With more and more interaction scenarios of cross-domain cooperation in different industries, the demand for information sharing and value exchange among organizations is increasing. How to obtain authentication from devices in other domains is one of the key technologies to realize data sharing among organizations. The traditional centralized authentication system is vulnerable to failure due to reliance on a single server. Existing solutions often overlook cross-domain authentication and suffer from inefficiencies caused by complex encryption processes, and they are not friendly enough for terminal devices with limited resources because many time-consuming cryptographic operations are involved. To address these issues, we propose a blockchain-based anonymous authentication scheme that realizes heterogeneous domain authentication with reduced computational overhead. We compare and analyze our scheme with the current researches in the same configuration environment. Experimental results show that the overall computational overhead of our scheme is reduced by 89% compared to schemes using bilinear mapping. Average latency and throughput, which tend to stabilize as the number of transactions increases, also support timely validation of cross-domain applications.