1 /* This Source Code Form is subject to the terms of the Mozilla Public 2 * License, v. 2.0. If a copy of the MPL was not distributed with this 3 * file, You can obtain one at http://mozilla.org/MPL/2.0/. */ 4 5 #ifndef __ecp_h_ 6 #define __ecp_h_ 7 8 #include "ecl-priv.h" 9 10 /* Checks if point P(px, py) is at infinity. Uses affine coordinates. */ 11 mp_err ec_GFp_pt_is_inf_aff(const mp_int *px, const mp_int *py); 12 13 /* Sets P(px, py) to be the point at infinity. Uses affine coordinates. */ 14 mp_err ec_GFp_pt_set_inf_aff(mp_int *px, mp_int *py); 15 16 /* Computes R = P + Q where R is (rx, ry), P is (px, py) and Q is (qx, 17 * qy). Uses affine coordinates. */ 18 mp_err ec_GFp_pt_add_aff(const mp_int *px, const mp_int *py, 19 const mp_int *qx, const mp_int *qy, mp_int *rx, 20 mp_int *ry, const ECGroup *group); 21 22 /* Computes R = P - Q. Uses affine coordinates. */ 23 mp_err ec_GFp_pt_sub_aff(const mp_int *px, const mp_int *py, 24 const mp_int *qx, const mp_int *qy, mp_int *rx, 25 mp_int *ry, const ECGroup *group); 26 27 /* Computes R = 2P. Uses affine coordinates. */ 28 mp_err ec_GFp_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx, 29 mp_int *ry, const ECGroup *group); 30 31 /* Validates a point on a GFp curve. */ 32 mp_err ec_GFp_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group); 33 34 #ifdef ECL_ENABLE_GFP_PT_MUL_AFF 35 /* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters 36 * a, b and p are the elliptic curve coefficients and the prime that 37 * determines the field GFp. Uses affine coordinates. */ 38 mp_err ec_GFp_pt_mul_aff(const mp_int *n, const mp_int *px, 39 const mp_int *py, mp_int *rx, mp_int *ry, 40 const ECGroup *group); 41 #endif 42 43 /* Converts a point P(px, py) from affine coordinates to Jacobian 44 * projective coordinates R(rx, ry, rz). */ 45 mp_err ec_GFp_pt_aff2jac(const mp_int *px, const mp_int *py, mp_int *rx, 46 mp_int *ry, mp_int *rz, const ECGroup *group); 47 48 /* Converts a point P(px, py, pz) from Jacobian projective coordinates to 49 * affine coordinates R(rx, ry). */ 50 mp_err ec_GFp_pt_jac2aff(const mp_int *px, const mp_int *py, 51 const mp_int *pz, mp_int *rx, mp_int *ry, 52 const ECGroup *group); 53 54 /* Checks if point P(px, py, pz) is at infinity. Uses Jacobian 55 * coordinates. */ 56 mp_err ec_GFp_pt_is_inf_jac(const mp_int *px, const mp_int *py, 57 const mp_int *pz); 58 59 /* Sets P(px, py, pz) to be the point at infinity. Uses Jacobian 60 * coordinates. */ 61 mp_err ec_GFp_pt_set_inf_jac(mp_int *px, mp_int *py, mp_int *pz); 62 63 /* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is 64 * (qx, qy, qz). Uses Jacobian coordinates. */ 65 mp_err ec_GFp_pt_add_jac_aff(const mp_int *px, const mp_int *py, 66 const mp_int *pz, const mp_int *qx, 67 const mp_int *qy, mp_int *rx, mp_int *ry, 68 mp_int *rz, const ECGroup *group); 69 70 /* Computes R = 2P. Uses Jacobian coordinates. */ 71 mp_err ec_GFp_pt_dbl_jac(const mp_int *px, const mp_int *py, 72 const mp_int *pz, mp_int *rx, mp_int *ry, 73 mp_int *rz, const ECGroup *group); 74 75 #ifdef ECL_ENABLE_GFP_PT_MUL_JAC 76 /* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters 77 * a, b and p are the elliptic curve coefficients and the prime that 78 * determines the field GFp. Uses Jacobian coordinates. */ 79 mp_err ec_GFp_pt_mul_jac(const mp_int *n, const mp_int *px, 80 const mp_int *py, mp_int *rx, mp_int *ry, 81 const ECGroup *group); 82 #endif 83 84 /* Computes R(x, y) = k1 * G + k2 * P(x, y), where G is the generator 85 * (base point) of the group of points on the elliptic curve. Allows k1 = 86 * NULL or { k2, P } = NULL. Implemented using mixed Jacobian-affine 87 * coordinates. Input and output values are assumed to be NOT 88 * field-encoded and are in affine form. */ 89 mp_err 90 ec_GFp_pts_mul_jac(const mp_int *k1, const mp_int *k2, const mp_int *px, 91 const mp_int *py, mp_int *rx, mp_int *ry, 92 const ECGroup *group); 93 94 /* Computes R = nP where R is (rx, ry) and P is the base point. Elliptic 95 * curve points P and R can be identical. Uses mixed Modified-Jacobian 96 * co-ordinates for doubling and Chudnovsky Jacobian coordinates for 97 * additions. Assumes input is already field-encoded using field_enc, and 98 * returns output that is still field-encoded. Uses 5-bit window NAF 99 * method (algorithm 11) for scalar-point multiplication from Brown, 100 * Hankerson, Lopez, Menezes. Software Implementation of the NIST Elliptic 101 * Curves Over Prime Fields. */ 102 mp_err 103 ec_GFp_pt_mul_jm_wNAF(const mp_int *n, const mp_int *px, const mp_int *py, 104 mp_int *rx, mp_int *ry, const ECGroup *group); 105 106 #endif /* __ecp_h_ */ 107