A method for authenticating an entity by a verifier, the entity having an identifier, the verifier having a pair of private and public keys, comprising: sending to the entity a first random number selected by the verifier; a step wherein the entity encrypts a value by means of the public key of the verifier, said value including the first random number and an authentication datum on which the identifier of the entity depends; and the entity of said encrypted value sending a reply to authenticate said entity. The invention can be applied to the field of low-cost cryptography, especially the field of radio-identification.