A Practical Off-line Electronic Cash System on Smart Cards Achieving Untraceability, Divisibility, and Transferability

A divisible off-line electronic cash system based on cut-and-choose has first been proposed by [OO91] and recently more efficient single term divisible cash system was presented in [EO94] which is based on Brand's scheme [Bra93]. In this paper, we present a different type of single term divisible electronic cash system which is more efficient than previously proposed systems such as [OO91], [YLR93], and [EO94] in the standpoint of the amount of communication, the number of modular multiplications required in the payment transactions, and the storage requirement in the withdrawal protocol. Our scheme is a modified version of [LL93], where the major improvement has been made in its withdrawal transaction to introduce untraceability and multi-spendability. We have borrowed the idea of the withdrawal protocol of our scheme from [EO94] with minor modifications. Transferability in our scheme allows only a finite number of transfer. Our scheme satisfies an the desirable properties of an electronic cash system such as untraceability, divisibility and transferability. In addition, we present a n-spendable cash. The basic idea of extension to multi-spendability has been borrowed from [Bra93] with minor modifications.