Scalable Divisible E-Cash

Divisible E-cash has been introduced twenty years ago but no construction is both fully secure in the standard model and efficiently scalable. In this paper, we fill this gap by providing an anonymous divisible E-cash construction with constant-time withdrawal and spending protocols. Moreover, the deposit protocol is constant-time for the merchant, whatever the spent value is. It just has to compute and store $2^l$ serial numbers when a value $2^l$ is deposited, compared to $2^n$ serial numbers whatever the spent amount (where $2^n$ is the global value of the coin) in the recent state-of-the-art paper. This makes a very huge difference when coins are spent in several times. Our approach follows the classical tree representation for the divisible coin. However we manage to build the values on the nodes in such a way that the elements necessary to recover the serial numbers are common to all the nodes of the same level: this leads to strong unlinkability and anonymity, the strongest security level for divisible E-cash.