Does anyone have an idea of what kind of public-key technologies are used in the bank perimeter ? Does banking card embedded x509 certificate ? OpenPGP ?
Perhaps a standard exists or a de-facto standard.
No, banks tend to use somewhat different technologies from the rest of the world. This doesn't necessarily mean that they use weak cryptography: banks tend to be good at risk management, and to put just enough money in security to make attacks rare without putting so much that security would cost more than the attacks that it would prevent. (As a customer of banks, the flaw in this approach is that it doesn't take account risk for the customer — that only enters the equation when banks are worried that some customers will be so unhappy that they'll change banks, which itself has a high cost for the customer.) For example, a lot of banking protocols still use 3DES when most of the rest of the world has standardized on AES.
The current standard used by major banking card providers is EMV. EMV uses some well-known building blocks: 3DES, SHA-1, RSA. This has been the standard protocol suite in Europe since the mid 2000s; a lot of other countries have migrated since then or are migrating. Many cards and terminals also support various legacy (often national) protocols for backward compatibility. Security is only as strong as the weakest link in the chain. Banks are pushing for EMV adoption by shifting liability for breaches to merchants when legacy protocols are used for a transaction, in order to convince merchants to renew their equipment to a newer generation that supports EMV.