Abstract
We present the first fair e-cash system with a compact wallet that enables users to spend efficiently k coins while only sending to the merchant \(\mathcal{O}(\lambda\log k)\) bits, where λ is a security parameter. The best previously known schemes require to transmit data of size at least linear in the number of spent coins. This result is achieved thanks to a new way to use the Batch RSA technique and a tree-based representation of the wallet. Moreover, we give a variant of our scheme with a less compact wallet but where the computational complexity of the spend operation does not depend on the number of spent coins, instead of being linear at best in existing systems.
This work has been financially supported by the French Agence Nationale de la Recherche and the TES Cluster under the PACE project while 2nd author was working at Orange Labs and 4th author at ENS.
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References
Camenisch, J., Hohenberger, S., Lysyanskaya, A.: Compact E-Cash. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 302–321. Springer, Heidelberg (2005)
Au, M.H., Wu, Q., Susilo, W., Mu, Y.: Compact E-Cash from Bounded Accumulator. In: Abe, M. (ed.) CT-RSA 2007. LNCS, vol. 4377, pp. 178–195. Springer, Heidelberg (2006)
Canard, S., Gouget, A., Hufschmitt, E.: A Handy Multi-coupon System. In: Zhou, J., Yung, M., Bao, F. (eds.) ACNS 2006. LNCS, vol. 3989, pp. 66–81. Springer, Heidelberg (2006)
Au, M.H., Susilo, W., Mu, Y.: Practical Compact E-Cash. In: Pieprzyk, J., Ghodosi, H., Dawson, E. (eds.) ACISP 2007. LNCS, vol. 4586, pp. 431–445. Springer, Heidelberg (2007)
Chaum, D.: Blind Signatures for Untraceable Payments. In: CRYPTO 1982, pp. 199–203 (1982)
Fiat, A.: Batch RSA. J. Crypt. 10(2), 75–88 (1997)
Chaum, D., Fiat, A., Naor, M.: Untraceable Electronic Cash. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 319–327. Springer, Heidelberg (1990)
Brands, S.: Untraceable Off-line Cash in Wallets with Observers (Extended Abstract). In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 302–318. Springer, Heidelberg (1994)
Traoré, J.: Group Signatures and Their Relevance to Privacy-Protecting Off-Line Electronic Cash Systems. In: Pieprzyk, J.P., Safavi-Naini, R., Seberry, J. (eds.) ACISP 1999. LNCS, vol. 1587, pp. 228–243. Springer, Heidelberg (1999)
Ferguson, N.: Single term off-line coins. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 318–328. Springer, Heidelberg (1994)
Brands, S., Chaum, D.: Distance-Bounding Protocols (Extended Abstract). In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 344–359. Springer, Heidelberg (1994)
Pavlovski, C., Boyd, C., Foo, E.: Detachable Electronic Coins. In: Varadharajan, V., Mu, Y. (eds.) ICICS 1999. LNCS, vol. 1726, pp. 54–70. Springer, Heidelberg (1999)
Boyd, C., Foo, E., Pavlovski, C.: Efficient Electronic Cash Using Batch Signatures. In: Pieprzyk, J.P., Safavi-Naini, R., Seberry, J. (eds.) ACISP 1999. LNCS, vol. 1587, pp. 244–257. Springer, Heidelberg (1999)
Chaum, D.: Blind Signature System. In: CRYPTO 1983, pp. 153 (1983)
Schnorr, C.: Efficient identification and signatures for smart cards. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 239–252. Springer, Heidelberg (1990)
Girault, M., Poupard, G., Stern, J.: On the Fly Authentication and Signature Schemes Based on Groups of Unknown Order. J. Crypt. 19(4), 463–487 (2006)
Boudot, F., Traoré, J.: Efficient Publicly Verifiable Secret Sharing Schemes with Fast or Delayed Recovery. In: Varadharajan, V., Mu, Y. (eds.) ICICS 1999. LNCS, vol. 1726, pp. 87–102. Springer, Heidelberg (1999)
Kiayias, A., Tsiounis, Y., Yung, M.: Traceable Signatures. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 571–589. Springer, Heidelberg (2004)
Canard, S., Coisel, I., Traoré, J.: Complex zero-knowledge proofs of knowledge are easy to use. In: Susilo, W., Liu, J.K., Mu, Y. (eds.) ProvSec 2007. LNCS, vol. 4784, pp. 122–137. Springer, Heidelberg (2007)
Camenisch, J., Kiayias, A., Yung, M.: On the portability of generalized schnorr proofs. In: Joux, A. (ed.) EUROCRYPT 2009. LNCS, vol. 5479, pp. 425–442. Springer, Heidelberg (2009)
Fiat, A., Shamir, A.: How to Prove Yourself: Practical Solutions to Identification and Signature Problems. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 186–194. Springer, Heidelberg (1987)
Camenisch, J., Lysyanskaya, A.: A Signature Scheme with Efficient Protocols. In: Cimato, S., Galdi, C., Persiano, G. (eds.) SCN 2002. LNCS, vol. 2576, pp. 268–289. Springer, Heidelberg (2003)
Bellare, M., Namprempre, C., Pointcheval, D., Semanko, M.: The One-More-RSA-Inversion Problems and the Security of Chaum’s Blind Signature Scheme. J. Crypt. 16(3), 185–215 (2003)
Pointcheval, D., Stern, J.: Security Arguments for Digital Signatures and Blind Signatures. J. Crypt. 13(3), 361–396 (2000)
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Canard, S. et al. (2009). Fair E-Cash: Be Compact, Spend Faster. In: Samarati, P., Yung, M., Martinelli, F., Ardagna, C.A. (eds) Information Security. ISC 2009. Lecture Notes in Computer Science, vol 5735. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04474-8_24
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