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 #ifndef ISOGENY_H_ #define ISOGENY_H_ // Computes [2^e](X:Z) on Montgomery curve with projective // constant via e repeated doublings. void sike_xDBLe( const point_proj_t P, point_proj_t Q, const f2elm_t A24plus, const f2elm_t C24, size_t e); // Simultaneous doubling and differential addition. void sike_xDBLADD( point_proj_t P, point_proj_t Q, const f2elm_t xPQ, const f2elm_t A24); // Tripling of a Montgomery point in projective coordinates (X:Z). void sike_xTPL( const point_proj_t P, point_proj_t Q, const f2elm_t A24minus, const f2elm_t A24plus); // Computes [3^e](X:Z) on Montgomery curve with projective constant // via e repeated triplings. void sike_xTPLe( const point_proj_t P, point_proj_t Q, const f2elm_t A24minus, const f2elm_t A24plus, size_t e); // Given the x-coordinates of P, Q, and R, returns the value A // corresponding to the Montgomery curve E_A: y^2=x^3+A*x^2+x such that R=Q-P on E_A. void sike_get_A( const f2elm_t xP, const f2elm_t xQ, const f2elm_t xR, f2elm_t A); // Computes the j-invariant of a Montgomery curve with projective constant. void sike_j_inv( const f2elm_t A, const f2elm_t C, f2elm_t jinv); // Computes the corresponding 4-isogeny of a projective Montgomery // point (X4:Z4) of order 4. void sike_get_4_isog( const point_proj_t P, f2elm_t A24plus, f2elm_t C24, f2elm_t* coeff); // Computes the corresponding 3-isogeny of a projective Montgomery // point (X3:Z3) of order 3. void sike_get_3_isog( const point_proj_t P, f2elm_t A24minus, f2elm_t A24plus, f2elm_t* coeff); // Computes the 3-isogeny R=phi(X:Z), given projective point (X3:Z3) // of order 3 on a Montgomery curve and a point P with coefficients given in coeff. void sike_eval_3_isog( point_proj_t Q, f2elm_t* coeff); // Evaluates the isogeny at the point (X:Z) in the domain of the isogeny. void sike_eval_4_isog( point_proj_t P, f2elm_t* coeff); // 3-way simultaneous inversion void sike_inv_3_way( f2elm_t z1, f2elm_t z2, f2elm_t z3); #endif // ISOGENY_H_