In a fair blind signature process, a user interacts with a signer in order to complete a 7-tuple (A,e,s,t,x.sub.u,x,m) such that A.sup.e=a.sub.0a.sub.1.sup.xa.sub.2.sup.ma.sub.3.sup.x.sup.ua.sub.4.sup.t- a.sub.5.sup.s (mod n), where a.sub.0, a.sub.1, a.sub.2, a.sub.3, a.sub.4 and a.sub.5 and n are elements of the Signer's public key (PUBK.sub.s). During the signature-issuing phase the user (U) provides the signer (S) with a data element (a.sub.1.sup.x) encrypted according to a key (f) known to a trusted authority (TA), and this data element (a.sub.1.sup.x) is disclosed during transmission of the signed message. Similarly, the signed message is transmitted associated with second encrypted data comprising a second data element (a.sub.3.sup.x.sup.u) encrypted according to a key (f) known to the trusted authority (TA), and this second data element (a.sub.3.sup.x.sup.u) is disclosed to the Signer during the signature-issuing phase. Thus, the trusted authority (TA) can revoke the anonymity of the digital signature.