An authentication method of a first module by a second module includes the steps of generating a first random datum by the second module to be sent to the first module, generating a first number by the first module starting from the first datum and by way of a private key, and generating a second number by the second module to be compared with the first number, so as to authenticate the first module. The step of generating the second number is performed starting from public parameters and is independent of the step of generating the first number.