To alleviate the problems of high computational burden, difficulties in privacy protection, and weak anti-interference ability in the distributed energy trading market on the distribution network, this paper designs a distributed energy trading model that considers privacy protection and decentralization. First, it constructs a centralized unified optimization model with the goal of maximizing social welfare. Then, the centralized model is decomposed into the corresponding distributed optimization model based on the gradient rise method and dual decomposition. Further, a consensus algorithm based on the combined adaptation is proposed by employing a diffusion strategy. The aim is to achieve optimal market clearing by only transmitting information such as the electricity price and supply-demand imbalance among entities without introducing market organizers, while protecting the personal privacy of market entities and alleviating computational burden. Finally, case studies are conducted to validate the effectiveness of the proposed trading model, as well as its robustness under factors such as the uncertainty of new energy power, market entities joining and exiting, and its scalability.