Third step in converting to C: group
This commit is contained in:
Pieter Wuille
parent
d73bad33e8
commit
f11ff5be70
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@ -11,9 +11,10 @@ using namespace secp256k1;
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int main() {
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secp256k1_num_start();
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secp256k1_fe_start();
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secp256k1_ge_start();
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secp256k1_fe_t x;
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const secp256k1_num_t &order = GetGroupConst().order;
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const secp256k1_num_t *order = &secp256k1_ge_consts->order;
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secp256k1_num_t r, s, m;
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secp256k1_num_init(&r);
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secp256k1_num_init(&s);
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@ -23,12 +24,12 @@ int main() {
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int cnt = 0;
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int good = 0;
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for (int i=0; i<1000000; i++) {
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secp256k1_num_set_rand(&r, &order);
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secp256k1_num_set_rand(&s, &order);
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secp256k1_num_set_rand(&m, &order);
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secp256k1_num_set_rand(&r, order);
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secp256k1_num_set_rand(&s, order);
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secp256k1_num_set_rand(&m, order);
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sig.SetRS(r,s);
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GroupElemJac pubkey; pubkey.SetCompressed(x, true);
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if (pubkey.IsValid()) {
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secp256k1_gej_t pubkey; secp256k1_gej_set_xo(&pubkey, &x, 1);
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if (secp256k1_gej_is_valid(&pubkey)) {
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cnt++;
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good += sig.Verify(pubkey, m);
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}
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@ -38,6 +39,8 @@ int main() {
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secp256k1_num_free(&s);
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secp256k1_num_free(&m);
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secp256k1_ge_stop();
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secp256k1_fe_stop();
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secp256k1_num_stop();
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return 0;
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}
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@ -6,22 +6,22 @@
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namespace secp256k1 {
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bool ParsePubKey(GroupElemJac &elem, const unsigned char *pub, int size) {
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bool ParsePubKey(secp256k1_gej_t &elem, const unsigned char *pub, int size) {
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if (size == 33 && (pub[0] == 0x02 || pub[0] == 0x03)) {
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secp256k1_fe_t x;
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secp256k1_fe_set_b32(&x, pub+1);
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elem.SetCompressed(x, pub[0] == 0x03);
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secp256k1_gej_set_xo(&elem, &x, pub[0] == 0x03);
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} else if (size == 65 && (pub[0] == 0x04 || pub[0] == 0x06 || pub[0] == 0x07)) {
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secp256k1_fe_t x,y;
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secp256k1_fe_set_b32(&x, pub+1);
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secp256k1_fe_set_b32(&y, pub+33);
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elem = GroupElem(x,y);
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secp256k1_gej_set_xy(&elem, &x, &y);
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if ((pub[0] == 0x06 || pub[0] == 0x07) && secp256k1_fe_is_odd(&y) != (pub[0] == 0x07))
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return false;
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} else {
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return false;
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}
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return elem.IsValid();
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return secp256k1_gej_is_valid(&elem);
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}
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bool Signature::Parse(const unsigned char *sig, int size) {
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@ -61,8 +61,8 @@ bool Signature::Serialize(unsigned char *sig, int *size) {
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return true;
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}
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bool Signature::RecomputeR(secp256k1_num_t &r2, const GroupElemJac &pubkey, const secp256k1_num_t &message) const {
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const GroupConstants &c = GetGroupConst();
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bool Signature::RecomputeR(secp256k1_num_t &r2, const secp256k1_gej_t &pubkey, const secp256k1_num_t &message) const {
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const secp256k1_ge_consts_t &c = *secp256k1_ge_consts;
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if (secp256k1_num_is_neg(&r) || secp256k1_num_is_neg(&s))
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return false;
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@ -79,9 +79,9 @@ bool Signature::RecomputeR(secp256k1_num_t &r2, const GroupElemJac &pubkey, cons
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secp256k1_num_mod_inverse(&sn, &s, &c.order);
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secp256k1_num_mod_mul(&u1, &sn, &message, &c.order);
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secp256k1_num_mod_mul(&u2, &sn, &r, &c.order);
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GroupElemJac pr; ECMult(pr, pubkey, u2, u1);
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if (!pr.IsInfinity()) {
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secp256k1_fe_t xr; pr.GetX(xr);
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secp256k1_gej_t pr; ECMult(pr, pubkey, u2, u1);
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if (!secp256k1_gej_is_infinity(&pr)) {
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secp256k1_fe_t xr; secp256k1_gej_get_x(&xr, &pr);
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secp256k1_fe_normalize(&xr);
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unsigned char xrb[32]; secp256k1_fe_get_b32(xrb, &xr);
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secp256k1_num_set_bin(&r2, xrb, 32);
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@ -94,7 +94,7 @@ bool Signature::RecomputeR(secp256k1_num_t &r2, const GroupElemJac &pubkey, cons
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return ret;
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}
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bool Signature::Verify(const GroupElemJac &pubkey, const secp256k1_num_t &message) const {
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bool Signature::Verify(const secp256k1_gej_t &pubkey, const secp256k1_num_t &message) const {
