The construction of GLV-friendly elliptic curves with fast point multiplication

Point multiplication is the dominant operation in elliptic curve cryptosystems. Many techniques are used to accelerate point multiplication. The Gallant-Lambert-Vanstone (GLV) method can be useful for point multiplication on elliptic curves with efficiently computable endomorphisms. Elliptic curves on which the GLV method is efficiently applied are called GLV-friendly elliptic curves. In this paper, we construct four families of GLV-friendly elliptic curves. When the GLV method is used to compute point multiplication on these elliptic curves, no extended Euclidean algorithm or lattice basis reduction algorithm is required and it is efficient. In the bandwidth limited environment, these elliptic curves can be applicable and useful. This result is crucial for advancing high speed cryptography on cryptographic applications.EI04268-275