src/group.h

   1 /**********************************************************************
   2  * Copyright (c) 2013, 2014 Pieter Wuille                             *
   3  * Distributed under the MIT software license, see the accompanying   *
   4  * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
   5  **********************************************************************/
   6
   7 #ifndef SECP256K1_GROUP_H
   8 #define SECP256K1_GROUP_H
   9
  10 #include "num.h"
  11 #include "field.h"
  12
  13 /** A group element of the secp256k1 curve, in affine coordinates. */
  14 typedef struct {
  15     secp256k1_fe x;
  16     secp256k1_fe y;
  17     int infinity; /* whether this represents the point at infinity */
  18 } secp256k1_ge;
  19
  20 #define SECP256K1_GE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), 0}
  21 #define SECP256K1_GE_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
  22
  23 /** A group element of the secp256k1 curve, in jacobian coordinates. */
  24 typedef struct {
  25     secp256k1_fe x; /* actual X: x/z^2 */
  26     secp256k1_fe y; /* actual Y: y/z^3 */
  27     secp256k1_fe z;
  28     int infinity; /* whether this represents the point at infinity */
  29 } secp256k1_gej;
  30
  31 #define SECP256K1_GEJ_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_CONST((i),(j),(k),(l),(m),(n),(o),(p)), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1), 0}
  32 #define SECP256K1_GEJ_CONST_INFINITY {SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 0), 1}
  33
  34 typedef struct {
  35     secp256k1_fe_storage x;
  36     secp256k1_fe_storage y;
  37 } secp256k1_ge_storage;
  38
  39 #define SECP256K1_GE_STORAGE_CONST(a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p) {SECP256K1_FE_STORAGE_CONST((a),(b),(c),(d),(e),(f),(g),(h)), SECP256K1_FE_STORAGE_CONST((i),(j),(k),(l),(m),(n),(o),(p))}
  40
  41 #define SECP256K1_GE_STORAGE_CONST_GET(t) SECP256K1_FE_STORAGE_CONST_GET(t.x), SECP256K1_FE_STORAGE_CONST_GET(t.y)
  42
  43 /** Set a group element equal to the point with given X and Y coordinates */
  44 static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y);
  45
  46 /** Set a group element (affine) equal to the point with the given X coordinate
  47  *  and a Y coordinate that is a quadratic residue modulo p. The return value
  48  *  is true iff a coordinate with the given X coordinate exists.
  49  */
  50 static int secp256k1_ge_set_xquad(secp256k1_ge *r, const secp256k1_fe *x);
  51
  52 /** Set a group element (affine) equal to the point with the given X coordinate, and given oddness
  53  *  for Y. Return value indicates whether the result is valid. */
  54 static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd);
  55
  56 /** Check whether a group element is the point at infinity. */
  57 static int secp256k1_ge_is_infinity(const secp256k1_ge *a);
  58
  59 /** Check whether a group element is valid (i.e., on the curve). */
  60 static int secp256k1_ge_is_valid_var(const secp256k1_ge *a);
  61
  62 static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a);
  63
  64 /** Set a group element equal to another which is given in jacobian coordinates */
  65 static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a);
  66
  67 /** Set a batch of group elements equal to the inputs given in jacobian coordinates */
  68 static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len, const secp256k1_callback *cb);
  69
  70 /** Set a batch of group elements equal to the inputs given in jacobian
  71  *  coordinates (with known z-ratios). zr must contain the known z-ratios such
  72  *  that mul(a[i].z, zr[i+1]) == a[i+1].z. zr[0] is ignored. */
  73 static void secp256k1_ge_set_table_gej_var(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zr, size_t len);
  74
  75 /** Bring a batch inputs given in jacobian coordinates (with known z-ratios) to
  76  *  the same global z "denominator". zr must contain the known z-ratios such
  77  *  that mul(a[i].z, zr[i+1]) == a[i+1].z. zr[0] is ignored. The x and y
  78  *  coordinates of the result are stored in r, the common z coordinate is
  79  *  stored in globalz. */
  80 static void secp256k1_ge_globalz_set_table_gej(size_t len, secp256k1_ge *r, secp256k1_fe *globalz, const secp256k1_gej *a, const secp256k1_fe *zr);
  81
  82 /** Set a group element (jacobian) equal to the point at infinity. */
  83 static void secp256k1_gej_set_infinity(secp256k1_gej *r);
  84
  85 /** Set a group element (jacobian) equal to another which is given in affine coordinates. */
  86 static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a);
  87
  88 /** Compare the X coordinate of a group element (jacobian). */
  89 static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a);
  90
  91 /** Set r equal to the inverse of a (i.e., mirrored around the X axis) */
  92 static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a);
  93
  94 /** Check whether a group element is the point at infinity. */
  95 static int secp256k1_gej_is_infinity(const secp256k1_gej *a);
  96
  97 /** Check whether a group element's y coordinate is a quadratic residue. */
  98 static int secp256k1_gej_has_quad_y_var(const secp256k1_gej *a);
  99
 100 /** Set r equal to the double of a. If rzr is not-NULL, r->z = a->z * *rzr (where infinity means an implicit z = 0).
 101  * a may not be zero. Constant time. */
 102 static void secp256k1_gej_double_nonzero(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr);
 103
 104 /** Set r equal to the double of a. If rzr is not-NULL, r->z = a->z * *rzr (where infinity means an implicit z = 0). */
 105 static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr);
 106
 107 /** Set r equal to the sum of a and b. If rzr is non-NULL, r->z = a->z * *rzr (a cannot be infinity in that case). */
 108 static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr);
 109
 110 /** Set r equal to the sum of a and b (with b given in affine coordinates, and not infinity). */
 111 static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b);
 112
 113 /** Set r equal to the sum of a and b (with b given in affine coordinates). This is more efficient
 114     than secp256k1_gej_add_var. It is identical to secp256k1_gej_add_ge but without constant-time
 115     guarantee, and b is allowed to be infinity. If rzr is non-NULL, r->z = a->z * *rzr (a cannot be infinity in that case). */
 116 static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr);
 117
 118 /** Set r equal to the sum of a and b (with the inverse of b's Z coordinate passed as bzinv). */
 119 static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv);
 120
 121 #ifdef USE_ENDOMORPHISM
 122 /** Set r to be equal to lambda times a, where lambda is chosen in a way such that this is very fast. */
 123 static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a);
 124 #endif
 125
 126 /** Clear a secp256k1_gej to prevent leaking sensitive information. */
 127 static void secp256k1_gej_clear(secp256k1_gej *r);
 128
 129 /** Clear a secp256k1_ge to prevent leaking sensitive information. */
 130 static void secp256k1_ge_clear(secp256k1_ge *r);
 131
 132 /** Convert a group element to the storage type. */
 133 static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a);
 134
 135 /** Convert a group element back from the storage type. */
 136 static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a);
 137
 138 /** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
 139 static void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag);
 140
 141 /** Rescale a jacobian point by b which must be non-zero. Constant-time. */
 142 static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *b);
 143
 144 #endif /* SECP256K1_GROUP_H */