A Secure and Efficient Off-line Electronic Payment System forWireless Networks


  • Horea Oros Department of Mathematics and Computer Science, University of Oradea Str. Universitatii 1, Oradea, Romania
  • Constantin Popescu Department of Mathematics and Computer Science, University of Oradea Str. Universitatii 1, Oradea, Romania


Electronic payment system, bilinear pairings, group signatures, membership certificate


An electronic cash system allows the exchange of digital coins with value assured by the bank’s signature and with concealed user identity. In an electronic cash system, a user can withdraw coins from the bank and then spends each coin anonymously and unlinkably. In this paper we propose a secure and efficient off-line electronic payment system based on bilinear pairings and group signature schemes. The anonymity of the customer is revocable by a trustee in case of a dispute. Because the amount of communication in the payment protocol is about 480 bits, the proposed off-line electronic payment system can be used in wireless networks with limited bandwidth.


M. Au, W. Susilo, Y. Mu, Practical anonymous divisible e-cash from bounded accumulators, Proceedings of Financial Cryptography and Data Security, Lecture Notes in Computer Science 5143 Springer-Verlag, pp. 287-301, 2008. http://dx.doi.org/10.1007/978-3-540-85230-8_26

D. Boneh and M. Franklin, Identity-based encryption from theWeil pairings. Advances in Cryptology-Crypto 2001, Lecture Notes in Computer Science 2139, Springer-Verlag, pp.213-229, 2001. http://dx.doi.org/10.1007/3-540-44647-8_13

D. Boneh, C. Gentry, B. Lynn, and H. Shacham, Aggregate and verifiably encrypted signatures from bilinear maps. In Advances in Cryptology - Eurocrypt'03, Lecture Notes in Computer Science 2656, Springer-Verlag, pp. 416-432, 2003. http://dx.doi.org/10.1007/3-540-39200-9_26

S. Canard, A. Gouget, Divisible e-cash systems can be truly anonymous, Proceedings of EUROCRYPT 2007, Lecture Notes in Computer Science 4515, Springer-Verlag, pp. 482-497, 2007. http://dx.doi.org/10.1007/978-3-540-72540-4_28

D. Chaum, Blind signature for untraceable payments. Proceddings of Eurocrypt'82, Plenum Press. pp.199- 203, 1983.

D. Chaum, A. Fiat, M. Naor, Untraceable electronic cash, Proceedings of the Crypto'88, pp. 319-327, 1990. http://dx.doi.org/10.1007/0-387-34799-2_25

X. Chen,F. Zhang, K. Kim, A New ID-based Group Signature Scheme from Bilinear Pairings. Journal of Electronics, 23, pp. 892-900, 2006. http://dx.doi.org/10.1007/s11767-005-0065-2

C. Fun, Ownership-attached unblinding of blind signatures for untraceable electronic cash, Information Science, 176(3), pp. 263-284, 2006. http://dx.doi.org/10.1016/j.ins.2004.10.010

M. Lee, G. Ahn, J. Kim, J. Park, B. Lee, K. Kim, H. Lee, Design and implementation of an efficient fair off-line e-cash system based on elliptic curve discrete logarithm problem, Journal of Communications and Networks, 4(2), pp. 81-89, 2002. http://dx.doi.org/10.1109/JCN.2002.6596898

T. Okamoto, K. Ohta, Universal electronic cash, Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology, pp. 324-337, 1992. http://dx.doi.org/10.1007/3-540-46766-1_27

T. Okamoto, An efficient divisible electronic cash scheme, Proceedings of Crypto'95, Lecture Notes in Computer Science 963, Springer-Verlag, pp. 438-451, 1995.

C. Popescu, An Electronic Cash System Based on Group Blind Signatures. Informatica, 17(4), pp. 551-564, 2006.

C.P. Schnorr, Efficient signature generation for smart cards, Journal of Cryptology, 4(1991), pp. 239-252, 1991.

Zuhua Shao, A provably secure short signature scheme based on discrete logarithms, Information Sciences: an International Journal, vol.177(23), pp. 5432-5440, 2007. http://dx.doi.org/10.1016/j.ins.2007.05.039

H. Wang, J. Cao, Y. Zhang, A flexible payment scheme and its role-based access control. IEEE Transactions Knowledge Data Engeneering, 17, pp. 425-436, 2005. http://dx.doi.org/10.1109/TKDE.2005.35

D. Yao, R. Tamassia, Cascaded Authorization with Anonymous-Signer Aggregate Signatures. Proceedings of the Seventh Annual IEEE Systems, Man and Cybernetics Information Asssurance Workshop, USA, pp.84-91, 2006.



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