Abstract. A blind signature scheme is a protocol for obtaining a signature from a signer such that the signer's view of the protocol cannot be linked to the resulting message-signature pair. Blind signature schemes are used in anonymous digital payment systems. Since the existing proposals of blind signature schemes provide perfect unlinkability, such payment systems could be misused by criminals, e.g. to safely obtain a ransom or to launder money. In this paper, a new type of blind signature schemes called fair blind signature schemes is proposed. Such schemes have the additional property that a trusted entity can deliver information allowing the signer to link his view of the protocol and the message-signature pair. Two types of fair blind signature schemes are distinguished and several realizations are presented. Keywords. Blind signatures, fair cryptosystems, electronic payment systems, cryptographic protocols.