Authentication and signature process with reduced number of calculations.The process involves a first entity called the "prover", which possesses a public key v and a secret key s, these keys verify the relation v=s.sup.-t (mod n), where n is an integer called modulus and t is a parameter, and a second entity called a "verifier", which knows the public key v. This process implies exchange of information following a "zero-knowledge protocol" between the verifier and the prover and cryptographic calculations on this information, some calculations being carried out "modulo n". The process of the invention is characterised by the fact that the modulus n is specific to the prover that communicates this modulus to the verifier.