summaryrefslogtreecommitdiff
path: root/crypto/secp256k1/libsecp256k1/src/field_impl.h
diff options
context:
space:
mode:
Diffstat (limited to 'crypto/secp256k1/libsecp256k1/src/field_impl.h')
-rw-r--r--crypto/secp256k1/libsecp256k1/src/field_impl.h315
1 files changed, 315 insertions, 0 deletions
diff --git a/crypto/secp256k1/libsecp256k1/src/field_impl.h b/crypto/secp256k1/libsecp256k1/src/field_impl.h
new file mode 100644
index 000000000..5127b279b
--- /dev/null
+++ b/crypto/secp256k1/libsecp256k1/src/field_impl.h
@@ -0,0 +1,315 @@
+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille *
+ * Distributed under the MIT software license, see the accompanying *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_FIELD_IMPL_H_
+#define _SECP256K1_FIELD_IMPL_H_
+
+#if defined HAVE_CONFIG_H
+#include "libsecp256k1-config.h"
+#endif
+
+#include "util.h"
+
+#if defined(USE_FIELD_10X26)
+#include "field_10x26_impl.h"
+#elif defined(USE_FIELD_5X52)
+#include "field_5x52_impl.h"
+#else
+#error "Please select field implementation"
+#endif
+
+SECP256K1_INLINE static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) {
+ secp256k1_fe na;
+ secp256k1_fe_negate(&na, a, 1);
+ secp256k1_fe_add(&na, b);
+ return secp256k1_fe_normalizes_to_zero(&na);
+}
+
+SECP256K1_INLINE static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b) {
+ secp256k1_fe na;
+ secp256k1_fe_negate(&na, a, 1);
+ secp256k1_fe_add(&na, b);
+ return secp256k1_fe_normalizes_to_zero_var(&na);
+}
+
+static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a) {
+ /** Given that p is congruent to 3 mod 4, we can compute the square root of
+ * a mod p as the (p+1)/4'th power of a.
+ *
+ * As (p+1)/4 is an even number, it will have the same result for a and for
+ * (-a). Only one of these two numbers actually has a square root however,
+ * so we test at the end by squaring and comparing to the input.
+ * Also because (p+1)/4 is an even number, the computed square root is
+ * itself always a square (a ** ((p+1)/4) is the square of a ** ((p+1)/8)).
+ */
+ secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
+ int j;
+
+ /** The binary representation of (p + 1)/4 has 3 blocks of 1s, with lengths in
+ * { 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block:
+ * 1, [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]
+ */
+
+ secp256k1_fe_sqr(&x2, a);
+ secp256k1_fe_mul(&x2, &x2, a);
+
+ secp256k1_fe_sqr(&x3, &x2);
+ secp256k1_fe_mul(&x3, &x3, a);
+
+ x6 = x3;
+ for (j=0; j<3; j++) {
+ secp256k1_fe_sqr(&x6, &x6);
+ }
+ secp256k1_fe_mul(&x6, &x6, &x3);
+
+ x9 = x6;
+ for (j=0; j<3; j++) {
+ secp256k1_fe_sqr(&x9, &x9);
+ }
+ secp256k1_fe_mul(&x9, &x9, &x3);
+
+ x11 = x9;
+ for (j=0; j<2; j++) {
+ secp256k1_fe_sqr(&x11, &x11);
+ }
+ secp256k1_fe_mul(&x11, &x11, &x2);
+
+ x22 = x11;
+ for (j=0; j<11; j++) {
+ secp256k1_fe_sqr(&x22, &x22);
+ }
+ secp256k1_fe_mul(&x22, &x22, &x11);
