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secp256k1
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Third step in converting to C: group

This commit is contained in:
Pieter Wuille 2013-03-31 17:02:52 +02:00
parent d73bad33e8
commit f11ff5be70
9 changed files with 395 additions and 454 deletions
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15
src/bench.cpp
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@ -11,9 +11,10 @@ using namespace secp256k1;
int main() { int main() {
secp256k1_num_start(); secp256k1_num_start();
secp256k1_fe_start(); secp256k1_fe_start();
secp256k1_ge_start();
secp256k1_fe_t x; secp256k1_fe_t x;
const secp256k1_num_t &order = GetGroupConst().order; const secp256k1_num_t *order = &secp256k1_ge_consts->order;
secp256k1_num_t r, s, m; secp256k1_num_t r, s, m;
secp256k1_num_init(&r); secp256k1_num_init(&r);
secp256k1_num_init(&s); secp256k1_num_init(&s);
@ -23,12 +24,12 @@ int main() {
int cnt = 0; int cnt = 0;
int good = 0; int good = 0;
for (int i=0; i<1000000; i++) { for (int i=0; i<1000000; i++) {
secp256k1_num_set_rand(&r, &order); secp256k1_num_set_rand(&r, order);
secp256k1_num_set_rand(&s, &order); secp256k1_num_set_rand(&s, order);
secp256k1_num_set_rand(&m, &order); secp256k1_num_set_rand(&m, order);
sig.SetRS(r,s); sig.SetRS(r,s);
GroupElemJac pubkey; pubkey.SetCompressed(x, true); secp256k1_gej_t pubkey; secp256k1_gej_set_xo(&pubkey, &x, 1);
if (pubkey.IsValid()) { if (secp256k1_gej_is_valid(&pubkey)) {
cnt++; cnt++;
good += sig.Verify(pubkey, m); good += sig.Verify(pubkey, m);
} }
@ -38,6 +39,8 @@ int main() {
secp256k1_num_free(&s); secp256k1_num_free(&s);
secp256k1_num_free(&m); secp256k1_num_free(&m);
secp256k1_ge_stop();
secp256k1_fe_stop(); secp256k1_fe_stop();
secp256k1_num_stop();
return 0; return 0;
} }

26
src/ecdsa.cpp
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@ -6,22 +6,22 @@
namespace secp256k1 { namespace secp256k1 {
bool ParsePubKey(GroupElemJac &elem, const unsigned char *pub, int size) { bool ParsePubKey(secp256k1_gej_t &elem, const unsigned char *pub, int size) {
if (size == 33 && (pub[0] == 0x02 || pub[0] == 0x03)) { if (size == 33 && (pub[0] == 0x02 || pub[0] == 0x03)) {
secp256k1_fe_t x; secp256k1_fe_t x;
secp256k1_fe_set_b32(&x, pub+1); secp256k1_fe_set_b32(&x, pub+1);
elem.SetCompressed(x, pub[0] == 0x03); secp256k1_gej_set_xo(&elem, &x, pub[0] == 0x03);
} else if (size == 65 && (pub[0] == 0x04 || pub[0] == 0x06 || pub[0] == 0x07)) { } else if (size == 65 && (pub[0] == 0x04 || pub[0] == 0x06 || pub[0] == 0x07)) {
secp256k1_fe_t x,y; secp256k1_fe_t x,y;
secp256k1_fe_set_b32(&x, pub+1); secp256k1_fe_set_b32(&x, pub+1);
secp256k1_fe_set_b32(&y, pub+33); secp256k1_fe_set_b32(&y, pub+33);
elem = GroupElem(x,y); secp256k1_gej_set_xy(&elem, &x, &y);
if ((pub[0] == 0x06 || pub[0] == 0x07) && secp256k1_fe_is_odd(&y) != (pub[0] == 0x07)) if ((pub[0] == 0x06 || pub[0] == 0x07) && secp256k1_fe_is_odd(&y) != (pub[0] == 0x07))
return false; return false;
} else { } else {
return false; return false;
} }
return elem.IsValid(); return secp256k1_gej_is_valid(&elem);
} }
bool Signature::Parse(const unsigned char *sig, int size) { bool Signature::Parse(const unsigned char *sig, int size) {
@ -61,8 +61,8 @@ bool Signature::Serialize(unsigned char *sig, int *size) {
return true; return true;
} }
bool Signature::RecomputeR(secp256k1_num_t &r2, const GroupElemJac &pubkey, const secp256k1_num_t &message) const { bool Signature::RecomputeR(secp256k1_num_t &r2, const secp256k1_gej_t &pubkey, const secp256k1_num_t &message) const {
const GroupConstants &c = GetGroupConst(); const secp256k1_ge_consts_t &c = *secp256k1_ge_consts;
if (secp256k1_num_is_neg(&r) || secp256k1_num_is_neg(&s)) if (secp256k1_num_is_neg(&r) || secp256k1_num_is_neg(&s))
