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In this paper, we propose a scheme for private data transmission using chaotic lasers, which is derived from the well-known public key cryptography. With this new approach, it is possible to exchange data between any couple of subscribers in a network, while schemes based on chaotic lasers are usually restricted to transmission between two specific users, sharing a twin laser pair. This is possible by introducing a provider, who is responsible of the network security. For each subscriber a couple of twin chaotic lasers is required, one being held by the provider and the other by the subscriber himself. The basic two-laser scheme of chaotic transmission is then used for secure data exchange, both between two subscribers and between a subscriber and the provider. Several arrangements can be considered, based on this architecture, including the use of an electro-optical repeater, which is studied in detail in this paper. More advanced solutions can be also implemented, e.g., using a three-laser scheme. The Lang-Kobayashi model is used for simulations. Experiments are performed using InP-integrated modules.