With the rapid advancement of cross-chain technology and its widespread adoption across various domains, cross-chain application scenarios are evolving toward greater specialization and segmentation. Existing cross-chain solutions primarily focus on asset exchanges between specific blockchain networks, yet they exhibit significant shortcomings in critical aspects such as unified cross-chain identity authentication and trustworthy regulatory oversight of data. To address these challenges, this paper introduces, for the first time, a cross-chain trustworthy regulatory market model that enables governmental bodies to perform reliable regulatory supervision over data exchanged across heterogeneous blockchain platforms. To facilitate seamless integration of diverse blockchain systems, we propose a novel key agreement algorithm based on Permutation Rational Functions over a Peninsula Group, which enables the establishment of a unified cross-chain regulatory registration mechanism. In addition, we design a one-time-per-session key update protocol to support efficient and trustworthy unified authentication for cross-chain interactions. Through experimental analysis and performance evaluation, we demonstrate that the proposed model outperforms existing approaches in terms of efficiency and scalability in transparent regulatory scenarios, while also exhibiting enhanced robustness against common security threats.