Abstract: Digital signature techniques are disclosed in which exponents may be selected by the message to be signed itself, by the signing party, by the party providing the message to the signing party for signature, and/or by a party to whom the signature is shown. When a message selects the exponent(s), the need for "hash functions" in known signature schemes is overcome. When the exponent is chosen by the party receiving the signature, to take another example, computation, storage and bandwidth requirements of known one-show blind signature systems may be improved. Also, the bank cannot falsely incriminate a payer for showing a signature more than once, even if the bank has unlimited computing resources.

Abstract: A cryptographic system allows, in one exemplary use, a supplier to cryptographically transform a plurality of messages responsive to secret keys; the transformed messages to be digitally signed by a signer; and the signed transformed messages returned to the supplier to be transformed by the supplier, responsive to the same secret keys, in such a way that a digital signature related to each original message is developed by the supplier. One important property of these systems is that the signer cannot determine which transformed message received for signing corresponds with which digital signature--even though the signer knows that such a correspondence must exist.

Abstract: 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.