+
+ x44 = x22;
+ for (j=0; j<22; j++) {
+ secp256k1_fe_sqr(&x44, &x44);
+ }
+ secp256k1_fe_mul(&x44, &x44, &x22);
+
+ x88 = x44;
+ for (j=0; j<44; j++) {
+ secp256k1_fe_sqr(&x88, &x88);
+ }
+ secp256k1_fe_mul(&x88, &x88, &x44);
+
+ x176 = x88;
+ for (j=0; j<88; j++) {
+ secp256k1_fe_sqr(&x176, &x176);
+ }
+ secp256k1_fe_mul(&x176, &x176, &x88);
+
+ x220 = x176;
+ for (j=0; j<44; j++) {
+ secp256k1_fe_sqr(&x220, &x220);
+ }
+ secp256k1_fe_mul(&x220, &x220, &x44);
+
+ x223 = x220;
+ for (j=0; j<3; j++) {
+ secp256k1_fe_sqr(&x223, &x223);
+ }
+ secp256k1_fe_mul(&x223, &x223, &x3);
+
+ /* The final result is then assembled using a sliding window over the blocks. */
+
+ t1 = x223;
+ for (j=0; j<23; j++) {
+ secp256k1_fe_sqr(&t1, &t1);
+ }
+ secp256k1_fe_mul(&t1, &t1, &x22);
+ for (j=0; j<6; j++) {
+ secp256k1_fe_sqr(&t1, &t1);
+ }
+ secp256k1_fe_mul(&t1, &t1, &x2);
+ secp256k1_fe_sqr(&t1, &t1);
+ secp256k1_fe_sqr(r, &t1);
+
+ /* Check that a square root was actually calculated */
+
+ secp256k1_fe_sqr(&t1, r);
+ return secp256k1_fe_equal(&t1, a);
+}
+
+static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a) {
+ secp256k1_fe x2, x3, x6, x9, x11, x22, x44, x88, x176, x220, x223, t1;
+ int j;
+
+ /** The binary representation of (p - 2) has 5 blocks of 1s, with lengths in
+ * { 1, 2, 22, 223 }. Use an addition chain to calculate 2^n - 1 for each block:
+ * [1], [2], 3, 6, 9, 11, [22], 44, 88, 176, 220, [223]
+ */
+
+ secp256k1_fe_sqr(&x2, a);
+ secp256k1_fe_mul(&x2, &x2, a);
+
+ secp256k1_fe_sqr(&x3, &x2);
+ secp256k1_fe_mul(&x3, &x3, a);
+
+ x6 = x3;
+ for (j=0; j<3; j++) {
+ secp256k1_fe_sqr(&x6, &x6);
+ }
+ secp256k1_fe_mul(&x6, &x6, &x3);
+
+ x9 = x6;
+ for (j=0; j<3; j++) {
+ secp256k1_fe_sqr(&x9, &x9);
+ }
+ secp256k1_fe_mul(&x9, &x9, &x3);
+
+ x11 = x9;
+ for (j=0; j<2; j++) {
+ secp256k1_fe_sqr(&x11, &x11);
+ }
+ secp256k1_fe_mul(&x11, &x11, &x2);
+
+ x22 = x11;
+ for (j=0; j<11; j++) {
+ secp256k1_fe_sqr(&x22, &x22);
+ }
+ secp256k1_fe_mul(&x22, &x22, &x11);
+
+ x44 = x22;
+ for (j=0; j<22; j++) {
+ secp256k1_fe_sqr(&x44, &x44);
+ }
+ secp256k1_fe_mul(&x44, &x44, &x22);
+
+ x88 = x44;
+ for (j=0; j<44; j++) {
+ secp256k1_fe_sqr(&x88, &x88);
+ }
+ secp256k1_fe_mul(&x88, &x88, &x44);
+
+ x176 = x88;
+ for (j=0; j<88; j++) {
+ secp256k1_fe_sqr(&x176, &x176);
+ }
+ secp256k1_fe_mul(&x176, &x176, &x88);
+
+ x220 = x176;
+ for (j=0; j<44; j++) {
+ secp256k1_fe_sqr(&x220, &x220);
+ }
+ secp256k1_fe_mul(&x220, &x220, &x44);
+
+ x223 = x220;
+ for (j=0; j<3; j++) {
+ secp256k1_fe_sqr(&x223, &x223);
+ }
+ secp256k1_fe_mul(&x223, &x223, &x3);
+
+ /* The final result is then assembled using a sliding window over the blocks. */
+
+ t1 = x223;
+ for (j=0; j<23; j++) {
+ secp256k1_fe_sqr(&t1, &t1);
+ }
+ secp256k1_fe_mul(&t1, &t1, &x22);
+ for (j=0; j<5; j++) {
+ secp256k1_fe_sqr(&t1, &t1);
+ }
+ secp256k1_fe_mul(&t1, &t1, a);
