Due to the increasing demand for cloud services and the threat of privacy invasion, the user is suggested to encrypt the data before it is outsourced to the remote server. The safe storage and efficient retrieval of d-dimensional data on an untrusted server has therefore crucial importance. The paper proposes a new encryption model which offers spatial order-preservation for d-dimensional data (SOPE model). The paper studies the operations for the construction of the encrypted database and suggests algorithms that exploit unique properties that this new model offers for the efficient execution of a whole range of well-known queries over the encrypted d-dimensional data. The new model utilizes well-known database indices, such as the B+-tree and the R-tree, as backbone structures in their traditional form, as it suggests no modifications to them for loading the data and for the efficient execution of the supporting query algorithms. An extensive experimental study that is also presented in the paper indicates the effectiveness and practicability of the proposed encryption model for real-life d-dimensional data applications.