In this paper we present a new fair off-line electronic cash system based on Elliptic Curve Discrete Logarithm Problem. To achieve this, we employed the fair off-line electronic cash system based on discrete logarithm problem suggested by Popescu and Oros [17] and extended it on an elliptic curve over the finite field GF(2n ) . This naturally reduces the message size to 72% compared with the original scheme and makes it possible to handle a smart card. The anonymity of the system can be revokable under certain conditions by an off-line trusted third party.
Cryptography, electronic cash system, blind signatures, elliptic curve discrete logarithm problem.
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