Set membership proofs in data processing systems

A method and apparatus for proving and a method and apparatus for verifying that a secret value is a member of a predetermined set of values. The proving mechanism receives a set of signatures which has respective values in the predetermined set signed using a private key. The proving mechanism sends to the verifying mechanism a commitment on the secret value of the proving mechanism. The proving mechanism and verifying mechanism then communicate to implement a proof of knowledge protocol demonstrating knowledge by the proving mechanism of a signature on the secret value committed to in the commitment, thus proving that the secret value is a member of the predetermined set.