Elliptic curve cryptosystem (ECC) is based on the diculty of the elliptic curve discrete logarithm problem (ECDLP). We try to improve Twist Attack and show the result of numerical experiments.
Twist of an Elliptic Curve, one interesting feature of this algorithm for our purposes is that the y-coordinates of the points is not needed. As a consequence, this algorithm is also valid for points (x : y : z) ∈ E with y ∈ Fp2 , instead of simply y ∈ Fp. This remark yields thus some interest on the subset of points with is a square is enough.
