The local digital network comprises: access devices, for receiving data originating from outside the network and transmitting them at a point of the network; and presentation devices for receiving the data flowing in the network and presenting them at a point of the network. The data flow in the network in encrypted form and all the devices of the network use a single key, the local key of the network, for the encryption and decryption of the data. Preferably, the local key of the network is formed by a pair of public and private keys. The purpose of this network is to make it possible to copy data in the local network whilst preventing pirate copies destined for other local networks.