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secp256k1_num_t r2;
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secp256k1_num_init(&r2);
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bool ret = false;
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@ -104,12 +104,12 @@ bool Signature::Verify(const GroupElemJac &pubkey, const secp256k1_num_t &messag
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}
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bool Signature::Sign(const secp256k1_num_t &seckey, const secp256k1_num_t &message, const secp256k1_num_t &nonce) {
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const GroupConstants &c = GetGroupConst();
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const secp256k1_ge_consts_t &c = *secp256k1_ge_consts;
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GroupElemJac rp;
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secp256k1_gej_t rp;
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ECMultBase(rp, nonce);
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secp256k1_fe_t rx;
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rp.GetX(rx);
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secp256k1_gej_get_x(&rx, &rp);
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unsigned char b[32];
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secp256k1_fe_normalize(&rx);
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secp256k1_fe_get_b32(b, &rx);
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@ -19,8 +19,8 @@ public:
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bool Parse(const unsigned char *sig, int size);
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bool Serialize(unsigned char *sig, int *size);
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bool RecomputeR(secp256k1_num_t &r2, const GroupElemJac &pubkey, const secp256k1_num_t &message) const;
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bool Verify(const GroupElemJac &pubkey, const secp256k1_num_t &message) const;
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bool RecomputeR(secp256k1_num_t &r2, const secp256k1_gej_t &pubkey, const secp256k1_num_t &message) const;
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bool Verify(const secp256k1_gej_t &pubkey, const secp256k1_num_t &message) const;
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bool Sign(const secp256k1_num_t &seckey, const secp256k1_num_t &message, const secp256k1_num_t &nonce);
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void SetRS(const secp256k1_num_t &rin, const secp256k1_num_t &sin);
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std::string ToString() const;
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124
src/ecmult.cpp
124
src/ecmult.cpp
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@ -14,35 +14,65 @@
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namespace secp256k1 {
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template<typename G, int W> class WNAFPrecomp {
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template<int W> class WNAFPrecompJac {
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private:
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G pre[1 << (W-2)];
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secp256k1_gej_t pre[1 << (W-2)];
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public:
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WNAFPrecomp() {}
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WNAFPrecompJac() {}
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void Build(const G &base) {
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void Build(const secp256k1_gej_t &base) {
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pre[0] = base;
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GroupElemJac x(base);
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GroupElemJac d; d.SetDouble(x);
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for (int i=1; i<(1 << (W-2)); i++) {
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x.SetAdd(d,pre[i-1]);
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pre[i].SetJac(x);
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}
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secp256k1_gej_t d; secp256k1_gej_double(&d, &pre[0]);
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for (int i=1; i<(1 << (W-2)); i++)
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secp256k1_gej_add(&pre[i], &d, &pre[i-1]);
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}
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WNAFPrecomp(const G &base) {
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WNAFPrecompJac(const secp256k1_gej_t &base) {
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Build(base);
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}
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void Get(G &out, int exp) const {
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void Get(secp256k1_gej_t &out, int exp) const {
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assert((exp & 1) == 1);
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assert(exp >= -((1 << (W-1)) - 1));
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assert(exp <= ((1 << (W-1)) - 1));
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if (exp > 0) {
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out = pre[(exp-1)/2];
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} else {
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out.SetNeg(pre[(-exp-1)/2]);
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secp256k1_gej_neg(&out, &pre[(-exp-1)/2]);
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}
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}
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};
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template<int W> class WNAFPrecompAff {
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private:
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secp256k1_ge_t pre[1 << (W-2)];
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public:
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WNAFPrecompAff() {}
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void Build(const secp256k1_ge_t &base) {
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pre[0] = base;
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secp256k1_gej_t x; secp256k1_gej_set_ge(&x, &base);
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secp256k1_gej_t d; secp256k1_gej_double(&d, &x);
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for (int i=1; i<(1 << (W-2)); i++) {
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secp256k1_gej_add_ge(&x, &d, &pre[i-1]);
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secp256k1_ge_set_gej(&pre[i], &x);
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}
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}
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WNAFPrecompAff(const secp256k1_ge_t &base) {
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Build(base);
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}
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void Get(secp256k1_ge_t &out, int exp) const {
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assert((exp & 1) == 1);
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assert(exp >= -((1 << (W-1)) - 1));
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assert(exp <= ((1 << (W-1)) - 1));
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if (exp > 0) {
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out = pre[(exp-1)/2];
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} else {
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secp256k1_ge_neg(&out, &pre[(-exp-1)/2]);
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}
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}
