Electronic commerce is an emerging area and one of the technological innovations of business management and information technology. A fair online electronic cash system with double spending tracing based on elliptic curve cryptography is presented in this paper. The security of the protocols is based on the computational hard elliptic curve discrete logarithm problem. In the proposed scheme, the anonymity of the user is maintained and is revocable by an on-line trusted third party under certain conditions. Dual spending of the same coin by the user is traced out by the bank. The proposed scheme is illustrated using Matlab 7.1

Cryptography, electronic cash system, elliptic curve, anonymity, unforgeability, double spending tracing

[1] Brands S, “Untraceable off-line cash in wallets with observers”, Advances in Cryptology: Proceedings of Crypto ’93, Lecture Notes in Computer Science, Springer-Verlag, (1994) pp. 302-318.
[2] Chaum D, “ Blind Signature for untraceable Payments”, Advances in Cryptology-Crypto’ 82, (1982) 199-203.
[3] Chaum D, Fiat A and Naor M, “Untraceable Electronic Cash” Advances in Cryptology CRYPTO `88, LNCS 403, Springer Verlag,(1988) 319-327.
[4] Chaum D , “Online Cash Checks” Advances in Cryptology-EUROCRYPT`89, LNCS 434, Springer-Verlag, (1989) 288-293.
[5] Hou X, Tan C H , “A New Electronic Cash Model”,Proceedings of the International Conference on Information Technology, Coding and Computing (ITCC’05).
[6] Hou X, Tan C H, “On Fair Traceable Electronic Cash”, Proceedings of the 3rd Annual Communication Networks and Services Research Conference (CNSR’05).
[7] Hankerson D, Menezes A and Vanstone S, “Guide to Elliptic Curve Cryptography”, Springer Verlag New York, Inc,2004.
[8] Hans Delfs and Helmut Knebl, “Introduction To Cryptography, Principles and Applications”,Springer ,(1998),91-109.
[9] Khalid O Elaalim and Shoubao Yang, “Secure Electronic Cash Using Elliptic Curve Cryptography Based On Zero Knowledge Proof”, International Journal Of Cryptology Research ,3(1) : (2011) 15-26.
[10] Khalid O Elaalim and Shoubao Yang, “Electronic Cash System With Double Spending Tracing Based On Elliptic Curve Cryptography”, Journal Of Computational Information Systems 6:9(2010), 2949-2957.
[11] Popescu C, “A Fair Off-line Electronic Cash System Based On Elliptic Curve Discrete Logarithm Problem”, Studies in Informatics and Control, Vol. 14, No. 4,(2005) 291-298.
[12] Popescu C, “ A Secure E-cash Transfer System based on the Elliptic Curve Discrete Logarithm Problem”, Informatica, Vol.22, No. 3,(2011) 395-409.
[13] Ziba Eslami and Mehdi Talebi, “A New Fair Untraceable Off-Line Electronic Commerce Research and Applications , 10(2011) 59-66.