return false; return false;
@ -79,9 +79,9 @@ bool Signature::RecomputeR(secp256k1_num_t &r2, const GroupElemJac &pubkey, cons
secp256k1_num_mod_inverse(&sn, &s, &c.order); secp256k1_num_mod_inverse(&sn, &s, &c.order);
secp256k1_num_mod_mul(&u1, &sn, &message, &c.order); secp256k1_num_mod_mul(&u1, &sn, &message, &c.order);
secp256k1_num_mod_mul(&u2, &sn, &r, &c.order); secp256k1_num_mod_mul(&u2, &sn, &r, &c.order);
GroupElemJac pr; ECMult(pr, pubkey, u2, u1); secp256k1_gej_t pr; ECMult(pr, pubkey, u2, u1);
if (!pr.IsInfinity()) { if (!secp256k1_gej_is_infinity(&pr)) {
secp256k1_fe_t xr; pr.GetX(xr); secp256k1_fe_t xr; secp256k1_gej_get_x(&xr, &pr);
secp256k1_fe_normalize(&xr); secp256k1_fe_normalize(&xr);
unsigned char xrb[32]; secp256k1_fe_get_b32(xrb, &xr); unsigned char xrb[32]; secp256k1_fe_get_b32(xrb, &xr);
secp256k1_num_set_bin(&r2, xrb, 32); secp256k1_num_set_bin(&r2, xrb, 32);
@ -94,7 +94,7 @@ bool Signature::RecomputeR(secp256k1_num_t &r2, const GroupElemJac &pubkey, cons
return ret; return ret;
} }
bool Signature::Verify(const GroupElemJac &pubkey, const secp256k1_num_t &message) const { bool Signature::Verify(const secp256k1_gej_t &pubkey, const secp256k1_num_t &message) const {
secp256k1_num_t r2; secp256k1_num_t r2;
secp256k1_num_init(&r2); secp256k1_num_init(&r2);
bool ret = false; bool ret = false;
@ -104,12 +104,12 @@ bool Signature::Verify(const GroupElemJac &pubkey, const secp256k1_num_t &messag
} }
bool Signature::Sign(const secp256k1_num_t &seckey, const secp256k1_num_t &message, const secp256k1_num_t &nonce) { bool Signature::Sign(const secp256k1_num_t &seckey, const secp256k1_num_t &message, const secp256k1_num_t &nonce) {
const GroupConstants &c = GetGroupConst(); const secp256k1_ge_consts_t &c = *secp256k1_ge_consts;
GroupElemJac rp; secp256k1_gej_t rp;
ECMultBase(rp, nonce); ECMultBase(rp, nonce);
secp256k1_fe_t rx; secp256k1_fe_t rx;
rp.GetX(rx); secp256k1_gej_get_x(&rx, &rp);
unsigned char b[32]; unsigned char b[32];
secp256k1_fe_normalize(&rx); secp256k1_fe_normalize(&rx);
secp256k1_fe_get_b32(b, &rx); secp256k1_fe_get_b32(b, &rx);

4
src/ecdsa.h
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@ -19,8 +19,8 @@ public:
bool Parse(const unsigned char *sig, int size); bool Parse(const unsigned char *sig, int size);
bool Serialize(unsigned char *sig, int *size); bool Serialize(unsigned char *sig, int *size);
bool RecomputeR(secp256k1_num_t &r2, const GroupElemJac &pubkey, const secp256k1_num_t &message) const; bool RecomputeR(secp256k1_num_t &r2, const secp256k1_gej_t &pubkey, const secp256k1_num_t &message) const;
bool Verify(const GroupElemJac &pubkey, const secp256k1_num_t &message) const; bool Verify(const secp256k1_gej_t &pubkey, const secp256k1_num_t &message) const;
bool Sign(const secp256k1_num_t &seckey, const secp256k1_num_t &message, const secp256k1_num_t &nonce); bool Sign(const secp256k1_num_t &seckey, const secp256k1_num_t &message, const secp256k1_num_t &nonce);
void SetRS(const secp256k1_num_t &rin, const secp256k1_num_t &sin); void SetRS(const secp256k1_num_t &rin, const secp256k1_num_t &sin);
std::string ToString() const; std::string ToString() const;

124
src/ecmult.cpp
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@ -14,35 +14,65 @@
namespace secp256k1 { namespace secp256k1 {
template<typename G, int W> class WNAFPrecomp { template<int W> class WNAFPrecompJac {
private: private:
G pre[1 << (W-2)]; secp256k1_gej_t pre[1 << (W-2)];
public: public:
WNAFPrecomp() {} WNAFPrecompJac() {}
void Build(const G &base) { void Build(const secp256k1_gej_t &base) {
pre[0] = base; pre[0] = base;
GroupElemJac x(base); secp256k1_gej_t d; secp256k1_gej_double(&d, &pre[0]);
