The invention concerns a cryptographic method whereby a second entity (B) verifies by means of a public key, a proof provided by a first entity (A), which consists in the generation by the first entity (A) of a first random number r much higher than any first integer s included in a private key kept secret by the first entity (A). The first entity (A) generates a first element of proof resulting from a modulo n exponentiation of a first integer G included or not in said public key and whereof the exponent is the first random number r. In combination with the first element of proof, a so-called common number, is generated so that the second entity (B) and the first entity (A) should have knowledge of the common number. The first entity (A) generates an image y of said private key by linear combination of the first random number r and of at least a first private key integer s. At least a multiplicative coefficient of the linear combination is said common number. Any one entity generates a second element of proof Y equal to a power modulo n of a second integer G included or not in said public key and whereof the exponent is the image y of said common number, and sends the second element of proof Y to the first entity (B). The second entity (B) verifies whether the first element of proof is in conformity with a product modulo n of a power of the second element of proof Y whereof the exponent is a third integer e and of a power of a fourth integer v included in said public key whereof the exponent is said common number c.