An Efficient Identity Authentication Mechanism Based on Algebraic Curves and Zero-Knowledge Proofs

Abstract

With the rapid development of the digital economy and the Internet of Things, identity authentication in resource-constrained environments faces challenges such as low efficiency and inadequate privacy protection. Addressing the high computational and communication overhead of traditional RSA and ECC authentication mechanisms, this study proposes an efficient identity authentication mechanism (AC-ZKP) based on algebraic curves and non-interactive zero-knowledge proofs (NIZK). This mechanism leverages algebraic curve group operations to achieve lightweight key management and employs zero-knowledge proofs to ensure information concealment and anti-forgery during identity verification. The paper conducts a systematic study across four dimensions: system modeling, algorithm design, security analysis, and performance evaluation. Experimental results demonstrate that while maintaining 128-bit security strength, the AC-ZKP mechanism reduces authentication latency by approximately 44% and communication overhead by about 40%. It also exhibits strong scalability and resistance to attacks, significantly outperforming traditional ECC schemes. These findings provide a viable solution for lightweight, high-security identity authentication in IoT, edge computing, and cross-border data exchange environments.