+ for (j=0; j<3; j++) {
+ secp256k1_fe_sqr(&t1, &t1);
+ }
+ secp256k1_fe_mul(&t1, &t1, &x2);
+ for (j=0; j<2; j++) {
+ secp256k1_fe_sqr(&t1, &t1);
+ }
+ secp256k1_fe_mul(r, a, &t1);
+}
+
+static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a) {
+#if defined(USE_FIELD_INV_BUILTIN)
+ secp256k1_fe_inv(r, a);
+#elif defined(USE_FIELD_INV_NUM)
+ secp256k1_num n, m;
+ static const secp256k1_fe negone = SECP256K1_FE_CONST(
+ 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL,
+ 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL, 0xFFFFFC2EUL
+ );
+ /* secp256k1 field prime, value p defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
+ static const unsigned char prime[32] = {
+ 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+ 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+ 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+ 0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F
+ };
+ unsigned char b[32];
+ int res;
+ secp256k1_fe c = *a;
+ secp256k1_fe_normalize_var(&c);
+ secp256k1_fe_get_b32(b, &c);
+ secp256k1_num_set_bin(&n, b, 32);
+ secp256k1_num_set_bin(&m, prime, 32);
+ secp256k1_num_mod_inverse(&n, &n, &m);
+ secp256k1_num_get_bin(b, 32, &n);
+ res = secp256k1_fe_set_b32(r, b);
+ (void)res;
+ VERIFY_CHECK(res);
+ /* Verify the result is the (unique) valid inverse using non-GMP code. */
+ secp256k1_fe_mul(&c, &c, r);
+ secp256k1_fe_add(&c, &negone);
+ CHECK(secp256k1_fe_normalizes_to_zero_var(&c));
+#else
+#error "Please select field inverse implementation"
+#endif
+}
+
+static void secp256k1_fe_inv_all_var(secp256k1_fe *r, const secp256k1_fe *a, size_t len) {
+ secp256k1_fe u;
+ size_t i;
+ if (len < 1) {
+ return;
+ }
+
+ VERIFY_CHECK((r + len <= a) || (a + len <= r));
+
+ r[0] = a[0];
+
+ i = 0;
+ while (++i < len) {
+ secp256k1_fe_mul(&r[i], &r[i - 1], &a[i]);
+ }
+
+ secp256k1_fe_inv_var(&u, &r[--i]);
+
+ while (i > 0) {
+ size_t j = i--;
+ secp256k1_fe_mul(&r[j], &r[i], &u);
+ secp256k1_fe_mul(&u, &u, &a[j]);
+ }
+
+ r[0] = u;
+}
+
+static int secp256k1_fe_is_quad_var(const secp256k1_fe *a) {
+#ifndef USE_NUM_NONE
+ unsigned char b[32];
+ secp256k1_num n;
+ secp256k1_num m;
+ /* secp256k1 field prime, value p defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
+ static const unsigned char prime[32] = {
+ 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+ 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+ 0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
+ 0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F
+ };
+
+ secp256k1_fe c = *a;
+ secp256k1_fe_normalize_var(&c);
+ secp256k1_fe_get_b32(b, &c);
+ secp256k1_num_set_bin(&n, b, 32);
+ secp256k1_num_set_bin(&m, prime, 32);
+ return secp256k1_num_jacobi(&n, &m) >= 0;
+#else
+ secp256k1_fe r;
+ return secp256k1_fe_sqrt(&r, a);
+#endif
+}
+
+#endif
generated by cgit v1.2.3 (git 2.44.0) at 2024-05-03 08:30:45 +0000