Analysis the Montgomery ladder algorithm for elliptic curves over ternary fields

Point multiplication is the dominant cost operation in elliptic curve cryptographic schemes. Montgomery ladder algorithm is one of the methods of speeding up point multiplication. It is originally proposed for elliptic curves over binary fields. In this paper, we consider the Montgomery ladder algorithm for elliptic curves over ternary fields. We propose a new Montgomery ladder algorithm and compare the performance with other algorithms. With the experimental data, we find that the Montgomery ladder algorithm doesn´t have advantages in speed. Moreover, we give the reason why the Montgomery ladder algorithm performs badly over ternary fields while performs well over binary fields.