notable advancements, challenges such as communication overhead, scalability limitations, and the lack of standardized evaluation frameworks persist, highlighting important directions for future research in developing efficient and quantum-resilient cloud security solutions.