A method for authenticating at least one client entity (A) by means of an authentication entity (B) based on a public key encryption (ASYM(PB,R))/decryption (ASYM(SB,R′)) algorithm, implemented on the client entity side and authentication entity side, respectively, including, on the client entity side: generation of a cryptogram (R′) by encryption of a message (R) containing identification data (idA) of said entity, secret data (KA), and an authentication counter value (CA, CB), guaranteeing that said authentication is not replayed, sending of the cryptogram to the authentication entity and, on the authentication entity side: decryption of said cryptogram, from a data base (DB) storing, for each client entity capable of being authenticated, a record containing at least the identification data for said client entity, determination of the record of said data base corresponding to the decrypted identification data, and verification of the correspondence between the decrypted secret data and the secret data of said client entity, obtained from said record.