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Ubiquitous computing systems typically have lots of security problems in the area of service supply. The service types and levels, the security delegation of services and the identity hiding of principal etc are all these unsolved problems. In this paper, UCSMssp, a new novel ubiquitous computing service model based on SPKI/SDSI and P2P is presented. SPKI-based authorization is exploited in UCSMssp to solve above problems in small-scale ubiquitous computing environments. The DHT and flooding or random walk technology of Peer-to-Peer overlay network over the Internet is expanded to solve the routing search in large-scale ubiquitous computing environments. The architecture of ubiquitous computing environment, the service authorization processes and the service supply processes etc of UCSMssp are described in the paper. The performance analysis shows that UCSMssp is a suitable security solution used in large-scale ubiquitous computing environments.