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};
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@ -112,33 +142,33 @@ public:
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class ECMultConsts {
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public:
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WNAFPrecomp<GroupElem,WINDOW_G> wpg;
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WNAFPrecomp<GroupElem,WINDOW_G> wpg128;
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GroupElem prec[64][16]; // prec[j][i] = 16^j * (i+1) * G
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GroupElem fin; // -(sum(prec[j][0], j=0..63))
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WNAFPrecompAff<WINDOW_G> wpg;
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WNAFPrecompAff<WINDOW_G> wpg128;
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secp256k1_ge_t prec[64][16]; // prec[j][i] = 16^j * (i+1) * G
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secp256k1_ge_t fin; // -(sum(prec[j][0], j=0..63))
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ECMultConsts() {
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const GroupElem &g = GetGroupConst().g;
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GroupElemJac g128j(g);
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const secp256k1_ge_t &g = secp256k1_ge_consts->g;
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secp256k1_gej_t g128j; secp256k1_gej_set_ge(&g128j, &g);
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for (int i=0; i<128; i++)
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g128j.SetDouble(g128j);
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GroupElem g128; g128.SetJac(g128j);
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secp256k1_gej_double(&g128j, &g128j);
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secp256k1_ge_t g128; secp256k1_ge_set_gej(&g128, &g128j);
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wpg.Build(g);
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wpg128.Build(g128);
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GroupElemJac gg(g);
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GroupElem ad(g);
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GroupElemJac fn;
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secp256k1_gej_t gg; secp256k1_gej_set_ge(&gg, &g);
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secp256k1_ge_t ad = g;
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secp256k1_gej_t fn; secp256k1_gej_set_infinity(&fn);
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for (int j=0; j<64; j++) {
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prec[j][0].SetJac(gg);
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fn.SetAdd(fn, gg);
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secp256k1_ge_set_gej(&prec[j][0], &gg);
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secp256k1_gej_add(&fn, &fn, &gg);
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for (int i=1; i<16; i++) {
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gg.SetAdd(gg, ad);
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prec[j][i].SetJac(gg);
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secp256k1_gej_add_ge(&gg, &gg, &ad);
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secp256k1_ge_set_gej(&prec[j][i], &gg);
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}
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ad = prec[j][15];
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}
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fn.SetNeg(fn);
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fin.SetJac(fn);
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secp256k1_ge_set_gej(&fin, &fn);
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secp256k1_ge_neg(&fin, &fin);
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}
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};
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@ -147,20 +177,20 @@ const ECMultConsts &GetECMultConsts() {
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return ecmult_consts;
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}
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void ECMultBase(GroupElemJac &out, const secp256k1_num_t &gn) {
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void ECMultBase(secp256k1_gej_t &out, const secp256k1_num_t &gn) {
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secp256k1_num_t n;
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secp256k1_num_init(&n);
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secp256k1_num_copy(&n, &gn);
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const ECMultConsts &c = GetECMultConsts();
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out.SetAffine(c.prec[0][secp256k1_num_shift(&n, 4)]);
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secp256k1_gej_set_ge(&out, &c.prec[0][secp256k1_num_shift(&n, 4)]);
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for (int j=1; j<64; j++) {
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out.SetAdd(out, c.prec[j][secp256k1_num_shift(&n, 4)]);
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secp256k1_gej_add_ge(&out, &out, &c.prec[j][secp256k1_num_shift(&n, 4)]);
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}
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secp256k1_num_free(&n);
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out.SetAdd(out, c.fin);
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secp256k1_gej_add_ge(&out, &out, &c.fin);
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}
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void ECMult(GroupElemJac &out, const GroupElemJac &a, const secp256k1_num_t &an, const secp256k1_num_t &gn) {
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void ECMult(secp256k1_gej_t &out, const secp256k1_gej_t &a, const secp256k1_num_t &an, const secp256k1_num_t &gn) {
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secp256k1_num_t an1, an2;
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secp256k1_num_t gn1, gn2;
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@ -169,7 +199,7 @@ void ECMult(GroupElemJac &out, const GroupElemJac &a, const secp256k1_num_t &an,
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secp256k1_num_init(&gn1);
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secp256k1_num_init(&gn2);
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SplitExp(an, an1, an2);
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secp256k1_gej_split_exp(&an1, &an2, &an);
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// printf("an=%s\n", an.ToString().c_str());
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// printf("an1=%s\n", an1.ToString().c_str());
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// printf("an2=%s\n", an2.ToString().c_str());
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@ -181,9 +211,9 @@ void ECMult(GroupElemJac &out, const GroupElemJac &a, const secp256k1_num_t &an,
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WNAF<128> wa2(an2, WINDOW_A);
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WNAF<128> wg1(gn1, WINDOW_G);
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WNAF<128> wg2(gn2, WINDOW_G);
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GroupElemJac a2; a2.SetMulLambda(a);
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WNAFPrecomp<GroupElemJac,WINDOW_A> wpa1(a);
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WNAFPrecomp<GroupElemJac,WINDOW_A> wpa2(a2);
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secp256k1_gej_t a2; secp256k1_gej_mul_lambda(&a2, &a);
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WNAFPrecompJac<WINDOW_A> wpa1(a);
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WNAFPrecompJac<WINDOW_A> wpa2(a2);
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const ECMultConsts &c = GetECMultConsts();