GroupElemJac d; d.SetDouble(x); for (int i=1; i<(1 << (W-2)); i++)
for (int i=1; i<(1 << (W-2)); i++) { secp256k1_gej_add(&pre[i], &d, &pre[i-1]);
x.SetAdd(d,pre[i-1]);
pre[i].SetJac(x);
}
} }
WNAFPrecomp(const G &base) { WNAFPrecompJac(const secp256k1_gej_t &base) {
Build(base); Build(base);
} }
void Get(G &out, int exp) const { void Get(secp256k1_gej_t &out, int exp) const {
assert((exp & 1) == 1); assert((exp & 1) == 1);
assert(exp >= -((1 << (W-1)) - 1)); assert(exp >= -((1 << (W-1)) - 1));
assert(exp <= ((1 << (W-1)) - 1)); assert(exp <= ((1 << (W-1)) - 1));
if (exp > 0) { if (exp > 0) {
out = pre[(exp-1)/2]; out = pre[(exp-1)/2];
} else { } else {
out.SetNeg(pre[(-exp-1)/2]); secp256k1_gej_neg(&out, &pre[(-exp-1)/2]);
}
}
};
template<int W> class WNAFPrecompAff {
private:
secp256k1_ge_t pre[1 << (W-2)];
public:
WNAFPrecompAff() {}
void Build(const secp256k1_ge_t &base) {
pre[0] = base;
secp256k1_gej_t x; secp256k1_gej_set_ge(&x, &base);
secp256k1_gej_t d; secp256k1_gej_double(&d, &x);
for (int i=1; i<(1 << (W-2)); i++) {
secp256k1_gej_add_ge(&x, &d, &pre[i-1]);
secp256k1_ge_set_gej(&pre[i], &x);
}
}
WNAFPrecompAff(const secp256k1_ge_t &base) {
Build(base);
}
void Get(secp256k1_ge_t &out, int exp) const {
assert((exp & 1) == 1);
assert(exp >= -((1 << (W-1)) - 1));
assert(exp <= ((1 << (W-1)) - 1));
if (exp > 0) {
out = pre[(exp-1)/2];
} else {
secp256k1_ge_neg(&out, &pre[(-exp-1)/2]);
} }
} }
}; };
@ -112,33 +142,33 @@ public:
class ECMultConsts { class ECMultConsts {
public: public:
WNAFPrecomp<GroupElem,WINDOW_G> wpg; WNAFPrecompAff<WINDOW_G> wpg;
WNAFPrecomp<GroupElem,WINDOW_G> wpg128; WNAFPrecompAff<WINDOW_G> wpg128;
GroupElem prec[64][16]; // prec[j][i] = 16^j * (i+1) * G secp256k1_ge_t prec[64][16]; // prec[j][i] = 16^j * (i+1) * G
GroupElem fin; // -(sum(prec[j][0], j=0..63)) secp256k1_ge_t fin; // -(sum(prec[j][0], j=0..63))
ECMultConsts() { ECMultConsts() {
const GroupElem &g = GetGroupConst().g; const secp256k1_ge_t &g = secp256k1_ge_consts->g;
GroupElemJac g128j(g); secp256k1_gej_t g128j; secp256k1_gej_set_ge(&g128j, &g);
for (int i=0; i<128; i++) for (int i=0; i<128; i++)
g128j.SetDouble(g128j); secp256k1_gej_double(&g128j, &g128j);
GroupElem g128; g128.SetJac(g128j); secp256k1_ge_t g128; secp256k1_ge_set_gej(&g128, &g128j);
wpg.Build(g); wpg.Build(g);
wpg128.Build(g128); wpg128.Build(g128);
GroupElemJac gg(g); secp256k1_gej_t gg; secp256k1_gej_set_ge(&gg, &g);
GroupElem ad(g); secp256k1_ge_t ad = g;
GroupElemJac fn; secp256k1_gej_t fn; secp256k1_gej_set_infinity(&fn);
for (int j=0; j<64; j++) { for (int j=0; j<64; j++) {
prec[j][0].SetJac(gg); secp256k1_ge_set_gej(&prec[j][0], &gg);
fn.SetAdd(fn, gg); secp256k1_gej_add(&fn, &fn, &gg);
for (int i=1; i<16; i++) { for (int i=1; i<16; i++) {
gg.SetAdd(gg, ad); secp256k1_gej_add_ge(&gg, &gg, &ad);
prec[j][i].SetJac(gg); secp256k1_ge_set_gej(&prec[j][i], &gg);
} }
ad = prec[j][15]; ad = prec[j][15];
} }
fn.SetNeg(fn); secp256k1_ge_set_gej(&fin, &fn);
fin.SetJac(fn); secp256k1_ge_neg(&fin, &fin);
} }
}; };
@ -147,20 +177,20 @@ const ECMultConsts &GetECMultConsts() {
return ecmult_consts; return ecmult_consts;
} }
void ECMultBase(GroupElemJac &out, const secp256k1_num_t &gn) { void ECMultBase(secp256k1_gej_t &out, const secp256k1_num_t &gn) {
secp256k1_num_t n; secp256k1_num_t n;
secp256k1_num_init(&n); secp256k1_num_init(&n);
secp256k1_num_copy(&n, &gn); secp256k1_num_copy(&n, &gn);
const ECMultConsts &c = GetECMultConsts(); const ECMultConsts &c = GetECMultConsts();
out.SetAffine(c.prec[0][secp256k1_num_shift(&n, 4)]); secp256k1_gej_set_ge(&out, &c.prec[0][secp256k1_num_shift(&n, 4)]);
for (int j=1; j<64; j++) { for (int j=1; j<64; j++) {
