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diff --git a/crypto/secp256k1/libsecp256k1/src/ecdsa_impl.h b/crypto/secp256k1/libsecp256k1/src/ecdsa_impl.h
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+/**********************************************************************
+ * Copyright (c) 2013-2015 Pieter Wuille *
+ * Distributed under the MIT software license, see the accompanying *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+
+#ifndef _SECP256K1_ECDSA_IMPL_H_
+#define _SECP256K1_ECDSA_IMPL_H_
+
+#include "scalar.h"
+#include "field.h"
+#include "group.h"
+#include "ecmult.h"
+#include "ecmult_gen.h"
+#include "ecdsa.h"
+
+/** Group order for secp256k1 defined as 'n' in "Standards for Efficient Cryptography" (SEC2) 2.7.1
+ * sage: for t in xrange(1023, -1, -1):
+ * .. p = 2**256 - 2**32 - t
+ * .. if p.is_prime():
+ * .. print '%x'%p
+ * .. break
+ * 'fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f'
+ * sage: a = 0
+ * sage: b = 7
+ * sage: F = FiniteField (p)
+ * sage: '%x' % (EllipticCurve ([F (a), F (b)]).order())
+ * 'fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141'
+ */
+static const secp256k1_fe secp256k1_ecdsa_const_order_as_fe = SECP256K1_FE_CONST(
+ 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
+ 0xBAAEDCE6UL, 0xAF48A03BUL, 0xBFD25E8CUL, 0xD0364141UL
+);
+
+/** Difference between field and order, values 'p' and 'n' values defined in
+ * "Standards for Efficient Cryptography" (SEC2) 2.7.1.
+ * sage: p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
+ * sage: a = 0
+ * sage: b = 7
+ * sage: F = FiniteField (p)
+ * sage: '%x' % (p - EllipticCurve ([F (a), F (b)]).order())
+ * '14551231950b75fc4402da1722fc9baee'
+ */
+static const secp256k1_fe secp256k1_ecdsa_const_p_minus_order = SECP256K1_FE_CONST(
+ 0, 0, 0, 1, 0x45512319UL, 0x50B75FC4UL, 0x402DA172UL, 0x2FC9BAEEUL
+);
+
+static int secp256k1_der_read_len(const unsigned char **sigp, const unsigned char *sigend) {
+ int lenleft, b1;
+ size_t ret = 0;
+ if (*sigp >= sigend) {
+ return -1;
+ }
+ b1 = *((*sigp)++);
+ if (b1 == 0xFF) {
+ /* X.690-0207 8.1.3.5.c the value 0xFF shall not be used. */
+ return -1;
+ }
+ if ((b1 & 0x80) == 0) {
+ /* X.690-0207 8.1.3.4 short form length octets */
+ return b1;
+ }
+ if (b1 == 0x80) {
+ /* Indefinite length is not allowed in DER. */
+ return -1;
+ }
+ /* X.690-207 8.1.3.5 long form length octets */
+ lenleft = b1 & 0x7F;
+ if (lenleft > sigend - *sigp) {
+ return -1;
+ }
+ if (**sigp == 0) {
+ /* Not the shortest possible length encoding. */
+ return -1;
+ }
+ if ((size_t)lenleft > sizeof(size_t)) {
+ /* The resulting length would exceed the range of a size_t, so
+ * certainly longer than the passed array size.