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int size_a1 = wa1.GetSize();
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@ -192,28 +222,28 @@ void ECMult(GroupElemJac &out, const GroupElemJac &a, const secp256k1_num_t &an,
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int size_g2 = wg2.GetSize();
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int size = std::max(std::max(size_a1, size_a2), std::max(size_g1, size_g2));
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out = GroupElemJac();
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GroupElemJac tmpj;
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GroupElem tmpa;
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out; secp256k1_gej_set_infinity(&out);
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secp256k1_gej_t tmpj;
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secp256k1_ge_t tmpa;
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for (int i=size-1; i>=0; i--) {
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out.SetDouble(out);
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secp256k1_gej_double(&out, &out);
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int nw;
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if (i < size_a1 && (nw = wa1.Get(i))) {
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wpa1.Get(tmpj, nw);
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out.SetAdd(out, tmpj);
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secp256k1_gej_add(&out, &out, &tmpj);
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}
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if (i < size_a2 && (nw = wa2.Get(i))) {
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wpa2.Get(tmpj, nw);
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out.SetAdd(out, tmpj);
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secp256k1_gej_add(&out, &out, &tmpj);
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}
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if (i < size_g1 && (nw = wg1.Get(i))) {
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c.wpg.Get(tmpa, nw);
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out.SetAdd(out, tmpa);
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secp256k1_gej_add_ge(&out, &out, &tmpa);
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}
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if (i < size_g2 && (nw = wg2.Get(i))) {
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c.wpg128.Get(tmpa, nw);
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out.SetAdd(out, tmpa);
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secp256k1_gej_add_ge(&out, &out, &tmpa);
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}
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}
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@ -1,13 +1,13 @@
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#ifndef _SECP256K1_ECMULT_
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#define _SECP256K1_ECMULT_
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#include "group.h"
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#include "num.h"
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#include "group.h"
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namespace secp256k1 {
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void ECMultBase(GroupElemJac &out, const secp256k1_num_t &gn);
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void ECMult(GroupElemJac &out, const GroupElemJac &a, const secp256k1_num_t &an, const secp256k1_num_t &gn);
|
||||
void ECMultBase(secp256k1_gej_t &out, const secp256k1_num_t &gn);
|
||||
void ECMult(secp256k1_gej_t &out, const secp256k1_gej_t &a, const secp256k1_num_t &an, const secp256k1_num_t &gn);
|
||||
|
||||
}
|
||||
|
||||
|
|
|
|||
492
src/group.cpp
492
src/group.cpp
|
|
@ -1,83 +1,126 @@
|
|||
#include <string>
|
||||
#include <string.h>
|
||||
|
||||
#include "num.h"
|
||||
#include "field.h"
|
||||
#include "group.h"
|
||||
|
||||
namespace secp256k1 {
|
||||
extern "C" {
|
||||
|
||||
GroupElem::GroupElem() {
|
||||
fInfinity = true;
|
||||
void static secp256k1_ge_set_infinity(secp256k1_ge_t *r) {
|
||||
r->infinity = 1;
|
||||
}
|
||||
|
||||
GroupElem::GroupElem(const secp256k1_fe_t &xin, const secp256k1_fe_t &yin) {
|
||||
fInfinity = false;
|
||||
x = xin;
|
||||
y = yin;
|
||||
void static secp256k1_ge_set_xy(secp256k1_ge_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y) {
|
||||
r->infinity = 0;
|
||||
r->x = *x;
|
||||
r->y = *y;
|
||||
}
|
||||
|
||||
bool GroupElem::IsInfinity() const {
|
||||
return fInfinity;
|
||||
int static secp256k1_ge_is_infinity(const secp256k1_ge_t *a) {
|
||||
return a->infinity;
|
||||
}
|
||||
|
||||
void GroupElem::SetNeg(const GroupElem &p) {
|
||||
*this = p;
|
||||
secp256k1_fe_normalize(&y);
|
||||
secp256k1_fe_negate(&y, &y, 1);
|
||||
void static secp256k1_ge_neg(secp256k1_ge_t *r, const secp256k1_ge_t *a) {
|
||||
r->infinity = a->infinity;
|
||||
r->x = a->x;
|
||||
r->y = a->y;
|
||||
secp256k1_fe_normalize(&r->y);
|
||||
secp256k1_fe_negate(&r->y, &r->y, 1);
|
||||
}
|
||||
|
||||
void GroupElem::GetX(secp256k1_fe_t &xout) {
|
||||
xout = x;
|
||||
void static secp256k1_ge_get_hex(char *r, int *rlen, const secp256k1_ge_t *a) {
|
||||
char cx[65]; int lx=65;
|
||||
char cy[65]; int ly=65;
|
||||
secp256k1_fe_get_hex(cx, &lx, &a->x);
|
||||
secp256k1_fe_get_hex(cy, &ly, &a->y);
|
||||
lx = strlen(cx);
|
||||
ly = strlen(cy);
|
||||
int len = lx + ly + 3 + 1;
|
||||
if (*rlen < len) {
|
||||
*rlen = len;
|
||||
return;
|
||||
}
|
||||
*rlen = len;
|
||||
r[0] = '(';
|
||||
memcpy(r+1, cx, lx);
|
||||
r[1+lx] = ',';
|
||||
memcpy(r+2+lx, cy, ly);
|
||||
r[2+lx+ly] = ')';
|
||||
r[3+lx+ly] = 0;
|
||||
}
|
||||
|
||||
void GroupElem::GetY(secp256k1_fe_t &yout) {
|
||||
yout = y;
|
||||
void static secp256k1_ge_set_gej(secp256k1_ge_t *r, secp256k1_gej_t *a) {
|
||||
secp256k1_fe_inv_var(&a->z, &a->z);
|
||||
secp256k1_fe_t z2; secp256k1_fe_sqr(&z2, &a->z);
|
||||
secp256k1_fe_t z3; secp256k1_fe_mul(&z3, &a->z, &z2);
|
||||
secp256k1_fe_mul(&a->x, &a->x, &z2);
|
||||
secp256k1_fe_mul(&a->y, &a->y, &z3);
|
||||
secp256k1_fe_set_int(&a->z, 1);
|
||||
r->infinity = a->infinity;
|
||||
r->x = a->x;
|
||||
r->y = a->y;
|
||||
}
|
||||
|
||||
std::string GroupElem::ToString() const {
|
||||
if (fInfinity)
|
||||
return "(inf)";
|
||||
secp256k1_fe_t xc = x, yc = y;
|
||||
char xo[65], yo[65];
|
||||
int xl = 65, yl = 65;
|
||||
secp256k1_fe_get_hex(xo, &xl, &xc);
|
||||
secp256k1_fe_get_hex(yo, &yl, &yc);
|
||||
return "(" + std::string(xo) + "," + std::string(yo) + ")";
|
||||
void static secp256k1_gej_set_infinity(secp256k1_gej_t *r) {
|
||||
r->infinity = 1;
|
||||
}
|
||||
|
||||
GroupElemJac::GroupElemJac() : GroupElem() {
|
||||
secp256k1_fe_set_int(&z, 1);
|
||||
void static secp256k1_gej_set_xy(secp256k1_gej_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y) {
|
||||
r->infinity = 0;
|
||||
r->x = *x;
|
||||
r->y = *y;
|
||||
secp256k1_fe_set_int(&r->z, 1);
|
||||
}
|
||||
|
||||
GroupElemJac::GroupElemJac(const secp256k1_fe_t &xin, const secp256k1_fe_t &yin) : GroupElem(xin,yin) {
|
||||
secp256k1_fe_set_int(&z, 1);
|
||||
void static secp256k1_gej_set_xo(secp256k1_gej_t *r, const secp256k1_fe_t *x, int odd) {
|
||||
r->x = *x;
|
||||
secp256k1_fe_t x2; secp256k1_fe_sqr(&x2, x);
|
||||
secp256k1_fe_t x3; secp256k1_fe_mul(&x3, x, &x2);
|
||||
r->infinity = false;
|
||||
secp256k1_fe_t c; secp256k1_fe_set_int(&c, 7);
|
||||
secp256k1_fe_add(&c, &x3);
|
||||
secp256k1_fe_sqrt(&r->y, &c);
|
||||
secp256k1_fe_set_int(&r->z, 1);
|
||||
secp256k1_fe_normalize(&r->y);
|
||||
if (secp256k1_fe_is_odd(&r->y) != odd)
|
||||
secp256k1_fe_negate(&r->y, &r->y, 1);
|
||||
}
|
||||
|
||||
GroupElemJac::GroupElemJac(const GroupElem &in) : GroupElem(in) {
|
||||
secp256k1_fe_set_int(&z, 1);
|
||||
void static secp256k1_gej_set_ge(secp256k1_gej_t *r, const secp256k1_ge_t *a) {
|
||||
r->infinity = a->infinity;