out.SetAdd(out, c.prec[j][secp256k1_num_shift(&n, 4)]); secp256k1_gej_add_ge(&out, &out, &c.prec[j][secp256k1_num_shift(&n, 4)]);
} }
secp256k1_num_free(&n); secp256k1_num_free(&n);
out.SetAdd(out, c.fin); secp256k1_gej_add_ge(&out, &out, &c.fin);
} }
void ECMult(GroupElemJac &out, const GroupElemJac &a, const secp256k1_num_t &an, 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) {
secp256k1_num_t an1, an2; secp256k1_num_t an1, an2;
secp256k1_num_t gn1, gn2; secp256k1_num_t gn1, gn2;
@ -169,7 +199,7 @@ void ECMult(GroupElemJac &out, const GroupElemJac &a, const secp256k1_num_t &an,
secp256k1_num_init(&gn1); secp256k1_num_init(&gn1);
secp256k1_num_init(&gn2); secp256k1_num_init(&gn2);
SplitExp(an, an1, an2); secp256k1_gej_split_exp(&an1, &an2, &an);
// printf("an=%s\n", an.ToString().c_str()); // printf("an=%s\n", an.ToString().c_str());
// printf("an1=%s\n", an1.ToString().c_str()); // printf("an1=%s\n", an1.ToString().c_str());
// printf("an2=%s\n", an2.ToString().c_str()); // printf("an2=%s\n", an2.ToString().c_str());
@ -181,9 +211,9 @@ void ECMult(GroupElemJac &out, const GroupElemJac &a, const secp256k1_num_t &an,
WNAF<128> wa2(an2, WINDOW_A); WNAF<128> wa2(an2, WINDOW_A);
WNAF<128> wg1(gn1, WINDOW_G); WNAF<128> wg1(gn1, WINDOW_G);
WNAF<128> wg2(gn2, WINDOW_G); WNAF<128> wg2(gn2, WINDOW_G);
GroupElemJac a2; a2.SetMulLambda(a); secp256k1_gej_t a2; secp256k1_gej_mul_lambda(&a2, &a);
WNAFPrecomp<GroupElemJac,WINDOW_A> wpa1(a); WNAFPrecompJac<WINDOW_A> wpa1(a);
WNAFPrecomp<GroupElemJac,WINDOW_A> wpa2(a2); WNAFPrecompJac<WINDOW_A> wpa2(a2);
const ECMultConsts &c = GetECMultConsts(); const ECMultConsts &c = GetECMultConsts();
int size_a1 = wa1.GetSize(); int size_a1 = wa1.GetSize();
@ -192,28 +222,28 @@ void ECMult(GroupElemJac &out, const GroupElemJac &a, const secp256k1_num_t &an,
int size_g2 = wg2.GetSize(); int size_g2 = wg2.GetSize();
int size = std::max(std::max(size_a1, size_a2), std::max(size_g1, size_g2)); int size = std::max(std::max(size_a1, size_a2), std::max(size_g1, size_g2));
out = GroupElemJac(); out; secp256k1_gej_set_infinity(&out);
GroupElemJac tmpj; secp256k1_gej_t tmpj;
GroupElem tmpa; secp256k1_ge_t tmpa;
for (int i=size-1; i>=0; i--) { for (int i=size-1; i>=0; i--) {
out.SetDouble(out); secp256k1_gej_double(&out, &out);
int nw; int nw;
if (i < size_a1 && (nw = wa1.Get(i))) { if (i < size_a1 && (nw = wa1.Get(i))) {
wpa1.Get(tmpj, nw); wpa1.Get(tmpj, nw);
out.SetAdd(out, tmpj); secp256k1_gej_add(&out, &out, &tmpj);
} }
if (i < size_a2 && (nw = wa2.Get(i))) { if (i < size_a2 && (nw = wa2.Get(i))) {
wpa2.Get(tmpj, nw); wpa2.Get(tmpj, nw);
out.SetAdd(out, tmpj); secp256k1_gej_add(&out, &out, &tmpj);
} }
if (i < size_g1 && (nw = wg1.Get(i))) { if (i < size_g1 && (nw = wg1.Get(i))) {
c.wpg.Get(tmpa, nw); c.wpg.Get(tmpa, nw);
out.SetAdd(out, tmpa); secp256k1_gej_add_ge(&out, &out, &tmpa);
} }
if (i < size_g2 && (nw = wg2.Get(i))) { if (i < size_g2 && (nw = wg2.Get(i))) {
c.wpg128.Get(tmpa, nw); c.wpg128.Get(tmpa, nw);
out.SetAdd(out, tmpa); secp256k1_gej_add_ge(&out, &out, &tmpa);
} }
} }

6
src/ecmult.h
View File

@ -1,13 +1,13 @@
#ifndef _SECP256K1_ECMULT_ #ifndef _SECP256K1_ECMULT_
#define _SECP256K1_ECMULT_ #define _SECP256K1_ECMULT_
#include "group.h"
#include "num.h" #include "num.h"
#include "group.h"
namespace secp256k1 { namespace secp256k1 {
void ECMultBase(GroupElemJac &out, const secp256k1_num_t &gn); void ECMultBase(secp256k1_gej_t &out, const secp256k1_num_t &gn);
void ECMult(GroupElemJac &out, const GroupElemJac &a, const secp256k1_num_t &an, 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);
} }

508
src/group.cpp
View File

@ -1,83 +1,126 @@
#include <string> #include <string.h>
#include "num.h" #include "num.h"
#include "field.h" #include "field.h"
#include "group.h" #include "group.h"
