The present invention relates to a method of authenticating, with an authentication server, a user having at his disposal a calculator storing at least one unique identifier specific to the calculator and one first secret key (KO) and calculating a non-invertible function (H); the method comprising: •reception of the unique identifier by the authentication server, which sends an item of information (challenge) and an action code; •reception by the authentication server of three results of the non-invertible function, •the first result (R0) depending on at least one item of data specific to a unique or quasi-unique element of the calculator (SN); •the second result (RT) depending on a Turing test, conditioned to the action code, carried out by the user; and •the third result (R1) depending on a second secret key (K1); •authentication of the user if all four of the unique identifier and the first, second and third results are valid.