It is common nowadays for data service providers to share their services through web service interfaces. Clients can access such services using web service request and response messages. A single data service often does not have all the information that a client requires. In such cases, multiple data service providers integrate (compose) their respective services to provide a complete solution to the client. This is called data service composition. A data service composition provides a unified interface such that a query to such a service composition is made as if all the data is available with a single data source. While this is useful and convenient, privacy becomes a serious concern wherein data service providers within the composition can infer information about data held with each other. This is somewhat mitigated with the use of a mediator to communicate between service providers. A mediator also makes it more convenient for service providers by working through the tasks of creating data composition plans and orchestrating the same. While mediators enable privacy between service providers, ensuring privacy between the mediators and service providers becomes the issue. Several research endeavours focus at ensuring privacy between mediators and service providers but in doing this lose track of whether the mediator is adhering to the shared data composition plan or not. In this paper, we propose a technique for ensuring that the mediator is strictly following the data composition plan whilst ensuring privacy between the mediator and service providers. The data service provider first authenticates that the input data is coming from the correct source as per the composition plan, and this is done whilst ensuring complete privacy between the mediator and other service providers. Similarly, data service providers also authenticate the destination of their output data. The approach is validated and its performance evaluated using a real world online retail dataset. Although it is not always possible to trust a mediator.