Short E-Cash
Abstract
We present a bandwidth-efficient off-line anonymous e-cash scheme with traceable coins. Once a user double-spends, his identity can be revealed and all his coins in the system can be traced, without resorting to TTP. For a security level comparable with 1024-bit standard RSA signature, the payment transcript size is only 512 bytes. Security of the proposed scheme is proven under the q-strong Diffie-Hellman assumption and the decisional linear assumption, in the random oracle model. The transcript size of our scheme can be further reduced to 192 bytes if external Diffie-Hellman assumption is made. Finally, we propose a variant such that there exists a TTP with the power to revoke the identity of a payee and trace all coins from the same user, which may be desirable when a malicious user is identified by some non-cryptographic means.
Keywords
E-cash Coin-traceability Bilinear PairingPreview
Unable to display preview. Download preview PDF.
References
- 1.Abe, M., Fujisaki, E.: How to Date Blind Signatures. In: Kim, K.-c., Matsumoto, T. (eds.) ASIACRYPT 1996. LNCS, vol. 1163, pp. 244–251. Springer, Heidelberg (1996)CrossRefGoogle Scholar
- 2.Ateniese, G., Camenisch, J., Joye, M., Tsudik, G.: A Practical and Provably Secure Coalition-Resistant Group Signature Scheme. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 255–270. Springer, Heidelberg (2000)CrossRefGoogle Scholar
- 3.Boneh, D., Boyen, X.: Short Signatures Without Random Oracles. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 56–73. Springer, Heidelberg (2004)CrossRefGoogle Scholar
- 4.Boneh, D., Boyen, X., Shacham, H.: Short Group Signatures. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 41–55. Springer, Heidelberg (2004)Google Scholar
- 5.Boneh, D., Lynn, B., Shacham, H.: Short Signatures from the Weil Pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514–532. Springer, Heidelberg (2001)CrossRefGoogle Scholar
- 6.Brands, S.: Untraceable Off-line Cash in Wallets with Observers. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 302–318. Springer, Heidelberg (1994)Google Scholar
- 7.Brickell, E., Gemmell, P., Kravitz, D.: Trustee-based Tracing Extensions to Anonymous Cash and the Making of Anonymous Change. In: SODA 1995: ACM-SIAM Symposium on Discrete Algorithms, pp. 457–466. SIAM, Philadelphia (1995)Google Scholar
- 8.Camenisch, J., Hohenberger, S., Lysyanskaya, A.: Compact E-Cash. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 302–321. Springer, Heidelberg (2005)CrossRefGoogle Scholar
- 9.Camenisch, J., Stadler, M.: Efficient Group Signature Schemes for Large Groups. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 410–424. Springer, Heidelberg (1997)Google Scholar
- 10.Canard, S., Traoré, J.: On Fair E-cash Systems Based on Group Signature Schemes. In: Safavi-Naini, R., Seberry, J. (eds.) ACISP 2003. LNCS, vol. 2727, pp. 237–248. Springer, Heidelberg (2003)CrossRefGoogle Scholar
- 11.Chaum, D.: Blind Signatures for Untraceable Payments. In: Advances in Cryptology 1981, pp. 199–203. Plenum, New York (1983)Google Scholar
- 12.Chaum, D., Fiat, A., Naor, M.: Untraceable Electronic Cash. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 319–327. Springer, Heidelberg (1990)Google Scholar
- 13.Chaum, D., van Heyst, E.: Group Signatures. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 257–265. Springer, Heidelberg (1991)CrossRefGoogle Scholar
- 14.Ferguson, N.: Single Term Off-Line Coins. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 318–328. Springer, Heidelberg (1994)CrossRefGoogle Scholar
- 15.Franklin, M.K., Yung, M.: Secure and Efficient Off-Line Digital Money (Extended Abstract). In: Lingas, A., Carlsson, S., Karlsson, R. (eds.) ICALP 1993. LNCS, vol. 700, pp. 265–276. Springer, Heidelberg (1993)Google Scholar
- 16.Jarecki, S., Shmatikov, V.: Handcuffing Big Brother: An Abuse-Resilient Transaction Escrow Scheme. In: Cachin, C., Camenisch, J.L. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 590–608. Springer, Heidelberg (2004)CrossRefGoogle Scholar
- 17.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)CrossRefGoogle Scholar
- 18.Lysyanskaya, A., Ramzan, Z.: Group Blind Digital Signatures: A Scalable Solution to Electronic Cash. In: Hirschfeld, R. (ed.) FC 1998. LNCS, vol. 1465, pp. 184–197. Springer, Heidelberg (1998)CrossRefGoogle Scholar
- 19.Maitland, G., Boyd, C.: Fair Electronic Cash Based on a Group Signature Scheme. In: Qing, S., Okamoto, T., Zhou, J. (eds.) ICICS 2001. LNCS, vol. 2229, pp. 461–465. Springer, Heidelberg (2001)CrossRefGoogle Scholar
- 20.Nakanishi, T., Haruna, N., Sugiyama, Y.: Unlinkable Electronic Coupon Protocol with Anonymity Control. In: Zheng, Y., Mambo, M. (eds.) ISW 1999. LNCS, vol. 1729, pp. 37–46. Springer, Heidelberg (1999)CrossRefGoogle Scholar
- 21.Okamoto, T.: An Efficient Divisible Electronic Cash Scheme. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 438–451. Springer, Heidelberg (1995)Google Scholar
- 22.Okamoto, T., Ohta, K.: Disposable Zero-Knowledge Authentications and Their Applications to Untraceable Electronic Cash. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 481–496. Springer, Heidelberg (1990)Google Scholar
- 23.Qiu, W., Chen, K., Gu, D.: A New Offline Privacy Protecting E-cash System with Revokable Anonymity. In: Chan, A.H., Gligor, V.D. (eds.) ISC 2002. LNCS, vol. 2433, pp. 177–190. Springer, Heidelberg (2002)CrossRefGoogle Scholar
- 24.Stadler, M., Piveteau, J.-M., Camenisch, J.: Fair Blind Signatures. In: Guillou, L.C., Quisquater, J.-J. (eds.) EUROCRYPT 1995. LNCS, vol. 921, pp. 209–219. Springer, Heidelberg (1995)CrossRefGoogle Scholar
- 25.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)CrossRefGoogle Scholar
- 26.Tsang, P.P., Wei, V.K.: Short Linkable Ring Signatures for E-Voting, E-Cash and Attestation. In: Deng, R.H., Bao, F., Pang, H., Zhou, J. (eds.) ISPEC 2005. LNCS, vol. 3439, pp. 48–60. Springer, Heidelberg (2005)CrossRefGoogle Scholar
- 27.von Solms, S., Naccache, D.: On Blind Signatures and Perfect Crimes. Computer Security 11(6), 581–583 (1992)CrossRefGoogle Scholar