+ */
+ return -1;
+ }
+ while (lenleft > 0) {
+ if ((ret >> ((sizeof(size_t) - 1) * 8)) != 0) {
+ }
+ ret = (ret << 8) | **sigp;
+ if (ret + lenleft > (size_t)(sigend - *sigp)) {
+ /* Result exceeds the length of the passed array. */
+ return -1;
+ }
+ (*sigp)++;
+ lenleft--;
+ }
+ if (ret < 128) {
+ /* Not the shortest possible length encoding. */
+ return -1;
+ }
+ return ret;
+}
+
+static int secp256k1_der_parse_integer(secp256k1_scalar *r, const unsigned char **sig, const unsigned char *sigend) {
+ int overflow = 0;
+ unsigned char ra[32] = {0};
+ int rlen;
+
+ if (*sig == sigend || **sig != 0x02) {
+ /* Not a primitive integer (X.690-0207 8.3.1). */
+ return 0;
+ }
+ (*sig)++;
+ rlen = secp256k1_der_read_len(sig, sigend);
+ if (rlen <= 0 || (*sig) + rlen > sigend) {
+ /* Exceeds bounds or not at least length 1 (X.690-0207 8.3.1). */
+ return 0;
+ }
+ if (**sig == 0x00 && rlen > 1 && (((*sig)[1]) & 0x80) == 0x00) {
+ /* Excessive 0x00 padding. */
+ return 0;
+ }
+ if (**sig == 0xFF && rlen > 1 && (((*sig)[1]) & 0x80) == 0x80) {
+ /* Excessive 0xFF padding. */
+ return 0;
+ }
+ if ((**sig & 0x80) == 0x80) {
+ /* Negative. */
+ overflow = 1;
+ }
+ while (rlen > 0 && **sig == 0) {
+ /* Skip leading zero bytes */
+ rlen--;
+ (*sig)++;
+ }
+ if (rlen > 32) {
+ overflow = 1;
+ }
+ if (!overflow) {
+ memcpy(ra + 32 - rlen, *sig, rlen);
+ secp256k1_scalar_set_b32(r, ra, &overflow);
+ }
+ if (overflow) {
+ secp256k1_scalar_set_int(r, 0);
+ }
+ (*sig) += rlen;
+ return 1;
+}
+
+static int secp256k1_ecdsa_sig_parse(secp256k1_scalar *rr, secp256k1_scalar *rs, const unsigned char *sig, size_t size) {
+ const unsigned char *sigend = sig + size;
+ int rlen;
+ if (sig == sigend || *(sig++) != 0x30) {
+ /* The encoding doesn't start with a constructed sequence (X.690-0207 8.9.1). */
+ return 0;
+ }
+ rlen = secp256k1_der_read_len(&sig, sigend);
+ if (rlen < 0 || sig + rlen > sigend) {
+ /* Tuple exceeds bounds */
+ return 0;
+ }
+ if (sig + rlen != sigend) {
+ /* Garbage after tuple. */
+ return 0;
+ }
+
+ if (!secp256k1_der_parse_integer(rr, &sig, sigend)) {
+ return 0;
+ }
+ if (!secp256k1_der_parse_integer(rs, &sig, sigend)) {
+ return 0;
+ }
+
+ if (sig != sigend) {
+ /* Trailing garbage inside tuple. */
+ return 0;
+ }
+
+ return 1;
+}
+
+static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, size_t *size, const secp256k1_scalar* ar, const secp256k1_scalar* as) {
+ unsigned char r[33] = {0}, s[33] = {0};
+ unsigned char *rp = r, *sp = s;
+ size_t lenR = 33, lenS = 33;
+ secp256k1_scalar_get_b32(&r[1], ar);
+ secp256k1_scalar_get_b32(&s[1], as);
+ while (lenR > 1 && rp[0] == 0 && rp[1] < 0x80) { lenR--; rp++; }
+ while (lenS > 1 && sp[0] == 0 && sp[1] < 0x80) { lenS--; sp++; }
+ if (*size < 6+lenS+lenR) {
+ *size = 6 + lenS + lenR;
+ return 0;
+ }
+ *size = 6 + lenS + lenR;
+ sig[0] = 0x30;
+ sig[1] = 4 + lenS + lenR;
+ sig[2] = 0x02;
+ sig[3] = lenR;
+ memcpy(sig+4, rp, lenR);
+ sig[4+lenR] = 0x02;
+ sig[5+lenR] = lenS;
+ memcpy(sig+lenR+6, sp, lenS);
+ return 1;
+}
+
+static int secp256k1_ecdsa_sig_verify(const secp256k1_ecmult_context *ctx, const secp256k1_scalar *sigr, const secp256k1_scalar *sigs, const secp256k1_ge *pubkey, const secp256k1_scalar *message) {
+ unsigned char c[32];
+ secp256k1_scalar sn, u1, u2;
+#if !defined(EXHAUSTIVE_TEST_ORDER)
+ secp256k1_fe xr;
+#endif
+ secp256k1_gej pubkeyj;
+ secp256k1_gej pr;
+
+ if (secp256k1_scalar_is_zero(sigr) || secp256k1_scalar_is_zero(sigs)) {
+ return 0;
+ }
+
+ secp256k1_scalar_inverse_var(&sn, sigs);
