A digital signature method and apparatus is provided in which a first party with a first public/private key pair forms an ambiguous signature on subject data using at least the private key of the first key pair, a keystone initially only known to the first party, and the public key of at least one other public/private key-pair. This signature is ambiguous in that a signature-checking party can only verify that the signature is in the set comprising a signature created by the first party and a respective signature created by the possessor of the private key of the or each of the key pairs the public key of which was used in creating the signature. Revelation of the keystone renders the signature unambiguous. Such an ambiguous signature can be used to implement a fair exchange of signatures between any number of parties, with the exchanged signatures being ambiguous signatures until revelation of the initial signer's keystone.