Provably Secure Electronic Cash Based on Blind Multisignature Schemes

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Though various blind multisignature schemes have been proposed for secure electronic cash, the formal model of security was not discussed. This paper first formalizes the security notions for e-cash schemes based on the blind multisignature scheme. We then construct a blind multisignature scheme and propose a new untraceable e-cash scheme which is provably secure under the DDH assumption in the random oracle model applying the blind multisignature scheme. The proposed scheme can ensure the framing attack by banks where they collude to simulate the double-spending of an honest user.