namespace secp256k1 { extern "C" {
GroupElem::GroupElem() { void static secp256k1_ge_set_infinity(secp256k1_ge_t *r) {
fInfinity = true; r->infinity = 1;
} }
GroupElem::GroupElem(const secp256k1_fe_t &xin, const secp256k1_fe_t &yin) { void static secp256k1_ge_set_xy(secp256k1_ge_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y) {
fInfinity = false; r->infinity = 0;
x = xin; r->x = *x;
y = yin; r->y = *y;
} }
bool GroupElem::IsInfinity() const { int static secp256k1_ge_is_infinity(const secp256k1_ge_t *a) {
return fInfinity; return a->infinity;
} }
void GroupElem::SetNeg(const GroupElem &p) { void static secp256k1_ge_neg(secp256k1_ge_t *r, const secp256k1_ge_t *a) {
*this = p; r->infinity = a->infinity;
secp256k1_fe_normalize(&y); r->x = a->x;
secp256k1_fe_negate(&y, &y, 1); r->y = a->y;
secp256k1_fe_normalize(&r->y);
secp256k1_fe_negate(&r->y, &r->y, 1);
} }
void GroupElem::GetX(secp256k1_fe_t &xout) { void static secp256k1_ge_get_hex(char *r, int *rlen, const secp256k1_ge_t *a) {
xout = x; 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) { void static secp256k1_ge_set_gej(secp256k1_ge_t *r, secp256k1_gej_t *a) {
yout = y; 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 { void static secp256k1_gej_set_infinity(secp256k1_gej_t *r) {
if (fInfinity) r->infinity = 1;
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) + ")";
} }
GroupElemJac::GroupElemJac() : GroupElem() { void static secp256k1_gej_set_xy(secp256k1_gej_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y) {
secp256k1_fe_set_int(&z, 1); 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) { void static secp256k1_gej_set_xo(secp256k1_gej_t *r, const secp256k1_fe_t *x, int odd) {
secp256k1_fe_set_int(&z, 1); 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) { void static secp256k1_gej_set_ge(secp256k1_gej_t *r, const secp256k1_ge_t *a) {
secp256k1_fe_set_int(&z, 1); 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) { void static secp256k1_gej_get_x(secp256k1_fe_t *r, const secp256k1_gej_t *a) {
*this = jac; 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) { void static secp256k1_gej_neg(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
fInfinity = aff.fInfinity; r->infinity = a->infinity;
x = aff.x; r->x = a->x;
y = aff.y; r->y = a->y;
secp256k1_fe_set_int(&z, 1); r->z = a->z;
secp256k1_fe_normalize(&r->y);
secp256k1_fe_negate(&r->y, &r->y, 1);
} }
bool GroupElemJac::IsValid() const { int static secp256k1_gej_is_infinity(const secp256k1_gej_t *a) {
if (IsInfinity()) return a->infinity;
}
int static secp256k1_gej_is_valid(const secp256k1_gej_t *a) {
if (a->infinity)
return false; return false;
// y^2 = x^3 + 7 // y^2 = x^3 + 7
// (Y/Z^3)^2 = (X/Z^2)^3 + 7 // (Y/Z^3)^2 = (X/Z^2)^3 + 7
// Y^2 / Z^6 = X^3 / Z^6 + 7 // Y^2 / Z^6 = X^3 / Z^6 + 7
// Y^2 = X^3 + 7*Z^6 // Y^2 = X^3 + 7*Z^6
secp256k1_fe_t y2; secp256k1_fe_sqr(&y2, &y); secp256k1_fe_t y2; secp256k1_fe_sqr(&y2, &a->y);
secp256k1_fe_t x3; secp256k1_fe_sqr(&x3, &x); secp256k1_fe_mul(&x3, &x3, &x); 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, &z); 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_t z6; secp256k1_fe_sqr(&z6, &z2); secp256k1_fe_mul(&z6, &z6, &z2);
secp256k1_fe_mul_int(&z6, 7); secp256k1_fe_mul_int(&z6, 7);
secp256k1_fe_add(&x3, &z6); secp256k1_fe_add(&x3, &z6);
@ -86,256 +129,136 @@ bool GroupElemJac::IsValid() const {
return secp256k1_fe_equal(&y2, &x3); return secp256k1_fe_equal(&y2, &x3);
} }
void GroupElemJac::GetAffine(GroupElem &aff) { void static secp256k1_gej_double(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
secp256k1_fe_inv_var(&z, &z); secp256k1_fe_t t5 = a->y;
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;
