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7 #ifndef SECP256K1_GROUP_IMPL_H
8 #define SECP256K1_GROUP_IMPL_H
13 #define SECP256K1_G_ORDER_13 SECP256K1_GE_CONST(\
14 0xc3459c3d, 0x35326167, 0xcd86cce8, 0x07a2417f,\
15 0x5b8bd567, 0xde8538ee, 0x0d507b0c, 0xd128f5bb,\
16 0x8e467fec, 0xcd30000a, 0x6cc1184e, 0x25d382c2,\
17 0xa2f4494e, 0x2fbe9abc, 0x8b64abac, 0xd005fb24\
19 #define SECP256K1_G_ORDER_199 SECP256K1_GE_CONST(\
20 0x226e653f, 0xc8df7744, 0x9bacbf12, 0x7d1dcbf9,\
21 0x87f05b2a, 0xe7edbd28, 0x1f564575, 0xc48dcf18,\
22 0xa13872c2, 0xe933bb17, 0x5d9ffd5b, 0xb5b6e10c,\
23 0x57fe3c00, 0xbaaaa15a, 0xe003ec3e, 0x9c269bae\
28 #define SECP256K1_G SECP256K1_GE_CONST(\
29 0x79BE667EUL, 0xF9DCBBACUL, 0x55A06295UL, 0xCE870B07UL,\
30 0x029BFCDBUL, 0x2DCE28D9UL, 0x59F2815BUL, 0x16F81798UL,\
31 0x483ADA77UL, 0x26A3C465UL, 0x5DA4FBFCUL, 0x0E1108A8UL,\
32 0xFD17B448UL, 0xA6855419UL, 0x9C47D08FUL, 0xFB10D4B8UL\
43 #if defined(EXHAUSTIVE_TEST_ORDER)
44 # if EXHAUSTIVE_TEST_ORDER == 13
48 0x3d3486b2, 0x159a9ca5, 0xc75638be, 0xb23a69bc,
49 0x946a45ab, 0x24801247, 0xb4ed2b8e, 0x26b6a417
51 # elif EXHAUSTIVE_TEST_ORDER == 199
55 0x2cca28fa, 0xfc614b80, 0x2a3db42b, 0x00ba00b1,
56 0xbea8d943, 0xdace9ab2, 0x9536daea, 0x0074defb
59 # error No known generator for the specified exhaustive test group order.
125 size_t last_i = SIZE_MAX;
127 for (i = 0; i < len; i++) {
132 if (last_i == SIZE_MAX) {
140 if (last_i == SIZE_MAX) {
148 if (!a[i].infinity) {
157 for (i = 0; i < len; i++) {
158 if (!a[i].infinity) {
338 secp256k1_fe z22, z12, u1, u2, s1, s2, h, i, i2, h2, h3,
t;
391 secp256k1_fe z12, u1, u2, s1, s2, h, i, i2, h2, h3,
t;
440 secp256k1_fe az, z12, u1, u2, s1, s2, h, i, i2, h2, h3,
t;
498 secp256k1_fe zz, u1, u2, s1, s2,
t, tt,
m, n, q, rr;
500 int infinity, degenerate;
652 0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul,
653 0x9cf04975ul, 0x12f58995ul, 0xc1396c28ul, 0x719501eeul
660 #ifdef EXHAUSTIVE_TEST_ORDER
666 for (i = 0; i < 32; ++i) {
#define VERIFY_CHECK(cond)
static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a)
Sets a field element to be the (modular) inverse of another.
static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge *a)
#define EXHAUSTIVE_TEST_ORDER
static int secp256k1_ge_is_infinity(const secp256k1_ge *a)
static void secp256k1_fe_normalize_var(secp256k1_fe *r)
Normalize a field element, without constant-time guarantee.
static void secp256k1_ge_set_gej_var(secp256k1_ge *r, secp256k1_gej *a)
static void secp256k1_fe_normalize(secp256k1_fe *r)
Field element module.
