Secure and efficient off-line digital money

Abstract

No off-line electronic coin scheme has yet been proposed which is both provably secure with respect to natural cryptographlc assumptions and efficient with respect to reasonable measures. We show that off-line coin schemes can be implemented securely and efficiently, where security is proven based on the hardness of the discrete log function and a pre-processing stage, and where efficiency is in a new sense that we put forth in this work: “a protocol is efficient if its communication complexity is independent of the computational complexity of its participants” (and thus the communication length and number of encryption operations is only a low-degree polynomial of the input).