secp256k1_fe_normalize(&t5); secp256k1_fe_normalize(&t5);
if (p.fInfinity || secp256k1_fe_is_zero(&t5)) { if (a->infinity || secp256k1_fe_is_zero(&t5)) {
fInfinity = true; r->infinity = true;
return; return;
} }
secp256k1_fe_t t1,t2,t3,t4; secp256k1_fe_t t1,t2,t3,t4;
secp256k1_fe_mul(&z, &t5, &p.z); secp256k1_fe_mul(&r->z, &t5, &a->z);
secp256k1_fe_mul_int(&z, 2); // Z' = 2*Y*Z (2) secp256k1_fe_mul_int(&r->z, 2); // Z' = 2*Y*Z (2)
secp256k1_fe_sqr(&t1, &p.x); secp256k1_fe_sqr(&t1, &a->x);
secp256k1_fe_mul_int(&t1, 3); // T1 = 3*X^2 (3) secp256k1_fe_mul_int(&t1, 3); // T1 = 3*X^2 (3)
secp256k1_fe_sqr(&t2, &t1); // T2 = 9*X^4 (1) secp256k1_fe_sqr(&t2, &t1); // T2 = 9*X^4 (1)
secp256k1_fe_sqr(&t3, &t5); secp256k1_fe_sqr(&t3, &t5);
secp256k1_fe_mul_int(&t3, 2); // T3 = 2*Y^2 (2) secp256k1_fe_mul_int(&t3, 2); // T3 = 2*Y^2 (2)
secp256k1_fe_sqr(&t4, &t3); secp256k1_fe_sqr(&t4, &t3);
secp256k1_fe_mul_int(&t4, 2); // T4 = 8*Y^4 (2) secp256k1_fe_mul_int(&t4, 2); // T4 = 8*Y^4 (2)
secp256k1_fe_mul(&t3, &p.x, &t3); // T3 = 2*X*Y^2 (1) secp256k1_fe_mul(&t3, &a->x, &t3); // T3 = 2*X*Y^2 (1)
x = t3; r->x = t3;
secp256k1_fe_mul_int(&x, 4); // X' = 8*X*Y^2 (4) secp256k1_fe_mul_int(&r->x, 4); // X' = 8*X*Y^2 (4)
secp256k1_fe_negate(&x, &x, 4); // X' = -8*X*Y^2 (5) secp256k1_fe_negate(&r->x, &r->x, 4); // X' = -8*X*Y^2 (5)
secp256k1_fe_add(&x, &t2); // X' = 9*X^4 - 8*X*Y^2 (6) 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_negate(&t2, &t2, 1); // T2 = -9*X^4 (2)
secp256k1_fe_mul_int(&t3, 6); // T3 = 12*X*Y^2 (6) 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_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_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) secp256k1_fe_add(&r->y, &t2); // Y' = 36*X^3*Y^2 - 27*X^6 - 8*Y^4 (4)
fInfinity = false; r->infinity = false;
} }
void GroupElemJac::SetAdd(const GroupElemJac &p, const GroupElemJac &q) { void static secp256k1_gej_add(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_gej_t *b) {
if (p.fInfinity) { if (a->infinity) {
*this = q; *r = *b;
return; return;
} }
if (q.fInfinity) { if (b->infinity) {
*this = p; *r = *a;
return; return;
} }
fInfinity = false; r->infinity = 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, &b->z);
secp256k1_fe_t z22; secp256k1_fe_sqr(&z22, &z2); secp256k1_fe_t z12; secp256k1_fe_sqr(&z12, &a->z);
secp256k1_fe_t z12; secp256k1_fe_sqr(&z12, &z1); secp256k1_fe_t u1; secp256k1_fe_mul(&u1, &a->x, &z22);
secp256k1_fe_t u1; secp256k1_fe_mul(&u1, &x1, &z22); secp256k1_fe_t u2; secp256k1_fe_mul(&u2, &b->x, &z12);
secp256k1_fe_t u2; secp256k1_fe_mul(&u2, &x2, &z12); secp256k1_fe_t s1; secp256k1_fe_mul(&s1, &a->y, &z22); secp256k1_fe_mul(&s1, &s1, &b->z);
secp256k1_fe_t s1; secp256k1_fe_mul(&s1, &y1, &z22); secp256k1_fe_mul(&s1, &s1, &z2); secp256k1_fe_t s2; secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
secp256k1_fe_t s2; secp256k1_fe_mul(&s2, &y2, &z12); secp256k1_fe_mul(&s2, &s2, &z1);
secp256k1_fe_normalize(&u1); secp256k1_fe_normalize(&u1);
secp256k1_fe_normalize(&u2); secp256k1_fe_normalize(&u2);
if (secp256k1_fe_equal(&u1, &u2)) { if (secp256k1_fe_equal(&u1, &u2)) {
secp256k1_fe_normalize(&s1); secp256k1_fe_normalize(&s1);
secp256k1_fe_normalize(&s2); secp256k1_fe_normalize(&s2);
if (secp256k1_fe_equal(&s1, &s2)) { if (secp256k1_fe_equal(&s1, &s2)) {
SetDouble(p); secp256k1_gej_double(r, a);
} else { } else {
fInfinity = true; r->infinity = true;
} }
return; return;
} }
secp256k1_fe_t h; secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2); 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 i; secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
secp256k1_fe_t r2; secp256k1_fe_sqr(&r2, &r); secp256k1_fe_t i2; secp256k1_fe_sqr(&i2, &i);
