Abstract: A method for authenticating, by a second user, the identity of a first user, that includes a challenge communication from the second user to the first user, a response communication from the first user to the second user, and a verification by the second user, includes the steps: selection by the first user of a private key f in a ring R and a public key that includes ?(f) in a ring B that is mapped from f using the ring homomorphism ?: R?B, and publication by the first user of the public key; generation of the challenge communication by the second user that includes selection of a challenge c in the ring R; generation of the response communication by the first user that includes computation of a response comprising h in the ring R, where h is a function of c and f; and performing of a verification by the second user that includes determination of ?(c) from c, ?(h) from h, and an evaluation that depends on ?(h), ?(c) and ?(f).