Jacobian curve

In mathematics, the Jacobi curve is a representation of an elliptic curve different from the usual one (Weierstrass equation). Sometimes it is used in cryptography instead of the Weierstrass form because it can provide a defence against simple and differential power analysis style (SPA) attacks; it is possible, indeed, to use the general addition formula also for doubling a point on an elliptic curve of this form: in this way the two operations become indistinguishable from some side-channel information. The Jacobi curve offers also faster arithmetic compared to the Weierstrass curve.