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A. When and P. , The implementation proposed by [6,16] uses a pair of points P and Q in E[ k ] that does not generate the full group E[ k ], in order to achieve better compression . The point P is chosen to be a point of order k , and Q is set as the image of P by the distortion map (x, y) ? (?x, iy) (where i 2 = ?1) They prove that because of this construction