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Compact E-Cash

  • Jan Camenisch
  • Susan Hohenberger
  • Anna Lysyanskaya
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3494)

Abstract

This paper presents efficient off-line anonymous e-cash schemes where a user can withdraw a wallet containing 2ℓ coins each of which she can spend unlinkably. Our first result is a scheme, secure under the strong RSA and the y-DDHI assumptions, where the complexity of the withdrawal and spend operations is \({\mathcal O}(\ell + k)\) and the user’s wallet can be stored using \({\mathcal O}(\ell + k)\) bits, where k is a security parameter. The best previously known schemes require at least one of these complexities to be \({\mathcal O}(2^{\rm \ell}\cdot k)\). In fact, compared to previous e-cash schemes, our whole wallet of 2ℓ coins has about the same size as one coin in these schemes. Our scheme also offers exculpability of users, that is, the bank can prove to third parties that a user has double-spent. We then extend our scheme to our second result, the first e-cash scheme that provides traceable coins without a trusted third party. That is, once a user has double spent one of the 2ℓ coins in her wallet, all her spendings of these coins can be traced. However, the price for this is that the complexity of the spending and of the withdrawal protocols becomes \({\mathcal O}(\ell \cdot k)\) and \({\mathcal O}(\ell \cdot k+k^{2})\) bits, respectively, and wallets take \({\mathcal O}(\ell \cdot k)\) bits of storage. All our schemes are secure in the random oracle model.

Keywords

Signature Scheme Random Oracle Blind Signature Trusted Third Party Random Oracle Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jan Camenisch
    • 1
  • Susan Hohenberger
    • 2
  • Anna Lysyanskaya
    • 3
  1. 1.Zurich Research LaboratoryIBM ResearchRüschlikonSwitzerland
  2. 2.CSAILMassachusetts Institute of TechnologyCambridgeUSA
  3. 3.Computer Science DepartmentBrown UniversityProvidenceUSA

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