|
||||
r->x = a->x;
|
||||
r->y = a->y;
|
||||
secp256k1_fe_set_int(&r->z, 1);
|
||||
}
|
||||
|
||||
void GroupElemJac::SetJac(const GroupElemJac &jac) {
|
||||
*this = jac;
|
||||
void static secp256k1_gej_get_x(secp256k1_fe_t *r, const secp256k1_gej_t *a) {
|
||||
secp256k1_fe_t zi2; secp256k1_fe_inv_var(&zi2, &a->z); secp256k1_fe_sqr(&zi2, &zi2);
|
||||
secp256k1_fe_mul(r, &a->x, &zi2);
|
||||
}
|
||||
|
||||
void GroupElemJac::SetAffine(const GroupElem &aff) {
|
||||
fInfinity = aff.fInfinity;
|
||||
x = aff.x;
|
||||
y = aff.y;
|
||||
secp256k1_fe_set_int(&z, 1);
|
||||
void static secp256k1_gej_neg(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
|
||||
r->infinity = a->infinity;
|
||||
r->x = a->x;
|
||||
r->y = a->y;
|
||||
r->z = a->z;
|
||||
secp256k1_fe_normalize(&r->y);
|
||||
secp256k1_fe_negate(&r->y, &r->y, 1);
|
||||
}
|
||||
|
||||
bool GroupElemJac::IsValid() const {
|
||||
if (IsInfinity())
|
||||
int static secp256k1_gej_is_infinity(const secp256k1_gej_t *a) {
|
||||
return a->infinity;
|
||||
}
|
||||
|
||||
int static secp256k1_gej_is_valid(const secp256k1_gej_t *a) {
|
||||
if (a->infinity)
|
||||
return false;
|
||||
// y^2 = x^3 + 7
|
||||
// (Y/Z^3)^2 = (X/Z^2)^3 + 7
|
||||
// Y^2 / Z^6 = X^3 / Z^6 + 7
|
||||
// Y^2 = X^3 + 7*Z^6
|
||||
secp256k1_fe_t y2; secp256k1_fe_sqr(&y2, &y);
|
||||
secp256k1_fe_t x3; secp256k1_fe_sqr(&x3, &x); secp256k1_fe_mul(&x3, &x3, &x);
|
||||
secp256k1_fe_t z2; secp256k1_fe_sqr(&z2, &z);
|
||||
secp256k1_fe_t y2; secp256k1_fe_sqr(&y2, &a->y);
|
||||
secp256k1_fe_t x3; secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
|
||||
secp256k1_fe_t z2; secp256k1_fe_sqr(&z2, &a->z);
|
||||
secp256k1_fe_t z6; secp256k1_fe_sqr(&z6, &z2); secp256k1_fe_mul(&z6, &z6, &z2);
|
||||
secp256k1_fe_mul_int(&z6, 7);
|
||||
secp256k1_fe_add(&x3, &z6);
|
||||
|
|
@ -86,256 +129,136 @@ bool GroupElemJac::IsValid() const {
|
|||
return secp256k1_fe_equal(&y2, &x3);
|
||||
}
|
||||
|
||||
void GroupElemJac::GetAffine(GroupElem &aff) {
|
||||
secp256k1_fe_inv_var(&z, &z);
|
||||
secp256k1_fe_t z2; secp256k1_fe_sqr(&z2, &z);
|
||||
secp256k1_fe_t z3; secp256k1_fe_mul(&z3, &z, &z2);
|
||||
secp256k1_fe_mul(&x, &x, &z2);
|
||||
secp256k1_fe_mul(&y, &y, &z3);
|
||||
secp256k1_fe_set_int(&z, 1);
|
||||
aff.fInfinity = fInfinity;
|
||||
aff.x = x;
|
||||
aff.y = y;
|
||||
}
|
||||
|
||||
void GroupElemJac::GetX(secp256k1_fe_t &xout) {
|
||||
secp256k1_fe_t zi2; secp256k1_fe_inv_var(&zi2, &z); secp256k1_fe_sqr(&zi2, &zi2);
|
||||
secp256k1_fe_mul(&xout, &x, &zi2);
|
||||
}
|
||||
|
||||
void GroupElemJac::GetY(secp256k1_fe_t &yout) {
|
||||
secp256k1_fe_t zi; secp256k1_fe_inv_var(&zi, &z);
|
||||
secp256k1_fe_t zi3; secp256k1_fe_sqr(&zi3, &zi); secp256k1_fe_mul(&zi3, &zi, &zi3);
|
||||
secp256k1_fe_mul(&yout, &y, &zi3);
|
||||
}
|
||||
|
||||
bool GroupElemJac::IsInfinity() const {
|
||||
return fInfinity;
|
||||
}
|
||||
|
||||
|
||||
void GroupElemJac::SetNeg(const GroupElemJac &p) {
|
||||
*this = p;
|
||||
secp256k1_fe_normalize(&y);
|
||||
secp256k1_fe_negate(&y, &y, 1);
|
||||
}
|
||||
|
||||
void GroupElemJac::SetCompressed(const secp256k1_fe_t &xin, bool fOdd) {
|
||||
x = xin;
|
||||
secp256k1_fe_t x2; secp256k1_fe_sqr(&x2, &x);
|
||||
secp256k1_fe_t x3; secp256k1_fe_mul(&x3, &x, &x2);
|
||||
fInfinity = false;
|
||||
secp256k1_fe_t c; secp256k1_fe_set_int(&c, 7);
|
||||
secp256k1_fe_add(&c, &x3);
|
||||
secp256k1_fe_sqrt(&y, &c);
|
||||
secp256k1_fe_set_int(&z, 1);
|
||||
secp256k1_fe_normalize(&y);
|
||||
if (secp256k1_fe_is_odd(&y) != fOdd)
|
||||
secp256k1_fe_negate(&y, &y, 1);
|
||||
}
|
||||
|
||||
void GroupElemJac::SetDouble(const GroupElemJac &p) {
|
||||
secp256k1_fe_t t5 = p.y;
|
||||
void static secp256k1_gej_double(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
|
||||
secp256k1_fe_t t5 = a->y;
|
||||
secp256k1_fe_normalize(&t5);
|
||||
if (p.fInfinity || secp256k1_fe_is_zero(&t5)) {
|
||||
fInfinity = true;
|
||||
if (a->infinity || secp256k1_fe_is_zero(&t5)) {
|
||||
r->infinity = true;
|
||||
return;
|
||||
}
|
||||
|
||||
secp256k1_fe_t t1,t2,t3,t4;
|
||||
secp256k1_fe_mul(&z, &t5, &p.z);
|
||||
secp256k1_fe_mul_int(&z, 2); // Z' = 2*Y*Z (2)
|
||||
secp256k1_fe_sqr(&t1, &p.x);
|
||||
secp256k1_fe_mul(&r->z, &t5, &a->z);
|
||||
secp256k1_fe_mul_int(&r->z, 2); // Z' = 2*Y*Z (2)
|
||||
secp256k1_fe_sqr(&t1, &a->x);
|
||||
secp256k1_fe_mul_int(&t1, 3); // T1 = 3*X^2 (3)
|
||||
secp256k1_fe_sqr(&t2, &t1); // T2 = 9*X^4 (1)
|
||||
secp256k1_fe_sqr(&t3, &t5);
|
||||
secp256k1_fe_mul_int(&t3, 2); // T3 = 2*Y^2 (2)
|
||||
secp256k1_fe_sqr(&t4, &t3);
|
||||
secp256k1_fe_mul_int(&t4, 2); // T4 = 8*Y^4 (2)
|
||||
secp256k1_fe_mul(&t3, &p.x, &t3); // T3 = 2*X*Y^2 (1)
|
||||
x = t3;
|
||||
secp256k1_fe_mul_int(&x, 4); // X' = 8*X*Y^2 (4)
|
||||
secp256k1_fe_negate(&x, &x, 4); // X' = -8*X*Y^2 (5)
|
||||
secp256k1_fe_add(&x, &t2); // X' = 9*X^4 - 8*X*Y^2 (6)
|
||||
secp256k1_fe_mul(&t3, &a->x, &t3); // T3 = 2*X*Y^2 (1)
|
||||
r->x = t3;
|
||||
secp256k1_fe_mul_int(&r->x, 4); // X' = 8*X*Y^2 (4)
|
||||
secp256k1_fe_negate(&r->x, &r->x, 4); // X' = -8*X*Y^2 (5)
|
||||
secp256k1_fe_add(&r->x, &t2); // X' = 9*X^4 - 8*X*Y^2 (6)
|
||||
secp256k1_fe_negate(&t2, &t2, 1); // T2 = -9*X^4 (2)
|
||||
secp256k1_fe_mul_int(&t3, 6); // T3 = 12*X*Y^2 (6)
|
||||
secp256k1_fe_add(&t3, &t2); // T3 = 12*X*Y^2 - 9*X^4 (8)
|
||||
secp256k1_fe_mul(&y, &t1, &t3); // Y' = 36*X^3*Y^2 - 27*X^6 (1)
|
||||
secp256k1_fe_mul(&r->y, &t1, &t3); // Y' = 36*X^3*Y^2 - 27*X^6 (1)
|
||||
secp256k1_fe_negate(&t2, &t4, 2); // T2 = -8*Y^4 (3)
|
||||
secp256k1_fe_add(&y, &t2); // Y' = 36*X^3*Y^2 - 27*X^6 - 8*Y^4 (4)
|
||||
fInfinity = false;
|
||||
secp256k1_fe_add(&r->y, &t2); // Y' = 36*X^3*Y^2 - 27*X^6 - 8*Y^4 (4)
|
||||
r->infinity = false;
|
||||
}
|
||||
|
||||
void GroupElemJac::SetAdd(const GroupElemJac &p, const GroupElemJac &q) {
|
||||
if (p.fInfinity) {
|
||||
*this = q;
|
||||
void static secp256k1_gej_add(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_gej_t *b) {
|
||||
if (a->infinity) {
|
||||
*r = *b;
|
||||
return;
|
||||
}
|
||||
if (q.fInfinity) {
|
||||
*this = p;
|
||||
if (b->infinity) {
|
||||
*r = *a;
|
||||
return;
|
||||
}
|
||||
fInfinity = false;
|
||||
const secp256k1_fe_t &x1 = p.x, &y1 = p.y, &z1 = p.z, &x2 = q.x, &y2 = q.y, &z2 = q.z;
|
||||
secp256k1_fe_t z22; secp256k1_fe_sqr(&z22, &z2);
|
||||
secp256k1_fe_t z12; secp256k1_fe_sqr(&z12, &z1);
|
||||
secp256k1_fe_t u1; secp256k1_fe_mul(&u1, &x1, &z22);
|
||||
secp256k1_fe_t u2; secp256k1_fe_mul(&u2, &x2, &z12);
|
||||
secp256k1_fe_t s1; secp256k1_fe_mul(&s1, &y1, &z22); secp256k1_fe_mul(&s1, &s1, &z2);
|
||||
secp256k1_fe_t s2; secp256k1_fe_mul(&s2, &y2, &z12); secp256k1_fe_mul(&s2, &s2, &z1);
|
||||
r->infinity = false;
|
||||
secp256k1_fe_t z22; secp256k1_fe_sqr(&z22, &b->z);
|
||||
secp256k1_fe_t z12; secp256k1_fe_sqr(&z12, &a->z);
|
||||
secp256k1_fe_t u1; secp256k1_fe_mul(&u1, &a->x, &z22);
|
||||
secp256k1_fe_t u2; secp256k1_fe_mul(&u2, &b->x, &z12);
|
||||
secp256k1_fe_t s1; secp256k1_fe_mul(&s1, &a->y, &z22); secp256k1_fe_mul(&s1, &s1, &b->z);
|
||||
secp256k1_fe_t s2; secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
|
||||
secp256k1_fe_normalize(&u1);
|
||||
secp256k1_fe_normalize(&u2);
|
||||
if (secp256k1_fe_equal(&u1, &u2)) {
|
||||
secp256k1_fe_normalize(&s1);
|
||||
secp256k1_fe_normalize(&s2);
|
||||
if (secp256k1_fe_equal(&s1, &s2)) {
|
||||
SetDouble(p);
|
||||
secp256k1_gej_double(r, a);
|
||||
} else {
|
||||
fInfinity = true;
|
||||
r->infinity = true;
|
||||
}
|
||||
return;
|
||||
}
|
||||
secp256k1_fe_t h; secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
|
||||
secp256k1_fe_t r; secp256k1_fe_negate(&r, &s1, 1); secp256k1_fe_add(&r, &s2);
|
||||
secp256k1_fe_t r2; secp256k1_fe_sqr(&r2, &r);
|
||||
secp256k1_fe_t i; secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
|
||||
secp256k1_fe_t i2; secp256k1_fe_sqr(&i2, &i);
|
||||
secp256k1_fe_t h2; secp256k1_fe_sqr(&h2, &h);
|
||||
secp256k1_fe_t h3; secp256k1_fe_mul(&h3, &h, &h2);
|
||||
