High Quality Content by WIKIPEDIA articles! In mathematics, the Twisted Hessian curve represents a generalization of Hessian curves; it was introduced in elliptic curve cryptography to speed up the addition and doubling formulas and to have strongly unified arithmetic. In some operations (see the last sections), it is close in speed to Edwards curves.It is interesting to analyze the group law of the elliptic curve, defining the addition and doubling formulas (because the SPA and DPA attacks are based on the running time of these operations). In general, the group law is defined in the following way: if three points lies in the same line then they sum up to zero. So, by this property, the explicit formulas for the group law depend on the curve shape.

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