A method of authentication of a contactless communication circuit (PICC) by a contactless communication terminal, successively comprising: a first phase comprising the transmission of an identifier of a first key (k) and an authentication control signal from the contactless communication terminal to the contactless communication circuit, the determination by the contactless communication circuit of a first random number (A 1) with no encryption operation using the first key (k), the first phase ending with the transmission of the first number (A 1) by the contactless communication circuit to the contactless communication terminal; a second phase comprising the determination by the contactless communication terminal of a second number (R b_pcd), by decryption of the first number by using the first key (k), the determination by the contactless communication terminal of a third number (R a_pcd ∥R' b _ pcd), obtained from the second number (R b_pcd) using a rotation of the bits of the second number by a plurality of bits, and the determination by the contactless communication terminal of a fourth number (B 1) by encryption of the third number (R a_pcd ∥R' b_pcd) by using the first key (k), the second phase ending with the transmission of the fourth number (B 1) by the contactless communication terminal to the contactless communication circuit; and a third phase comprising the decryption by the contactless communication circuit of the fourth number (B 1) by using the first key (k) to obtain the third number (R a_pcd ∥R' b_pcd) and the interruption by the contactless communication circuit of the authentication if a sixth number (R' b_pcd) obtained from the third number (R a_pcd ∥R'b b_pcd)is different from a seventh number (R' b), the seventh number (R' b) being determined by the contactless communication circuit (PICC) based on an eighth number (R b) obtained by decryption by the contactless communication circuit (PICC) of the first number (A 1) by using the first key (k), the method further comprising, in the first phase, a ninth number (R 1) being random is determined by the contactless communication circuit (PICC) with no operation of encryption, and the first number (A 1) is obtained by encryption, by the contactless communication circuit (PICC), of the ninth number by using a second key different from the first key (k), the second key having the same size as the first key, the encryption algorithm using the second key being the same as the encryption algorithm using the first key or in that, in the first phase, the first number (A 1) is obtained by encryption, by the contactless communication circuit (PICC), of a tenth non-random number by using a third key which is random, the third key having the same size as the first key, the encryption algorithm using the third key being the same as the encryption algorithm using the first key. a first phase comprising the transmission of an identifier of a first key (k) and an authentication control signal from the contactless communication terminal to the contactless communication circuit, the determination by the contactless communication circuit of a first random number (A 1) with no encryption operation using the first key (k), the first phase ending with the transmission of the first number (A 1) by the contactless communication circuit to the contactless communication terminal; a second phase comprising the determination by the contactless communication terminal of a second number (R b_pcd), by decryption of the first number by using the first key (k), the determination by the contactless communication terminal of a third number (R a_pcd ∥R' b _ pcd), obtained from the second number (R b_pcd) using a rotation of the bits of the second number by a plurality of bits, and the determination by the contactless communication terminal of a fourth number (B 1) by encryption of the third number (R a_pcd ∥R' b_pcd) by using the first key (k), the second phase ending with the transmission of the fourth number (B 1) by the contactless communication terminal to the contactless communication circuit; and a third phase comprising the decryption by the contactless communication circuit of the fourth number (B 1) by using the first key (k) to obtain the third number (R a_pcd ∥R' b_pcd) and the interruption by the contactless communication circuit of the authentication if a sixth number (R' b_pcd) obtained from the third number (R a_pcd ∥R'b b_pcd)is different from a seventh number (R' b), the seventh number (R' b) being determined by the contactless communication circuit (PICC) based on an eighth number (R b) obtained by decryption by the contactless communication circuit (PICC) of the first number (A 1) by using the first key (k), the method further comprising, in the first phase, a ninth number (R 1) being random is determined by the contactless communication circuit (PICC) with no operation of encryption, and the first number (A 1) is obtained by encryption, by the contactless communication circuit (PICC), of the ninth number by using a second key different from the first key (k), the second key having the same size as the first key, the encryption algorithm using the second key being the same as the encryption algorithm using the first key or in that, in the first phase, the first number (A 1) is obtained by encryption, by the contactless communication circuit (PICC), of a tenth non-random number by using a third key which is random, the third key having the same size as the first key, the encryption algorithm using the third key being the same as the encryption algorithm using the first key.