secp256k1_fe_mul(&z, &z1, &z2); secp256k1_fe_mul(&z, &z, &h);
|
||||
secp256k1_fe_mul(&r->z, &a->z, &b->z); secp256k1_fe_mul(&r->z, &r->z, &h);
|
||||
secp256k1_fe_t t; secp256k1_fe_mul(&t, &u1, &h2);
|
||||
x = t; secp256k1_fe_mul_int(&x, 2); secp256k1_fe_add(&x, &h3); secp256k1_fe_negate(&x, &x, 3); secp256k1_fe_add(&x, &r2);
|
||||
secp256k1_fe_negate(&y, &x, 5); secp256k1_fe_add(&y, &t); secp256k1_fe_mul(&y, &y, &r);
|
||||
r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
|
||||
secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
|
||||
secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
|
||||
secp256k1_fe_add(&y, &h3);
|
||||
secp256k1_fe_add(&r->y, &h3);
|
||||
}
|
||||
|
||||
void GroupElemJac::SetAdd(const GroupElemJac &p, const GroupElem &q) {
|
||||
if (p.fInfinity) {
|
||||
x = q.x;
|
||||
y = q.y;
|
||||
fInfinity = q.fInfinity;
|
||||
secp256k1_fe_set_int(&z, 1);
|
||||
void static secp256k1_gej_add_ge(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b) {
|
||||
if (a->infinity) {
|
||||
r->infinity = b->infinity;
|
||||
r->x = b->x;
|
||||
r->y = b->y;
|
||||
secp256k1_fe_set_int(&r->z, 1);
|
||||
return;
|
||||
}
|
||||
if (q.fInfinity) {
|
||||
*this = p;
|
||||
if (b->infinity) {
|
||||
*r = *a;
|
||||
return;
|
||||
}
|
||||
fInfinity = false;
|
||||
const secp256k1_fe_t &x1 = p.x, &y1 = p.y, &z1 = p.z, &x2 = q.x, &y2 = q.y;
|
||||
secp256k1_fe_t z12; secp256k1_fe_sqr(&z12, &z1);
|
||||
secp256k1_fe_t u1 = x1; secp256k1_fe_normalize(&u1);
|
||||
secp256k1_fe_t u2; secp256k1_fe_mul(&u2, &x2, &z12);
|
||||
secp256k1_fe_t s1 = y1; secp256k1_fe_normalize(&s1);
|
||||
secp256k1_fe_t s2; secp256k1_fe_mul(&s2, &y2, &z12); secp256k1_fe_mul(&s2, &s2, &z1);
|
||||
r->infinity = false;
|
||||
secp256k1_fe_t z12; secp256k1_fe_sqr(&z12, &a->z);
|
||||
secp256k1_fe_t u1 = a->x; secp256k1_fe_normalize(&u1);
|
||||
secp256k1_fe_t u2; secp256k1_fe_mul(&u2, &b->x, &z12);
|
||||
secp256k1_fe_t s1 = a->y; secp256k1_fe_normalize(&s1);
|
||||
secp256k1_fe_t s2; secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
|
||||
secp256k1_fe_normalize(&u1);
|
||||
secp256k1_fe_normalize(&u2);
|
||||
if (secp256k1_fe_equal(&u1, &u2)) {
|
||||
secp256k1_fe_normalize(&s1);
|
||||
secp256k1_fe_normalize(&s2);
|
||||
if (secp256k1_fe_equal(&s1, &s2)) {
|
||||
SetDouble(p);
|
||||
secp256k1_gej_double(r, a);
|
||||
} else {
|
||||
fInfinity = true;
|
||||
r->infinity = true;
|
||||
}
|
||||
return;
|
||||
}
|
||||
secp256k1_fe_t h; secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
|
||||
secp256k1_fe_t r; secp256k1_fe_negate(&r, &s1, 1); secp256k1_fe_add(&r, &s2);
|
||||
secp256k1_fe_t r2; secp256k1_fe_sqr(&r2, &r);
|
||||
secp256k1_fe_t i; secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
|
||||
secp256k1_fe_t i2; secp256k1_fe_sqr(&i2, &i);
|
||||
secp256k1_fe_t h2; secp256k1_fe_sqr(&h2, &h);
|
||||
secp256k1_fe_t h3; secp256k1_fe_mul(&h3, &h, &h2);
|
||||
z = p.z; secp256k1_fe_mul(&z, &z, &h);
|
||||
r->z = a->z; secp256k1_fe_mul(&r->z, &r->z, &h);
|
||||
secp256k1_fe_t t; secp256k1_fe_mul(&t, &u1, &h2);
|
||||
x = t; secp256k1_fe_mul_int(&x, 2); secp256k1_fe_add(&x, &h3); secp256k1_fe_negate(&x, &x, 3); secp256k1_fe_add(&x, &r2);
|
||||
secp256k1_fe_negate(&y, &x, 5); secp256k1_fe_add(&y, &t); secp256k1_fe_mul(&y, &y, &r);
|
||||
r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
|
||||
secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
|
||||
secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
|
||||
secp256k1_fe_add(&y, &h3);
|
||||
secp256k1_fe_add(&r->y, &h3);
|
||||
}
|
||||
|
||||
std::string GroupElemJac::ToString() const {
|
||||
GroupElemJac cop = *this;
|
||||
GroupElem aff;
|
||||
cop.GetAffine(aff);
|
||||
return aff.ToString();
|
||||
void static secp256k1_gej_get_hex(char *r, int *rlen, const secp256k1_gej_t *a) {
|
||||
secp256k1_gej_t c = *a;
|
||||
secp256k1_ge_t t; secp256k1_ge_set_gej(&t, &c);
|
||||
secp256k1_ge_get_hex(r, rlen, &t);
|
||||
}
|
||||
|
||||
void GroupElem::SetJac(GroupElemJac &jac) {
|
||||
jac.GetAffine(*this);
|
||||
void static secp256k1_gej_mul_lambda(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
|
||||
const secp256k1_fe_t *beta = &secp256k1_ge_consts->beta;
|
||||
*r = *a;
|
||||
secp256k1_fe_mul(&r->x, &r->x, beta);
|
||||
}
|
||||
|
||||
static const unsigned char order_[] = {0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
|
||||
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
|
||||
0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
|
||||
0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41};
|
||||
|
||||
static const unsigned char g_x_[] = {0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,
|
||||
0x55,0xA0,0x62,0x95,0xCE,0x87,0x0B,0x07,
|
||||
0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,
|
||||
0x59,0xF2,0x81,0x5B,0x16,0xF8,0x17,0x98};
|
||||
|
||||
static const unsigned char g_y_[] = {0x48,0x3A,0xDA,0x77,0x26,0xA3,0xC4,0x65,
|
||||
0x5D,0xA4,0xFB,0xFC,0x0E,0x11,0x08,0xA8,
|
||||
0xFD,0x17,0xB4,0x48,0xA6,0x85,0x54,0x19,
|
||||
0x9C,0x47,0xD0,0x8F,0xFB,0x10,0xD4,0xB8};
|
||||
|
||||
// properties of secp256k1's efficiently computable endomorphism
|
||||
static const unsigned char lambda_[] = {0x53,0x63,0xad,0x4c,0xc0,0x5c,0x30,0xe0,
|
||||
0xa5,0x26,0x1c,0x02,0x88,0x12,0x64,0x5a,
|
||||
0x12,0x2e,0x22,0xea,0x20,0x81,0x66,0x78,
|
||||
0xdf,0x02,0x96,0x7c,0x1b,0x23,0xbd,0x72};
|
||||
static const unsigned char beta_[] = {0x7a,0xe9,0x6a,0x2b,0x65,0x7c,0x07,0x10,
|
||||
0x6e,0x64,0x47,0x9e,0xac,0x34,0x34,0xe9,
|
||||
0x9c,0xf0,0x49,0x75,0x12,0xf5,0x89,0x95,
|
||||
0xc1,0x39,0x6c,0x28,0x71,0x95,0x01,0xee};
|
||||
static const unsigned char a1b2_[] = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,
|
||||
0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15};
|
||||
static const unsigned char b1_[] = {0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28,
|
||||
0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3};
|
||||
static const unsigned char a2_[] = {0x01,
|
||||
0x14,0xca,0x50,0xf7,0xa8,0xe2,0xf3,0xf6,
|
||||
0x57,0xc1,0x10,0x8d,0x9d,0x44,0xcf,0xd8};
|
||||
|
||||
GroupConstants::GroupConstants() {
|
||||
secp256k1_num_init(&order);
|
||||
secp256k1_num_init(&lambda);
|
||||
secp256k1_num_init(&a1b2);
|
||||
secp256k1_num_init(&b1);
|
||||
secp256k1_num_init(&a2);
|
||||
|
||||
secp256k1_fe_set_b32(&g_x, g_x_);
|
||||
secp256k1_fe_set_b32(&g_y, g_y_);
|
||||
secp256k1_fe_set_b32(&beta, beta_);
|
||||
|
||||
g = GroupElem(g_x, g_y);
|
||||
|
||||
secp256k1_num_set_bin(&order, order_, sizeof(order_));
|
||||
secp256k1_num_set_bin(&lambda, lambda_, sizeof(lambda_));
|
||||
secp256k1_num_set_bin(&a1b2, a1b2_, sizeof(a1b2_));
|
||||
secp256k1_num_set_bin(&b1, b1_, sizeof(b1_));
|
||||
secp256k1_num_set_bin(&a2, a2_, sizeof(a2_));
|
||||
}
|
||||
|
||||
GroupConstants::~GroupConstants() {
|
||||
secp256k1_num_free(&order);
|
||||
secp256k1_num_free(&lambda);
|
||||
secp256k1_num_free(&a1b2);
|
||||
secp256k1_num_free(&b1);
|
||||
secp256k1_num_free(&a2);
|
||||
}
|
||||
|
||||
const GroupConstants &GetGroupConst() {
|
||||
static const GroupConstants group_const;
|
||||
return group_const;
|
||||
}
|
||||
|
||||
void GroupElemJac::SetMulLambda(const GroupElemJac &p) {
|
||||
const secp256k1_fe_t &beta = GetGroupConst().beta;
|
||||
*this = p;
|
||||
secp256k1_fe_mul(&x, &x, &beta);
|
||||
}
|
||||
|
||||
void SplitExp(const secp256k1_num_t &exp, secp256k1_num_t &exp1, secp256k1_num_t &exp2) {
|
||||
const GroupConstants &c = GetGroupConst();
|
||||
void static secp256k1_gej_split_exp(secp256k1_num_t *r1, secp256k1_num_t *r2, const secp256k1_num_t *a) {
|
||||
const secp256k1_ge_consts_t *c = secp256k1_ge_consts;
|
||||
secp256k1_num_t bnc1, bnc2, bnt1, bnt2, bnn2;
|
||||
|
||||
secp256k1_num_init(&bnc1);
|
||||
|
|
@ -344,24 +267,24 @@ void SplitExp(const secp256k1_num_t &exp, secp256k1_num_t &exp1, secp256k1_num_t
|
|||
secp256k1_num_init(&bnt2);
|
||||
secp256k1_num_init(&bnn2);
|
||||
|
||||
secp256k1_num_copy(&bnn2, &c.order);
|
||||
secp256k1_num_copy(&bnn2, &c->order);
