Procedure of authentication and signing messages using links small size and corresponding systems.

Authentication procedure that uses a first entity called a "authenticator" (A) and a second entity called "authenticator" (B), this method comprising the following operations: - the entity to be authenticated (A) sends at least one link c to the authenticating entity (B) having this link a certain size counted in number of bits, - the authenticating entity (B) receives the link c, chooses a random number e called the "question" and sends this question e to the entity to authenticating (a), - the entity to be authenticated (a) receives the question e, carries out calculations using this question e, the result of these calculations constituting a response y and sends this response to the authenticating entity (B), - the entity authenticating (B) receives the response and performs a calculation using this response y and verifies that this calculation returns the link received c, a security level equal to 1-2 -k is obtained by this authenticates tion where k is an integer that is fixed according to the desired security level, this method being characterized by the authenticating entity (B) measures the time interval (DeltaT) elapsing between the moment it addresses the entity to authenticated (a) and the moment it receives the response from the entity to be authenticated (a), and verifies that the measured time interval (DeltaT) is below a given time interval deltatmax, and in that the entity to be authenticated ( a) has a calculation capacity of around 2 P in said determined time interval (DELTAMAX), the link c used by the entity to be authenticated (a) has a size equal to at least (k + P) bits.