secp256k1_fe_t h2; secp256k1_fe_sqr(&h2, &h); secp256k1_fe_t h2; secp256k1_fe_sqr(&h2, &h);
secp256k1_fe_t h3; secp256k1_fe_mul(&h3, &h, &h2); 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); 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); 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(&y, &x, 5); secp256k1_fe_add(&y, &t); secp256k1_fe_mul(&y, &y, &r); 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_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) { void static secp256k1_gej_add_ge(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b) {
if (p.fInfinity) { if (a->infinity) {
x = q.x; r->infinity = b->infinity;
y = q.y; r->x = b->x;
fInfinity = q.fInfinity; r->y = b->y;
secp256k1_fe_set_int(&z, 1); secp256k1_fe_set_int(&r->z, 1);
return; return;
} }
if (q.fInfinity) { if (b->infinity) {
*this = p; *r = *a;
return; return;
} }
fInfinity = false; r->infinity = 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, &a->z);
secp256k1_fe_t z12; secp256k1_fe_sqr(&z12, &z1); secp256k1_fe_t u1 = a->x; secp256k1_fe_normalize(&u1);
secp256k1_fe_t u1 = x1; secp256k1_fe_normalize(&u1); secp256k1_fe_t u2; secp256k1_fe_mul(&u2, &b->x, &z12);
secp256k1_fe_t u2; secp256k1_fe_mul(&u2, &x2, &z12); secp256k1_fe_t s1 = a->y; secp256k1_fe_normalize(&s1);
secp256k1_fe_t s1 = y1; secp256k1_fe_normalize(&s1); secp256k1_fe_t s2; secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
secp256k1_fe_t s2; secp256k1_fe_mul(&s2, &y2, &z12); secp256k1_fe_mul(&s2, &s2, &z1);
secp256k1_fe_normalize(&u1); secp256k1_fe_normalize(&u1);
secp256k1_fe_normalize(&u2); secp256k1_fe_normalize(&u2);
if (secp256k1_fe_equal(&u1, &u2)) { if (secp256k1_fe_equal(&u1, &u2)) {
secp256k1_fe_normalize(&s1); secp256k1_fe_normalize(&s1);
secp256k1_fe_normalize(&s2); secp256k1_fe_normalize(&s2);
if (secp256k1_fe_equal(&s1, &s2)) { if (secp256k1_fe_equal(&s1, &s2)) {
SetDouble(p); secp256k1_gej_double(r, a);
} else { } else {
fInfinity = true; r->infinity = true;
} }
return; return;
} }
secp256k1_fe_t h; secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2); 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 i; secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
secp256k1_fe_t r2; secp256k1_fe_sqr(&r2, &r); secp256k1_fe_t i2; secp256k1_fe_sqr(&i2, &i);
secp256k1_fe_t h2; secp256k1_fe_sqr(&h2, &h); secp256k1_fe_t h2; secp256k1_fe_sqr(&h2, &h);
secp256k1_fe_t h3; secp256k1_fe_mul(&h3, &h, &h2); 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); 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); 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(&y, &x, 5); secp256k1_fe_add(&y, &t); secp256k1_fe_mul(&y, &y, &r); 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_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 { void static secp256k1_gej_get_hex(char *r, int *rlen, const secp256k1_gej_t *a) {
GroupElemJac cop = *this; secp256k1_gej_t c = *a;
GroupElem aff; secp256k1_ge_t t; secp256k1_ge_set_gej(&t, &c);
cop.GetAffine(aff); secp256k1_ge_get_hex(r, rlen, &t);
return aff.ToString();
} }
void GroupElem::SetJac(GroupElemJac &jac) { void static secp256k1_gej_mul_lambda(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
jac.GetAffine(*this); 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, void static secp256k1_gej_split_exp(secp256k1_num_t *r1, secp256k1_num_t *r2, const secp256k1_num_t *a) {
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE, const secp256k1_ge_consts_t *c = secp256k1_ge_consts;
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();
secp256k1_num_t bnc1, bnc2, bnt1, bnt2, bnn2; secp256k1_num_t bnc1, bnc2, bnt1, bnt2, bnn2;
secp256k1_num_init(&bnc1); 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(&bnt2);
secp256k1_num_init(&bnn2); secp256k1_num_init(&bnn2);