|
||||
secp256k1_num_shift(&bnn2, 1);
|
||||
|
||||
secp256k1_num_mul(&bnc1, &exp, &c.a1b2);
|
||||
secp256k1_num_mul(&bnc1, a, &c->a1b2);
|
||||
secp256k1_num_add(&bnc1, &bnc1, &bnn2);
|
||||
secp256k1_num_div(&bnc1, &bnc1, &c.order);
|
||||
secp256k1_num_div(&bnc1, &bnc1, &c->order);
|
||||
|
||||
secp256k1_num_mul(&bnc2, &exp, &c.b1);
|
||||
secp256k1_num_mul(&bnc2, a, &c->b1);
|
||||
secp256k1_num_add(&bnc2, &bnc2, &bnn2);
|
||||
secp256k1_num_div(&bnc2, &bnc2, &c.order);
|
||||
secp256k1_num_div(&bnc2, &bnc2, &c->order);
|
||||
|
||||
secp256k1_num_mul(&bnt1, &bnc1, &c.a1b2);
|
||||
secp256k1_num_mul(&bnt2, &bnc2, &c.a2);
|
||||
secp256k1_num_mul(&bnt1, &bnc1, &c->a1b2);
|
||||
secp256k1_num_mul(&bnt2, &bnc2, &c->a2);
|
||||
secp256k1_num_add(&bnt1, &bnt1, &bnt2);
|
||||
secp256k1_num_sub(&exp1, &exp, &bnt1);
|
||||
secp256k1_num_mul(&bnt1, &bnc1, &c.b1);
|
||||
secp256k1_num_mul(&bnt2, &bnc2, &c.a1b2);
|
||||
secp256k1_num_sub(&exp2, &bnt1, &bnt2);
|
||||
secp256k1_num_sub(r1, a, &bnt1);
|
||||
secp256k1_num_mul(&bnt1, &bnc1, &c->b1);
|
||||
secp256k1_num_mul(&bnt2, &bnc2, &c->a1b2);
|
||||
secp256k1_num_sub(r2, &bnt1, &bnt2);
|
||||
|
||||
secp256k1_num_free(&bnc1);
|
||||
secp256k1_num_free(&bnc2);
|
||||
|
|
@ -370,4 +293,87 @@ void SplitExp(const secp256k1_num_t &exp, secp256k1_num_t &exp1, secp256k1_num_t
|
|||
secp256k1_num_free(&bnn2);
|
||||
}
|
||||
|
||||
static const unsigned char secp256k1_ge_consts_order[] = {
|
||||
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
|
||||
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
|
||||
0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
|
||||
0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
|
||||
};
|
||||
|
||||
static const unsigned char secp256k1_ge_consts_g_x[] = {
|
||||
0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,
|
||||
0x55,0xA0,0x62,0x95,0xCE,0x87,0x0B,0x07,
|
||||
0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,
|
||||
0x59,0xF2,0x81,0x5B,0x16,0xF8,0x17,0x98
|
||||
};
|
||||
|
||||
static const unsigned char secp256k1_ge_consts_g_y[] = {
|
||||
0x48,0x3A,0xDA,0x77,0x26,0xA3,0xC4,0x65,
|
||||
0x5D,0xA4,0xFB,0xFC,0x0E,0x11,0x08,0xA8,
|
||||
0xFD,0x17,0xB4,0x48,0xA6,0x85,0x54,0x19,
|
||||
0x9C,0x47,0xD0,0x8F,0xFB,0x10,0xD4,0xB8
|
||||
};
|
||||
|
||||
// properties of secp256k1's efficiently computable endomorphism
|
||||
static const unsigned char secp256k1_ge_consts_lambda[] = {
|
||||
0x53,0x63,0xad,0x4c,0xc0,0x5c,0x30,0xe0,
|
||||
0xa5,0x26,0x1c,0x02,0x88,0x12,0x64,0x5a,
|
||||
0x12,0x2e,0x22,0xea,0x20,0x81,0x66,0x78,
|
||||
0xdf,0x02,0x96,0x7c,0x1b,0x23,0xbd,0x72
|
||||
};
|
||||
static const unsigned char secp256k1_ge_consts_beta[] = {
|
||||
0x7a,0xe9,0x6a,0x2b,0x65,0x7c,0x07,0x10,
|
||||
0x6e,0x64,0x47,0x9e,0xac,0x34,0x34,0xe9,
|
||||
0x9c,0xf0,0x49,0x75,0x12,0xf5,0x89,0x95,
|
||||
0xc1,0x39,0x6c,0x28,0x71,0x95,0x01,0xee
|
||||
};
|
||||
static const unsigned char secp256k1_ge_consts_a1b2[] = {
|
||||
0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,
|
||||
0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15
|
||||
};
|
||||
static const unsigned char secp256k1_ge_consts_b1[] = {
|
||||
0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28,
|
||||
0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3
|
||||
};
|
||||
static const unsigned char secp256k1_ge_consts_a2[] = {
|
||||
0x01,
|
||||
0x14,0xca,0x50,0xf7,0xa8,0xe2,0xf3,0xf6,
|
||||
0x57,0xc1,0x10,0x8d,0x9d,0x44,0xcf,0xd8
|
||||
};
|
||||
|
||||
void static secp256k1_ge_start(void) {
|
||||
if (secp256k1_ge_consts == NULL) {
|
||||
secp256k1_ge_consts_t *ret = (secp256k1_ge_consts_t*)malloc(sizeof(secp256k1_ge_consts_t));
|
||||
secp256k1_num_init(&ret->order);
|
||||
secp256k1_num_init(&ret->lambda);
|
||||
secp256k1_num_init(&ret->a1b2);
|
||||
secp256k1_num_init(&ret->a2);
|
||||
secp256k1_num_init(&ret->b1);
|
||||
secp256k1_num_set_bin(&ret->order, secp256k1_ge_consts_order, sizeof(secp256k1_ge_consts_order));
|
||||
secp256k1_num_set_bin(&ret->lambda, secp256k1_ge_consts_lambda, sizeof(secp256k1_ge_consts_lambda));
|
||||
secp256k1_num_set_bin(&ret->a1b2, secp256k1_ge_consts_a1b2, sizeof(secp256k1_ge_consts_a1b2));
|
||||
secp256k1_num_set_bin(&ret->a2, secp256k1_ge_consts_a2, sizeof(secp256k1_ge_consts_a2));
|
||||
secp256k1_num_set_bin(&ret->b1, secp256k1_ge_consts_b1, sizeof(secp256k1_ge_consts_b1));
|
||||
secp256k1_fe_set_b32(&ret->beta, secp256k1_ge_consts_beta);
|
||||
secp256k1_fe_t g_x, g_y;
|
||||
secp256k1_fe_set_b32(&g_x, secp256k1_ge_consts_g_x);
|
||||
secp256k1_fe_set_b32(&g_y, secp256k1_ge_consts_g_y);
|
||||
secp256k1_ge_set_xy(&ret->g, &g_x, &g_y);
|
||||
secp256k1_ge_consts = ret;
|
||||
}
|
||||
}
|
||||
|
||||
void static secp256k1_ge_stop(void) {
|
||||
if (secp256k1_ge_consts != NULL) {
|
||||
secp256k1_ge_consts_t *c = (secp256k1_ge_consts_t*)secp256k1_ge_consts;
|
||||
secp256k1_num_free(&c->order);
|
||||
secp256k1_num_free(&c->lambda);
|
||||
secp256k1_num_free(&c->a1b2);
|
||||
secp256k1_num_free(&c->a2);
|
||||
secp256k1_num_free(&c->b1);
|
||||
free((void*)c);
|
||||
secp256k1_ge_consts = NULL;
|
||||
}
|
||||
}
|
||||
|
||||
}
|
||||
|
|
|
|||
111
src/group.h
111
src/group.h
|
|
@ -1,8 +1,6 @@
|
|||
#ifndef _SECP256K1_GROUP_
|
||||
#define _SECP256K1_GROUP_
|
||||
|
||||
#include <string>
|
||||
|
||||
#include "num.h"
|
||||
#include "field.h"
|
||||
|
||||
|
|
@ -37,15 +35,16 @@ void static secp256k1_ge_set_xy(secp256k1_ge_t *r, const secp256k1_fe_t *x, cons
|
|||
int static secp256k1_ge_is_infinity(const secp256k1_ge_t *a);
|
||||
void static secp256k1_ge_neg(secp256k1_ge_t *r, const secp256k1_ge_t *a);
|
||||
void static secp256k1_ge_get_hex(char *r, int *rlen, const secp256k1_ge_t *a);
|
||||
void static secp256k1_ge_set_gej(secp256k1_ge_t *r, const secp256k1_gej_t *a);
|
||||
void static secp256k1_ge_set_gej(secp256k1_ge_t *r, secp256k1_gej_t *a);
|
||||
|
||||
void static secp256k1_gej_set_infinity(secp256k1_gej_t *r);
|
||||
void static secp256k1_gej_set_xy(secp256k1_gej_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y);
|
||||
void static secp256k1_gej_set_xo(secp256k1_gej_t *r, const secp256k1_fe_t *x, int compressed);
|
||||
void static secp256k1_gej_set_xo(secp256k1_gej_t *r, const secp256k1_fe_t *x, int odd);
|
||||
void static secp256k1_gej_set_ge(secp256k1_gej_t *r, const secp256k1_ge_t *a);
|
||||
void static secp256k1_gej_get_x(secp256k1_fe_t *r, const secp256k1_gej_t *a);
|
||||
void static secp256k1_gej_neg(secp256k1_gej_t *r, const secp256k1_gej_t *a);
|
||||
int static secp256k1_gej_is_infinity(const secp256k1_gej_t *a);
|
||||
int static secp256k1_gej_is_valid(const secp256k1_gej_t *a);
|
||||
void static secp256k1_gej_double(secp256k1_gej_t *r, const secp256k1_gej_t *a);
|
||||
void static secp256k1_gej_add(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_gej_t *b);
|
||||
void static secp256k1_gej_add_ge(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b);
|
||||
|
|
@ -55,108 +54,4 @@ void static secp256k1_gej_split_exp(secp256k1_num_t *r1, secp256k1_num_t *r2, co
|
|||
|
||||
}
|
||||
|
||||
namespace secp256k1 {
|
||||
|
||||
class GroupElemJac;
|
||||
|
||||
/** Defines a point on the secp256k1 curve (y^2 = x^3 + 7) */
|
||||
class GroupElem {
|
||||
protected:
|
||||
bool fInfinity;
|
||||
secp256k1_fe_t x;
|
||||
secp256k1_fe_t y;
|
||||
|
||||
public:
|
||||
|
||||
/** Creates the point at infinity */
|
||||
GroupElem();
|
||||
|
||||
/** Creates the point with given affine coordinates */
|
||||
GroupElem(const secp256k1_fe_t &xin, const secp256k1_fe_t &yin);
|
||||
|
||||
/** Checks whether this is the point at infinity */
|
||||
bool IsInfinity() const;
|
||||
|
||||
void SetNeg(const GroupElem &p);
|
||||
|
||||
void GetX(secp256k1_fe_t &xout);
|
||||
|
||||
void GetY(secp256k1_fe_t &yout);
|
||||
|
||||
std::string ToString() const;
|
||||
|
||||
void SetJac(GroupElemJac &jac);
|
||||
|
||||
friend class GroupElemJac;
|
||||
};
|
||||
|
||||
/** Represents a point on the secp256k1 curve, with jacobian coordinates */
