This paper investigates the situation where users must utilize each credential according to the desired services, and clarifies the problems in the situation and the issues addressed by the concept of ``identity federation''. Japan has the GakuNin, which is an academic access management federation, and the HPCI, which is a distributed high performance computing infrastructure. For the provision of the HPCI resources, the HPCI cannot simply behave as a service provider in the GakuNin. Consequently, in performing academic research, especially HPCI users belonging to academic institutions are compelled to manage both the GakuNin and the HPCI credentials. In this paper, based on the situation in Japan mentioned above, we discuss a credential integration model in order to more efficiently utilize a wide variety of services. We first characterize services in an academic federation from the point of view of authorization and investigate the problem that users must utilize each credential issued by different identity providers. Thus, we discuss the issues to integrate user's credentials, and consider a model that solves the issues.