An authentication method is performed between a first party and a second party. The method includes: i) determining a challenge; ii) sending the challenge to the second party; receiving a response from the second party including a second cryptogram; computing a first cryptogram using the challenge and the key of the first party; determining if the first cryptogram matches the second cryptogram received from the second party. If the first cryptogram does not match the second cryptogram, the method further includes performing a computation using the first cryptogram and the second cryptogram; and comparing a result of the computation with a stored set of results to recover a first data element carried by the second cryptogram.