To address the challenges of high energy consumption and significant risks of privacy breaches in device identity authentication processes within the centralized platforms of the Internet of Things, this paper introduces a novel blockchain-driven distributed identity authentication framework, termed BDIA-Sensor. This framework is specifically designed to offer a secure, decentralized, and energy-efficient solution for the identity verification of sensors engaged in carbon data collection for carbon capture, utilization, and storage (CCUS) systems. The security of BDIA-Sensor is reinforced through the application of Pairing Signature and Shamir’s Secret Sharing Scheme for the creation of robust identity certificates. Its distributed nature is realized via a shared parameter setup and cooperative credential generation, ensuring a resilient and scalable architecture. Energy efficiency is achieved by leveraging succinct commitments and zero-knowledge proof (ZKP) technologies, which facilitate the verifiable operations of sensors while minimizing computational demands. The identity certificate and related information are securely stored via an innovative block data structure known as the Verkle tree. A thorough analysis of the security of the proposed mechanism is conducted across the stages of system initialization, identity registration, and authentication. Additionally, a comparative analysis of computational overhead highlights its superior performance. The experimental results demonstrate that BDIA-Sensor effectively thwarts various forms of malicious attacks, ensuring a highly secure and distributed IoT identity authentication process with notable performance benefits. This makes BDIA-Sensor a valuable reference for enhancing sensor-based carbon data capture in CCUS applications.