Confidential provisioning of secret keys over the air

For personalizing a smart card (SC) coupled with a communication device (CD) of a user being a subscriber of a first telecommunication network (TN1) and wishing to become a subscriber of a second telecommunication network (TN2), a first authentication key (AK_1) being stored in the smart card (SC) and in an first application server (AS1) included in the first telecommunication network, the smart card: establishes a secure session with a second application server (AS2) included in the second telecommunication network (TN2) via the first telecommunication network, negotiates with the first application server (AS1) and the second application server in order that the smart card (SC) and the second application server agree on an second authentication key (AK_2), by exchanging messages referring to shared values and shared functions by means of a secure multiparty computation protocol involving the smart card, the first application server and the second application server, and computing the second authentication key (AK_2) depending on at least a shared value and a shared function, replaces the first authentication key by the second authentication key.