Since elliptic curve was came up in 1985 by Miller and Koblitz, elliptic curve cryptography has been become one of the most important croptography algorithms in decades. The efficiency of its implementation attracted many researchers attention. Scalar multiplication as one of the heaviest computations in elliptic curve, some efficient technique like Gallant–Lambert– Vanstone method which adopt scalar decompositions using efficient endomorphisms has been applied broadly in practical.

In this paper, we focus on the vulnerability analysis for GLV method in binary curve for corner cases, and provide a thoroughly analysis for implementation of GLV method in special curve.