# Scalable Divisible E-cash

3 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
DI-ENS - Département d'informatique - ENS Paris, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR 8548
Abstract : 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 many 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.
Document type :
Reports

https://hal.inria.fr/hal-01139400
Contributor : David Pointcheval Connect in order to contact the contributor
Submitted on : Saturday, April 4, 2015 - 7:02:33 PM
Last modification on : Thursday, March 17, 2022 - 10:08:37 AM

### Identifiers

• HAL Id : hal-01139400, version 1

### Citation

Sébastien Canard, David Pointcheval, Olivier Sanders, Jacques Traoré. Scalable Divisible E-cash. [Research Report] Cryptology ePrint Archive: Report 2015/300, IACR. 2015. ⟨hal-01139400⟩

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