A Comprehensive Review of Number-Theoretic Foundations of Attribute-Based Encryption Schemes: Security Models, Optimization Techniques, and Emerging Computing Applications

Abstract

Attribute-Based Encryption (ABE) has emerged as a powerful cryptographic paradigm enabling fine-grained access control over encrypted data, particularly in distributed and cloud-based systems. The number-theoretic foundations of ABE, including bilinear pairings, modular arithmetic, elliptic curves, and lattice-based constructions, play a central role in determining both security guarantees and computational efficiency. This paper presents a comprehensive review of the number-theoretic principles underlying ABE schemes, analyzing their evolution across diverse security models, optimization strategies, and emerging computational environments. The study systematically evaluates recent advancements from 2018 to 2025, focusing on improvements in ciphertext-policy and key-policy ABE, resistance to quantum attacks, and integration with modern paradigms such as edge computing and Generative AI-assisted cryptographic design. The findings reveal a strong trend toward lightweight, scalable, and quantum-resilient constructions, alongside increasing adoption in secure software engineering pipelines. This work contributes a structured synthesis of 30 recent studies, identifies research gaps in efficiency-security trade-offs, and highlights future directions in AI-driven cryptographic optimization and post-quantum ABE design.