|
||||
class GroupElemJac : private GroupElem {
|
||||
protected:
|
||||
secp256k1_fe_t z;
|
||||
|
||||
public:
|
||||
/** Creates the point at infinity */
|
||||
GroupElemJac();
|
||||
|
||||
/** Creates the point with given affine coordinates */
|
||||
GroupElemJac(const secp256k1_fe_t &xin, const secp256k1_fe_t &yin);
|
||||
|
||||
GroupElemJac(const GroupElem &in);
|
||||
|
||||
void SetJac(const GroupElemJac &jac);
|
||||
|
||||
void SetAffine(const GroupElem &aff);
|
||||
|
||||
/** Checks whether this is a non-infinite point on the curve */
|
||||
bool IsValid() const;
|
||||
|
||||
/** Returns the affine coordinates of this point */
|
||||
void GetAffine(GroupElem &aff);
|
||||
|
||||
void GetX(secp256k1_fe_t &xout);
|
||||
void GetY(secp256k1_fe_t &yout);
|
||||
|
||||
bool IsInfinity() const;
|
||||
|
||||
void SetNeg(const GroupElemJac &p);
|
||||
|
||||
/** Sets this point to have a given X coordinate & given Y oddness */
|
||||
void SetCompressed(const secp256k1_fe_t &xin, bool fOdd);
|
||||
|
||||
/** Sets this point to be the EC double of another */
|
||||
void SetDouble(const GroupElemJac &p);
|
||||
|
||||
/** Sets this point to be the EC addition of two others */
|
||||
void SetAdd(const GroupElemJac &p, const GroupElemJac &q);
|
||||
|
||||
/** Sets this point to be the EC addition of two others (one of which is in affine coordinates) */
|
||||
void SetAdd(const GroupElemJac &p, const GroupElem &q);
|
||||
|
||||
std::string ToString() const;
|
||||
|
||||
void SetMulLambda(const GroupElemJac &p);
|
||||
};
|
||||
|
||||
class GroupConstants {
|
||||
private:
|
||||
secp256k1_fe_t g_x;
|
||||
secp256k1_fe_t g_y;
|
||||
|
||||
public:
|
||||
secp256k1_num_t order;
|
||||
GroupElem g;
|
||||
secp256k1_fe_t beta;
|
||||
secp256k1_num_t lambda, a1b2, b1, a2;
|
||||
|
||||
GroupConstants();
|
||||
~GroupConstants();
|
||||
};
|
||||
|
||||
const GroupConstants &GetGroupConst();
|
||||
|
||||
void SplitExp(const secp256k1_num_t &exp, secp256k1_num_t &exp1, secp256k1_num_t &exp2);
|
||||
|
||||
}
|
||||
|
||||
#endif
|
||||
|
|
|
|||
|
|
@ -10,11 +10,12 @@ namespace secp256k1 {
|
|||
extern "C" void secp256k1_start(void) {
|
||||
secp256k1_num_start();
|
||||
secp256k1_fe_start();
|
||||
GetGroupConst();
|
||||
secp256k1_ge_start();
|
||||
GetECMultConsts();
|
||||
}
|
||||
|
||||
extern "C" void secp256k1_stop(void) {
|
||||
secp256k1_ge_stop();
|
||||
secp256k1_fe_stop();
|
||||
secp256k1_num_stop();
|
||||
}
|
||||
|
|
@ -24,7 +25,7 @@ extern "C" int secp256k1_ecdsa_verify(const unsigned char *msg, int msglen, cons
|
|||
secp256k1_num_t m;
|
||||
secp256k1_num_init(&m);
|
||||
Signature s;
|
||||
GroupElemJac q;
|
||||
secp256k1_gej_t q;
|
||||
secp256k1_num_set_bin(&m, msg, msglen);
|
||||
if (!ParsePubKey(q, pubkey, pubkeylen)) {
|
||||
ret = -1;
|
||||
|
|
|
|||
|
|
@ -15,7 +15,7 @@ void test_run_ecmult_chain() {
|
|||
// random starting point A (on the curve)
|
||||
secp256k1_fe_t ax; secp256k1_fe_set_hex(&ax, "8b30bbe9ae2a990696b22f670709dff3727fd8bc04d3362c6c7bf458e2846004", 64);
|
||||
secp256k1_fe_t ay; secp256k1_fe_set_hex(&ay, "a357ae915c4a65281309edf20504740f0eb3343990216b4f81063cb65f2f7e0f", 64);
|
||||
GroupElemJac a(ax,ay);
|
||||
secp256k1_gej_t a; secp256k1_gej_set_xy(&a, &ax, &ay);
|
||||
// two random initial factors xn and gn
|
||||
secp256k1_num_t xn;
|
||||
secp256k1_num_init(&xn);
|
||||
|
|
@ -38,29 +38,32 @@ void test_run_ecmult_chain() {
|
|||
secp256k1_num_init(&ge);
|
||||
secp256k1_num_set_int(&ge, 0);
|
||||
// the point being computed
|
||||
GroupElemJac x = a;
|
||||
const secp256k1_num_t &order = GetGroupConst().order;
|
||||
secp256k1_gej_t x = a;
|
||||
const secp256k1_num_t *order = &secp256k1_ge_consts->order;
|
||||
for (int i=0; i<200*COUNT; i++) {
|
||||
// in each iteration, compute X = xn*X + gn*G;
|
||||
ECMult(x, x, xn, gn);
|
||||
// also compute ae and ge: the actual accumulated factors for A and G
|
||||
// if X was (ae*A+ge*G), xn*X + gn*G results in (xn*ae*A + (xn*ge+gn)*G)
|
||||
secp256k1_num_mod_mul(&ae, &ae, &xn, &order);
|
||||
secp256k1_num_mod_mul(&ge, &ge, &xn, &order);
|
||||
secp256k1_num_mod_mul(&ae, &ae, &xn, order);
|
||||
secp256k1_num_mod_mul(&ge, &ge, &xn, order);
|
||||
secp256k1_num_add(&ge, &ge, &gn);
|
||||
secp256k1_num_mod(&ge, &ge, &order);
|
||||
secp256k1_num_mod(&ge, &ge, order);
|
||||
// modify xn and gn
|
||||
secp256k1_num_mod_mul(&xn, &xn, &xf, &order);
|
||||
secp256k1_num_mod_mul(&gn, &gn, &gf, &order);
|
||||
secp256k1_num_mod_mul(&xn, &xn, &xf, order);
|
||||
secp256k1_num_mod_mul(&gn, &gn, &gf, order);
|
||||
}
|
||||
std::string res = x.ToString();
|
||||
char res[132]; int resl = 132;
|
||||
secp256k1_gej_get_hex(res, &resl, &x);
|
||||
if (COUNT == 100) {
|
||||
assert(res == "(D6E96687F9B10D092A6F35439D86CEBEA4535D0D409F53586440BD74B933E830,B95CBCA2C77DA786539BE8FD53354D2D3B4F566AE658045407ED6015EE1B2A88)");
|
||||
assert(strcmp(res, "(D6E96687F9B10D092A6F35439D86CEBEA4535D0D409F53586440BD74B933E830,B95CBCA2C77DA786539BE8FD53354D2D3B4F566AE658045407ED6015EE1B2A88)") == 0);
|
||||
}
|
||||
// redo the computation, but directly with the resulting ae and ge coefficients:
|
||||
GroupElemJac x2; ECMult(x2, a, ae, ge);
|
||||
std::string res2 = x2.ToString();
|
||||
assert(res == res2);
|
||||
secp256k1_gej_t x2; ECMult(x2, a, ae, ge);
|
||||
char res2[132]; int resl2 = 132;
|
||||
secp256k1_gej_get_hex(res2, &resl2, &x2);
|
||||
assert(strcmp(res, res2) == 0);
|
||||
assert(strlen(res) == 131);
|
||||
secp256k1_num_free(&xn);
|
||||
secp256k1_num_free(&gn);
|
||||
secp256k1_num_free(&xf);
|
||||
|
|
@ -69,25 +72,25 @@ void test_run_ecmult_chain() {
|
|||
secp256k1_num_free(&ge);
|
||||
}
|
||||
|
||||
void test_point_times_order(const GroupElemJac &point) {
|
||||
void test_point_times_order(const secp256k1_gej_t &point) {
|
||||
// either the point is not on the curve, or multiplying it by the order results in O
|
||||
if (!point.IsValid())
|
||||
if (!secp256k1_gej_is_valid(&point))
|
||||
return;
|
||||
|
||||
const GroupConstants &c = GetGroupConst();
|
||||
const secp256k1_num_t *order = &secp256k1_ge_consts->order;
|
||||
secp256k1_num_t zero;
|
||||
secp256k1_num_init(&zero);
|
||||
secp256k1_num_set_int(&zero, 0);
|
||||
GroupElemJac res;
|
||||
ECMult(res, point, c.order, zero); // calc res = order * point + 0 * G;
|
||||
assert(res.IsInfinity());
|
||||
secp256k1_gej_t res;
|
||||
ECMult(res, point, *order, zero); // calc res = order * point + 0 * G;
|
||||
assert(secp256k1_gej_is_infinity(&res));
|
||||
secp256k1_num_free(&zero);
|
||||
}
|
||||
|
||||
void test_run_point_times_order() {
|
||||
secp256k1_fe_t x; secp256k1_fe_set_hex(&x, "02", 2);
|
||||
for (int i=0; i<500; i++) {
|
||||
GroupElemJac j; j.SetCompressed(x, true);
|
||||
secp256k1_gej_t j; secp256k1_gej_set_xo(&j, &x, true);
|
||||
test_point_times_order(j);
|
||||
secp256k1_fe_sqr(&x, &x);
|
||||
}
|
||||
|
|
@ -147,14 +150,14 @@ void test_run_wnaf() {
|
|||
}
|
||||
|
||||
void test_ecdsa_sign_verify() {
|
||||
const GroupConstants &c = GetGroupConst();
|
||||
const secp256k1_ge_consts_t &c = *secp256k1_ge_consts;
|
||||
secp256k1_num_t msg, key, nonce;
|
||||
secp256k1_num_init(&msg);
|
||||
secp256k1_num_set_rand(&msg, &c.order);
|
||||
secp256k1_num_init(&key);
|
||||
secp256k1_num_set_rand(&key, &c.order);
|
||||
secp256k1_num_init(&nonce);
|
||||
GroupElemJac pub; ECMultBase(pub, key);
|
||||
secp256k1_gej_t pub; ECMultBase(pub, key);
|
||||
Signature sig;
|
||||
do {
|
||||
secp256k1_num_set_rand(&nonce, &c.order);
|
||||
|
|
@ -176,12 +179,15 @@ void test_run_ecdsa_sign_verify() {
|
|||
int main(void) {
|
||||
secp256k1_num_start();
|
||||
secp256k1_fe_start();
|
||||
secp256k1_ge_start();
|
||||
|
||||
test_run_wnaf();
|
||||
test_run_point_times_order();
|
||||
test_run_ecmult_chain();
|
||||
test_run_ecdsa_sign_verify();
|
||||
|
||||
secp256k1_ge_stop();
|
||||
secp256k1_fe_stop();
|
||||
secp256k1_num_stop();
|
||||
return 0;
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in New Issue