Untraceable off-line cash in wallet with observers

Abstract

Incorporating the property of untraceability of payments into off-line electronic cash systems has turned out to be no easy matter. Two key concepts have been proposed in order to attain the same level of security against double-spending as can be trivially attained in systems with full traceability of payments. The first of these, one-show blind signatures, ensures traceability of double-spenders after the fact. The realizations of this concept that have been proposed unfortunately require either a great sacrifice in efficiency or seem to have questionable security, if not both. The second concept, wallets with observers, guarantees prior restraint of double-spending, while still offering traceability of double-spenders after the fact in case tamper-resistance is compromised. No realization of this concept has yet been proposed in literature, which is a serious problem. It seems that the known cash systems cannot be extended to this important setting without significantly worsening the problems related to efficiency and security. We introduce a new primitive that we call restrictive blind signatures. In conjunction with the so-called representation problem in groups of prime order this gives rise to highly efficient off-line cash systems that can be extended at virtually no extra cost to wallets with observers under the most stringent of privacy requirements. The workload for the observer is so small that it can be performed by a tamper-resistant smart card capable of performing the Schnorr identification scheme. We also introduce new extensions in functionality (unconditional protection against framing, anonymous accounts, multi-spendable coins) and improve some known constructions (computional protection against framing, electronic checks). The security of our cash system and all its extensions can be derived directly from the security of the well-known Schnorr identification and signature schemes, and the security of our new primitive.