Blind unanticipated signature systems

An improved blind signature system not requiring computation during blinding for anticipating which of a plurality of possible signatures will be made during signing, while still allowing the blinding party to unblind and recover the unanticipated kind of signature on what was blinded. An exemplary embodiment blinds by forming a product including a plurality of generators raised to powers normally secret from the signing party, and unblinds by forming a product with the multiplicative inverse of a signed form of the generators raised to the original powers. Re-blinding allows a signature on a value to be transformed into a signature on a particular blinded form of the value.