1. In a cloud computing environment composed of a plurality of servers and client terminals suitable for connecting to the cloud, one of the servers comprising a processor and a main memory enabling the execution of hypervisor software in order to assign virtual machines to the client terminals, a device comprising: an encrypted memory image generation module for generating, in response to a request to connect to the cloud from a client terminal, an encrypted memory image of a virtual machine assigned to the client terminal; a storage server to store the encrypted memory image; and a security module coupled to the storage server and to said one of the servers, to execute, in response to data read/write requests received from the processor of one of the servers, on-the-fly encryption and decryption operations of the data stream associated with said encrypted memory image.