Abstract
In this paper, we introduce the concept of Additive Non-Interactive Zero Knowledge (NIZK). We extend the notion of NIZK proofs to include the prover’s identity as part of the theorem being proved. An additive proof allows a verifier to construct a new proof of knowledge using the information from an old proof. Intuitively, an additive proof is a proof of knowledge of knowledge. As an application of this concept, we propose a digital cash scheme with transferable coins.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Wiles, A.: Modular elliptic curves and Fermat’s last theorem. AM 141(3), 443–551 (1995)
Goldreich, O.: Zero-knowledge twenty years after its invention (2002)
Goldreich, O., Oren, Y.: Definitions and properties of zero-knowledge proof systems. Journal of Cryptology 7(1), 1–32 (1994)
Goldreich, O.: Foundations of Cryptography. volume Basic Tools. Cambridge University Press, Cambridge (2001)
Goldwasser, S.: New directions in cryptography: Twenty some years later (or cryptography and complexity theory: A match made in heaven). In: 38th Annual Symposium on Foundations of Computer Science, pp. 314–324. IEEE, Los Alamitos (1997)
Blum, M., Feldman, P., Micali, S.: Non-interactive zero-knowledge and its applications. In: STOC 1988: Proceedings of the twentieth annual ACM symposium on Theory of computing, pp. 103–112. ACM Press, New York (1988)
Blum, M., Santis, A.D., Micali, S., Persiano, G.: Noninteractive zero-knowledge. SIAM J. Comput. 20(6), 1084–1118 (1991)
Bellare, M., Goldwasser, S.: New paradigms for digital signatures and message authentication based on non-interactive zero knowledge proofs. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 194–211. Springer, Heidelberg (1990)
Feige, U., Lapidot, D., Shamir, A.: Multiple noninteractive zero knowledge proofs under general assumptions. SIAM J. Comput. 29(1), 1–28 (2000)
Camenisch, J., Maurer, U.M., Stadler, M.: Digital payment systems with passive anonymity-revoking trustees. In: Martella, G., Kurth, H., Montolivo, E., Bertino, E. (eds.) ESORICS 1996. LNCS, vol. 1146, pp. 33–43. Springer, Heidelberg (1996)
Panurach, P.: Money in electronic commerce: digital cash, electronic fund transfer, and ecash. Commun. ACM 39(6), 45–50 (1996)
Rabi, M., Sherman, A.T.: An observation on associative one-way functions in complexity theory. Inf. Process. Lett. 64(5), 239–244 (1997)
Saxena, A., Soh, B.: A new paradigm for group cryptosystems using quick keys. In: Proceedings of the The 11th IEEE International Conference on Networks (ICON 2003), Sydney, Australia, pp. 385–389 (2003)
Hemaspaandra, L.A., Rothe, J., Saxena, A.: Enforcing and defying associativity, commutativity, totality, and strong noninvertibility for one-way functions in complexity theory. Technical Report UR CSD;854, University of Rochester, December 2004 (2004)
Hemaspaandra, L.A., Pasanen, K., Rothe, J.: If p ≠ np then some strongly noninvertible functions are invertible. In: Freivalds, R. (ed.) FCT 2001. LNCS, vol. 2138, pp. 162–171. Springer, Heidelberg (2001)
Saxena, A., Soh, B.: Contributory approaches to centralized key agreement in dynamic peer groups. In: Proceedings of the The 11th IEEE International Conference on Networks (ICON 2003), Sydney, Australia, pp. 397–402 (2003)
Saxena, A., Soh, B.: A novel method for authenticating mobile agents with one-way signature chaining. In: Proceedings of The 7th International Symposium on Autonomous Decentralized Systems (ISADS 2005), China (2005) (to appear)
Saxena, A., Soh, B.: Authenticating mobile agent platforms using signature chaining without trusted third parties. In: Proceedings of The 2005 IEEE International Conference on e-Technology, e-Commerce and e-Service (EEE 2005), Hong kong (2005) (to appear)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Saxena, A., Soh, B., Zantidis, D. (2005). A Digital Cash Protocol Based on Additive Zero Knowledge. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2005. ICCSA 2005. Lecture Notes in Computer Science, vol 3482. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11424857_74
Download citation
DOI: https://doi.org/10.1007/11424857_74
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25862-9
Online ISBN: 978-3-540-32045-6
eBook Packages: Computer ScienceComputer Science (R0)