1. A Direct Anonymous Attestation, DAA, method by which a Signer computing entity uses a credential supplied by an Issuer to prove to a Verifier without the identity of the Signer being revealed, Issuer attestation to the Signer's possession of a particular characteristic, the method using a non-degenerate, computable, bilinear map e of the form: G 1 ×G 2 εG where G 1 , G 2 , and G are cyclic groups, and the credential being a CL-LRSW signature on a secret f known only to the Signer; the method comprising the Signer computing entity: forming an Alternative CL-LRSW signature by exponentiation, using a random exponent, of components of the credential; forming a signature proof of knowledge, incorporating the Alternative CL-LRSW signature, to prove knowledge of the secret f and the random exponent; and sending the signature proof of knowledge to the Verifier; the Signer computing entity comprising a Host with an associated entity that possesses the characteristic attested to by the credential and holds the secret f secret from the Host; the Host and the associated entity cooperating in the forming of the signature proof of knowledge, wherein the signature proof of knowledge comprises: the Host using a component of the Alternate CL-LRSW signature and the map e to compute an element in G which the Host then provides to the associated entity; the associated entity using this element to compute a component of the signature proof of knowledge; and associated entity checking that the element provided by the Host belongs to G.