Correction on 'A.Scalar Multiplication Algorithm with Recovery of the y-Coordinate on the Montgomery Form and Analysis of Efficiency for Elliptic Curve Cryptosystems'

摘要

In [4], Okeya and Sakurai proposed the recovery of the y-coordinate on a Montgomery-form elliptic curve. With their method, it can calculate efficiently coordinates of scalar multiplication of point, in which we need only x-coordinate and finally, (x,y) of the terminal point can be recovered. The method is very suitable for some applications such as ECDSA-V and MQV, etc. Unfortunately, there is a significant fault in that paper. Thus, many results about computation amount are wrong due to the significant fault. First, we will show this fault, and then raise the correction of the significant fault. Finally, Table A·1 about comparison of computation amount in [4] is also corrected.