1. In a cloud computing environment composed of a plurality of Virtual Machine (VM) servers wherein each VM server comprises a processor enabling an execution of hypervisor software in order to assign virtual machines to client terminals through a user network, and of at least one authentication server enabling a bilaterally authenticated connection between a client terminal and the cloud, a device for executing encrypted programs comprising: a bilaterally authenticated connection establishment module for establishing a bilaterally authenticated connection between a client terminal and the cloud; an encrypted memory image generation module for generating, in response to a request to connect to the cloud from said client terminal, an encrypted memory image for a virtual machine assigned to said client terminal; and a security module for execution in response to requests of read/write of data into said encrypted memory image received from the processor of said virtual machine, of on-the-fly encryption and decryption operations in read/write of the data associated with said encrypted memory image, wherein the encrypted memory image generation module comprises means for: generating a private encryption key to assign a virtual memory image to said client terminal; downloading to said client terminal the assigned virtual memory image; encrypting the assigned virtual memory image; and uploading the assigned and encrypted virtual memory image to the cloud; and wherein the bilaterally authenticated connection establishment module for establishing the authenticated connection between said client terminal and the cloud comprise chip card reader type means coupled to said client terminal to calculate an encryption key as a function of a personal code stored on the chip card and means coupled to an authentication server of the cloud for performing an authentication upon reception of the personal code.