1. Method for checking the authenticity of a document, such as credit-card, bank-card, check, access badge, etc., as well as the identity of the holder thereof by data processing, wherein said document is provided with data including a secret message for confirming the document holder identity to control the match between said document holder identity to control the match between said document and message, which comprises: providing said document with a specific characteristic which does not necessarily have to be kept secret but which defines a hidden relation notably with said message; feeding the data pertaining to the message and document characteristic to a computer; performing with said computer, from said data and possibly also from another remotely-conveyed, non-secret information, a first enciphering according to a first public-key cryptography method using only a first public key to produce first enciphered information; performing a second enciphering according to a second public-key cryptography method using only a second public key to produce a second enciphered information; and checking with the computer, by a third party and/or remotely with another computer, whether a match exists between said second enciphered information and at least one non-secret reference number, independent from the document, wherein the authenticity checking method involves only public-key encryption of said secret message.