A system comprising a remote processing centre, an on-board device installed on a vehicle and at least an external device present in the vehicle, installed on-board the vehicle or arranged in the vicinity of the vehicle; the on-board device being adapted and configured to acquire data relating to motion and/or driving parameters of the vehicle, the on-board device comprising: - at least one data source (13, 14) internal to the on-board device adapted to provide in output a first data signal containing data correlated to motion and/or driving parameters of the vehicle; - a data processing unit operatively connected to the internal data source (13, 14) to receive and process said first data signal; - a long-range radio communication interface operatively connected to the data processing unit to allow a data transmission on a telecommunications network between the data processing unit and the remote processing centre; - a first short-range Bluetooth radio communication interface operatively connected to the data processing unit to allow the on-board device to receive at least one data signal from the external device, wherein the external device comprises a data source external to the on-board device and a second short-range Bluetooth radio communication interface; wherein: - the on-board device is adapted and configured and in particular programmed in such a way that the first short-range Bluetooth radio connection interface is adapted and configured for allow the on-board device to receive data signals from the external device on at least one advertising channel of the first short-range Bluetooth radio connection interface; - the on-board device is programmed to receive encrypted data signals on the advertising channel and wherein the processing unit is programmed to decode said data; - said data signals are encrypted with a common encryption key known to both said on-board device and to said external device, the common encryption key being set in the on-board device and the external device during a production phase; - said on-board device, after installation on the vehicle, is adapted and configured to receive a new encryption key from the remote processing centre through the long-range communication interface and to transmit said encryption key to said external device through the short-range Bluetooth radio communication interface. - at least one data source (13, 14) internal to the on-board device adapted to provide in output a first data signal containing data correlated to motion and/or driving parameters of the vehicle; - a data processing unit operatively connected to the internal data source (13, 14) to receive and process said first data signal; - a long-range radio communication interface operatively connected to the data processing unit to allow a data transmission on a telecommunications network between the data processing unit and the remote processing centre; - a first short-range Bluetooth radio communication interface operatively connected to the data processing unit to allow the on-board device to receive at least one data signal from the external device, wherein the external device comprises a data source external to the on-board device and a second short-range Bluetooth radio communication interface; - the on-board device is adapted and configured and in particular programmed in such a way that the first short-range Bluetooth radio connection interface is adapted and configured for allow the on-board device to receive data signals from the external device on at least one advertising channel of the first short-range Bluetooth radio connection interface; - the on-board device is programmed to receive encrypted data signals on the advertising channel and wherein the processing unit is programmed to decode said data; - said data signals are encrypted with a common encryption key known to both said on-board device and to said external device, the common encryption key being set in the on-board device and the external device during a production phase; - said on-board device, after installation on the vehicle, is adapted and configured to receive a new encryption key from the remote processing centre through the long-range communication interface and to transmit said encryption key to said external device through the short-range Bluetooth radio communication interface.