bitcoin-core/src/ecdsa_impl.h

/**********************************************************************
 * 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_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"

static const secp256k1_fe_t secp256k1_ecdsa_const_order_as_fe = SECP256K1_FE_CONST(
    0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
    0xBAAEDCE6UL, 0xAF48A03BUL, 0xBFD25E8CUL, 0xD0364141UL
);

static const secp256k1_fe_t secp256k1_ecdsa_const_p_minus_order = SECP256K1_FE_CONST(
    0, 0, 0, 1, 0x45512319UL, 0x50B75FC4UL, 0x402DA172UL, 0x2FC9BAEEUL
);

static int secp256k1_ecdsa_sig_parse(secp256k1_ecdsa_sig_t *r, const unsigned char *sig, int size) {
    if (sig[0] != 0x30) return 0;
    int lenr = sig[3];
    if (5+lenr >= size) return 0;
    int lens = sig[lenr+5];
    if (sig[1] != lenr+lens+4) return 0;
    if (lenr+lens+6 > size) return 0;
    if (sig[2] != 0x02) return 0;
    if (lenr == 0) return 0;
    if (sig[lenr+4] != 0x02) return 0;
    if (lens == 0) return 0;
    const unsigned char *sp = sig + 6 + lenr;
    while (lens > 0 && sp[0] == 0) {
        lens--;
        sp++;
    }
    if (lens > 32) return 0;
    const unsigned char *rp = sig + 4;
    while (lenr > 0 && rp[0] == 0) {
        lenr--;
        rp++;
    }
    if (lenr > 32) return 0;
    unsigned char ra[32] = {0}, sa[32] = {0};
    memcpy(ra + 32 - lenr, rp, lenr);
    memcpy(sa + 32 - lens, sp, lens);
    int overflow = 0;
    secp256k1_scalar_set_b32(&r->r, ra, &overflow);
    if (overflow) return 0;
    secp256k1_scalar_set_b32(&r->s, sa, &overflow);
    if (overflow) return 0;
    return 1;
}

static int secp256k1_ecdsa_sig_serialize(unsigned char *sig, int *size, const secp256k1_ecdsa_sig_t *a) {
    unsigned char r[33] = {0}, s[33] = {0};
    secp256k1_scalar_get_b32(&r[1], &a->r);
    secp256k1_scalar_get_b32(&s[1], &a->s);
    unsigned char *rp = r, *sp = s;
    int lenR = 33, lenS = 33;
    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)
        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_ecdsa_sig_t *sig, const secp256k1_ge_t *pubkey, const secp256k1_scalar_t *message) {
    if (secp256k1_scalar_is_zero(&sig->r) || secp256k1_scalar_is_zero(&sig->s))
        return 0;

    secp256k1_scalar_t sn, u1, u2;
    secp256k1_scalar_inverse_var(&sn, &sig->s);
    secp256k1_scalar_mul(&u1, &sn, message);
    secp256k1_scalar_mul(&u2, &sn, &sig->r);
    secp256k1_gej_t pubkeyj; secp256k1_gej_set_ge(&pubkeyj, pubkey);
    secp256k1_gej_t pr; secp256k1_ecmult(&pr, &pubkeyj, &u2, &u1);
    if (secp256k1_gej_is_infinity(&pr)) {
        return 0;
    }
    unsigned char c[32];
    secp256k1_scalar_get_b32(c, &sig->r);
    secp256k1_fe_t xr;
    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.x == xr * xr.z^2 mod p, so the signature is valid. */
        return 1;
    }
    if (secp256k1_fe_cmp_var(&xr, &secp256k1_ecdsa_const_p_minus_order) >= 0) {
        /* xr + p >= n, 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;
}

static int secp256k1_ecdsa_sig_recover(const secp256k1_ecdsa_sig_t *sig, secp256k1_ge_t *pubkey, const secp256k1_scalar_t *message, int recid) {
    if (secp256k1_scalar_is_zero(&sig->r) || secp256k1_scalar_is_zero(&sig->s))
        return 0;

    unsigned char brx[32];
    secp256k1_scalar_get_b32(brx, &sig->r);
    secp256k1_fe_t fx;
    VERIFY_CHECK(secp256k1_fe_set_b32(&fx, brx)); /* brx comes from a scalar, so is less than the order; certainly less than p */
    if (recid & 2) {
        if (secp256k1_fe_cmp_var(&fx, &secp256k1_ecdsa_const_p_minus_order) >= 0)
            return 0;
        secp256k1_fe_add(&fx, &secp256k1_ecdsa_const_order_as_fe);
    }
    secp256k1_ge_t x;
    if (!secp256k1_ge_set_xo_var(&x, &fx, recid & 1))
        return 0;
    secp256k1_gej_t xj;
    secp256k1_gej_set_ge(&xj, &x);
    secp256k1_scalar_t rn, u1, u2;
    secp256k1_scalar_inverse_var(&rn, &sig->r);
    secp256k1_scalar_mul(&u1, &rn, message);
    secp256k1_scalar_negate(&u1, &u1);
    secp256k1_scalar_mul(&u2, &rn, &sig->s);
    secp256k1_gej_t qj;
    secp256k1_ecmult(&qj, &xj, &u2, &u1);
    secp256k1_ge_set_gej_var(pubkey, &qj);
    return !secp256k1_gej_is_infinity(&qj);
}

static int secp256k1_ecdsa_sig_sign(secp256k1_ecdsa_sig_t *sig, const secp256k1_scalar_t *seckey, const secp256k1_scalar_t *message, const secp256k1_scalar_t *nonce, int *recid) {
    secp256k1_gej_t rp;
    secp256k1_ecmult_gen(&rp, nonce);
    secp256k1_ge_t r;
    secp256k1_ge_set_gej(&r, &rp);
    unsigned char b[32];
    secp256k1_fe_normalize(&r.x);
    secp256k1_fe_normalize(&r.y);
    secp256k1_fe_get_b32(b, &r.x);
    int overflow = 0;
    secp256k1_scalar_set_b32(&sig->r, b, &overflow);
    if (secp256k1_scalar_is_zero(&sig->r)) {
        /* P.x = order is on the curve, so technically sig->r could end up zero, which would be an invalid signature. */
        secp256k1_gej_clear(&rp);
        secp256k1_ge_clear(&r);
        return 0;
    }
    if (recid)
        *recid = (overflow ? 2 : 0) | (secp256k1_fe_is_odd(&r.y) ? 1 : 0);
    secp256k1_scalar_t n;
    secp256k1_scalar_mul(&n, &sig->r, seckey);
    secp256k1_scalar_add(&n, &n, message);
    secp256k1_scalar_inverse(&sig->s, nonce);
    secp256k1_scalar_mul(&sig->s, &sig->s, &n);
    secp256k1_scalar_clear(&n);
    secp256k1_gej_clear(&rp);
    secp256k1_ge_clear(&r);
    if (secp256k1_scalar_is_zero(&sig->s))
        return 0;
    if (secp256k1_scalar_is_high(&sig->s)) {
        secp256k1_scalar_negate(&sig->s, &sig->s);
        if (recid)
            *recid ^= 1;
    }
    return 1;
}

#endif