So far an electronic cash is based on the discrete logarithm on $GF(q)^*$ for its security. But there is a efficient attack called the index calculus attack. Whereas at present no subexponential algorithm is known for the discrete logarithm problem on a general elliptic curve. Hence in this paper we construct an electronic cash over an elliptic curve, and improve the divisibility of the previous ones. We modify the Brands' scheme and Lim-Lee's. This satisfies all the criteria of Okamoto for an ideal cash.