+ secp256k1_scalar_mul(&u1, &sn, message);
+ secp256k1_scalar_mul(&u2, &sn, sigr);
+ secp256k1_gej_set_ge(&pubkeyj, pubkey);
+ secp256k1_ecmult(ctx, &pr, &pubkeyj, &u2, &u1);
+ if (secp256k1_gej_is_infinity(&pr)) {
+ return 0;
+ }
+
+#if defined(EXHAUSTIVE_TEST_ORDER)
+{
+ secp256k1_scalar computed_r;
+ secp256k1_ge pr_ge;
+ secp256k1_ge_set_gej(&pr_ge, &pr);
+ secp256k1_fe_normalize(&pr_ge.x);
+
+ secp256k1_fe_get_b32(c, &pr_ge.x);
+ secp256k1_scalar_set_b32(&computed_r, c, NULL);
+ return secp256k1_scalar_eq(sigr, &computed_r);
+}
+#else
+ secp256k1_scalar_get_b32(c, sigr);
+ secp256k1_fe_set_b32(&xr, c);
+
+ /** We now have the recomputed R point in pr, and its claimed x coordinate (modulo n)
+ * in xr. Naively, we would extract the x coordinate from pr (requiring a inversion modulo p),
+ * compute the remainder modulo n, and compare it to xr. However:
+ *
+ * xr == X(pr) mod n
+ * <=> exists h. (xr + h * n < p && xr + h * n == X(pr))
+ * [Since 2 * n > p, h can only be 0 or 1]
+ * <=> (xr == X(pr)) || (xr + n < p && xr + n == X(pr))
+ * [In Jacobian coordinates, X(pr) is pr.x / pr.z^2 mod p]
+ * <=> (xr == pr.x / pr.z^2 mod p) || (xr + n < p && xr + n == pr.x / pr.z^2 mod p)
+ * [Multiplying both sides of the equations by pr.z^2 mod p]
+ * <=> (xr * pr.z^2 mod p == pr.x) || (xr + n < p && (xr + n) * pr.z^2 mod p == pr.x)
+ *
+ * Thus, we can avoid the inversion, but we have to check both cases separately.
+ * secp256k1_gej_eq_x implements the (xr * pr.z^2 mod p == pr.x) test.
+ */
+ if (secp256k1_gej_eq_x_var(&xr, &pr)) {
+ /* xr * pr.z^2 mod p == pr.x, so the signature is valid. */
+ return 1;
+ }
+ if (secp256k1_fe_cmp_var(&xr, &secp256k1_ecdsa_const_p_minus_order) >= 0) {
+ /* xr + n >= p, so we can skip testing the second case. */
+ return 0;
+ }
+ secp256k1_fe_add(&xr, &secp256k1_ecdsa_const_order_as_fe);
+ if (secp256k1_gej_eq_x_var(&xr, &pr)) {
+ /* (xr + n) * pr.z^2 mod p == pr.x, so the signature is valid. */
+ return 1;
+ }
+ return 0;
+#endif
+}
+
+static int secp256k1_ecdsa_sig_sign(const secp256k1_ecmult_gen_context *ctx, secp256k1_scalar *sigr, secp256k1_scalar *sigs, const secp256k1_scalar *seckey, const secp256k1_scalar *message, const secp256k1_scalar *nonce, int *recid) {
+ unsigned char b[32];
+ secp256k1_gej rp;
+ secp256k1_ge r;
+ secp256k1_scalar n;
+ int overflow = 0;
+
+ secp256k1_ecmult_gen(ctx, &rp, nonce);
+ secp256k1_ge_set_gej(&r, &rp);
+ secp256k1_fe_normalize(&r.x);
+ secp256k1_fe_normalize(&r.y);
+ secp256k1_fe_get_b32(b, &r.x);
+ secp256k1_scalar_set_b32(sigr, b, &overflow);
+ /* These two conditions should be checked before calling */
+ VERIFY_CHECK(!secp256k1_scalar_is_zero(sigr));
+ VERIFY_CHECK(overflow == 0);
+
+ if (recid) {
+ /* The overflow condition is cryptographically unreachable as hitting it requires finding the discrete log
+ * of some P where P.x >= order, and only 1 in about 2^127 points meet this criteria.
+ */
+ *recid = (overflow ? 2 : 0) | (secp256k1_fe_is_odd(&r.y) ? 1 : 0);
+ }
+ secp256k1_scalar_mul(&n, sigr, seckey);
+ secp256k1_scalar_add(&n, &n, message);
+ secp256k1_scalar_inverse(sigs, nonce);
+ secp256k1_scalar_mul(sigs, sigs, &n);
+ secp256k1_scalar_clear(&n);
+ secp256k1_gej_clear(&rp);
+ secp256k1_ge_clear(&r);
+ if (secp256k1_scalar_is_zero(sigs)) {
+ return 0;
+ }
+ if (secp256k1_scalar_is_high(sigs)) {
+ secp256k1_scalar_negate(sigs, sigs);
+ if (recid) {
+ *recid ^= 1;
+ }
+ }
+ return 1;
+}
+
+#endif
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