Achieving Optimal Anonymity in Transferable E-Cash with a Judge

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Abstract

Electronic cash (e-cash) refers to money exchanged electronically. The main features of traditional cash are usually considered desirable also in the context of e-cash. One such property is off-line transferability, meaning the recipient of a coin in a transaction can transfer it in a later payment transaction to a third person without contacting a central authority. Among security properties, the anonymity of the payer in such transactions has been widely studied. This paper proposes the first efficient and secure transferable e-cash scheme with the strongest achievable anonymity properties, introduced by Canard and Gouget. In particular, it should not be possible for adversaries who receive a coin to decide whether they have owned that coin before. Our proposal is based on two recent cryptographic primitives: the proof system by Groth and Sahai, whose randomizability enables strong anonymity, and the commuting signatures by Fuchsbauer, which allow one to sign values that are only given as encryptions.

This work has been supported by the French Agence Nationale de la Recherche under the PACE 07 TCOM Project, the European Commission through the ICT Program under Contract ICT-2007-216676 ECRYPT II and EPSRC Grant EP/H043454/1. Work done while the third author was at École normale supérieure, Paris, France.