#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0)
static void secp256k1_ge_set_all_gej_var(secp256k1_ge *r, const secp256k1_gej *a, size_t len)
#define SECP256K1_G_ORDER_13
static int secp256k1_gej_is_infinity(const secp256k1_gej *a)
static void secp256k1_gej_add_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_gej *b, secp256k1_fe *rzr)
static int secp256k1_fe_normalizes_to_zero(const secp256k1_fe *r)
Verify whether a field element represents zero i.e.
static SECP256K1_INLINE void secp256k1_gej_double(secp256k1_gej *r, const secp256k1_gej *a)
static void secp256k1_gej_set_infinity(secp256k1_gej *r)
static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b)
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)
static void secp256k1_gej_set_ge(secp256k1_gej *r, const secp256k1_ge *a)
static void secp256k1_ge_set_gej(secp256k1_ge *r, secp256k1_gej *a)
static const secp256k1_ge secp256k1_ge_const_g
A group element of the secp256k1 curve, in jacobian coordinates.
static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a)
If a has a square root, it is computed in r and 1 is returned.
static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b)
Same as secp256k1_fe_equal, but may be variable time.
static int secp256k1_fe_is_odd(const secp256k1_fe *a)
Check the "oddness" of a field element.
static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe *SECP256K1_RESTRICT b)
Sets a field element to be the product of two others.
#define SECP256K1_G
Generator for secp256k1, value 'g' defined in "Standards for Efficient Cryptography" (SEC2) 2....
static void secp256k1_fe_clear(secp256k1_fe *a)
Sets a field element equal to zero, initializing all fields.
static void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag)
If flag is true, set *r equal to *a; otherwise leave it.
static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd)
static void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a)
Convert a field element back from the storage type.
static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const secp256k1_fe *y)
static const secp256k1_fe secp256k1_fe_const_b
static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a)
Adds a field element to another.
static int secp256k1_gej_eq_x_var(const secp256k1_fe *x, const secp256k1_gej *a)
static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a)
Convert a field element to the storage type.
static void secp256k1_fe_set_int(secp256k1_fe *r, int a)
Set a field element equal to a small (not greater than 0x7FFF), non-negative integer.
static void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag)
If flag is true, set *r equal to *a; otherwise leave it.
static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a)
Sets a field element to be the square of another.
static int secp256k1_fe_is_zero(const secp256k1_fe *a)
Verify whether a field element is zero.
static void secp256k1_ge_set_infinity(secp256k1_ge *r)
static void secp256k1_gej_add_zinv_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, const secp256k1_fe *bzinv)
static void secp256k1_ge_set_gej_zinv(secp256k1_ge *r, const secp256k1_gej *a, const secp256k1_fe *zi)
static SECP256K1_INLINE void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag)
static void secp256k1_gej_add_ge_var(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_ge *b, secp256k1_fe *rzr)
static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m)
Set a field element equal to the additive inverse of another.
static void secp256k1_ge_mul_lambda(secp256k1_ge *r, const secp256k1_ge *a)
#define SECP256K1_G_ORDER_199
static int secp256k1_ge_is_valid_var(const secp256k1_ge *a)
static void secp256k1_fe_normalize_weak(secp256k1_fe *r)
Weakly normalize a field element: reduce its magnitude to 1, but don't fully normalize.
static void secp256k1_fe_mul_int(secp256k1_fe *r, int a)
Multiplies the passed field element with a small integer constant.
static void secp256k1_ge_clear(secp256k1_ge *r)
static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *s)
static void secp256k1_ge_neg(secp256k1_ge *r, const secp256k1_ge *a)
static void secp256k1_gej_clear(secp256k1_gej *r)
A group element of the secp256k1 curve, in affine coordinates.
static int secp256k1_ge_is_in_correct_subgroup(const secp256k1_ge *ge)
static int secp256k1_fe_normalizes_to_zero_var(const secp256k1_fe *r)
Verify whether a field element represents zero i.e.
static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a)
Potentially faster version of secp256k1_fe_inv, without constant-time guarantee.
static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr)
static void secp256k1_gej_neg(secp256k1_gej *r, const secp256k1_gej *a)
static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a)