A remark on the MOV algorithm for non-supersingular elliptic curves
In recent years, the study of the security of Elliptic Curve Cryptosystems (ECCs) have been received much at attention. The MOV algorithm, which reduces the elliptic curve discrete log problem (ECDLP) to the discrete log problem in finite fields with the Well pairing, is a representative attack on ECCs. Recently Kanayama et ai. observed a realization of the MOV algorithm for non-supersingular elliptic curves under the weakest condition. Shikata et al. independently considered a realization of the MOV algorithm for non-supersingular elliptic curves and proposed a generalization of the MOV algorithm. This short note explicitly shows that, under a usual cryptographical condition, me can apply the MOV algorithm to non-supersingular elliptic curves by using the multiplication by constant maps as in the case of supersingular. Namely, it is explicitly showed that we don't need such a generalization in order to realize the MOV algorithm for non-supersingular elliptic curves under a usual cryptographical condition.
mov algorithm elliptic curve discrete logarithm problem