Electronic cash protocol over elliptic curves

Abstract

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.