secp256k1_num_copy(&bnn2, &c.order); secp256k1_num_copy(&bnn2, &c->order);
secp256k1_num_shift(&bnn2, 1); 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_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_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(&bnt1, &bnc1, &c->a1b2);
secp256k1_num_mul(&bnt2, &bnc2, &c.a2); secp256k1_num_mul(&bnt2, &bnc2, &c->a2);
secp256k1_num_add(&bnt1, &bnt1, &bnt2); secp256k1_num_add(&bnt1, &bnt1, &bnt2);
secp256k1_num_sub(&exp1, &exp, &bnt1); secp256k1_num_sub(r1, a, &bnt1);
secp256k1_num_mul(&bnt1, &bnc1, &c.b1); secp256k1_num_mul(&bnt1, &bnc1, &c->b1);
secp256k1_num_mul(&bnt2, &bnc2, &c.a1b2); secp256k1_num_mul(&bnt2, &bnc2, &c->a1b2);
secp256k1_num_sub(&exp2, &bnt1, &bnt2); secp256k1_num_sub(r2, &bnt1, &bnt2);
secp256k1_num_free(&bnc1); secp256k1_num_free(&bnc1);
secp256k1_num_free(&bnc2); 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); 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
View File

@ -1,8 +1,6 @@
#ifndef _SECP256K1_GROUP_ #ifndef _SECP256K1_GROUP_
#define _SECP256K1_GROUP_ #define _SECP256K1_GROUP_
#include <string>
#include "num.h" #include "num.h"
#include "field.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); 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_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_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_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_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_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_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); 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_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_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(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); 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 #endif

5
src/secp256k1.cpp
View File

@ -10,11 +10,12 @@ namespace secp256k1 {
extern "C" void secp256k1_start(void) { extern "C" void secp256k1_start(void) {
secp256k1_num_start(); secp256k1_num_start();
secp256k1_fe_start(); secp256k1_fe_start();
GetGroupConst(); secp256k1_ge_start();
GetECMultConsts(); GetECMultConsts();
} }
extern "C" void secp256k1_stop(void) { extern "C" void secp256k1_stop(void) {
secp256k1_ge_stop();
secp256k1_fe_stop(); secp256k1_fe_stop();
secp256k1_num_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_t m;
secp256k1_num_init(&m); secp256k1_num_init(&m);
Signature s; Signature s;
GroupElemJac q; secp256k1_gej_t q;
secp256k1_num_set_bin(&m, msg, msglen); secp256k1_num_set_bin(&m, msg, msglen);
if (!ParsePubKey(q, pubkey, pubkeylen)) { if (!ParsePubKey(q, pubkey, pubkeylen)) {
ret = -1; ret = -1;

50
src/tests.cpp
View File

@ -15,7 +15,7 @@ void test_run_ecmult_chain() {
// random starting point A (on the curve) // random starting point A (on the curve)
secp256k1_fe_t ax; secp256k1_fe_set_hex(&ax, "8b30bbe9ae2a990696b22f670709dff3727fd8bc04d3362c6c7bf458e2846004", 64); secp256k1_fe_t ax; secp256k1_fe_set_hex(&ax, "8b30bbe9ae2a990696b22f670709dff3727fd8bc04d3362c6c7bf458e2846004", 64);
secp256k1_fe_t ay; secp256k1_fe_set_hex(&ay, "a357ae915c4a65281309edf20504740f0eb3343990216b4f81063cb65f2f7e0f", 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 // two random initial factors xn and gn
secp256k1_num_t xn; secp256k1_num_t xn;
secp256k1_num_init(&xn); secp256k1_num_init(&xn);
@ -38,29 +38,32 @@ void test_run_ecmult_chain() {
secp256k1_num_init(&ge); secp256k1_num_init(&ge);
secp256k1_num_set_int(&ge, 0); secp256k1_num_set_int(&ge, 0);
// the point being computed // the point being computed
GroupElemJac x = a; secp256k1_gej_t x = a;
const secp256k1_num_t &order = GetGroupConst().order; const secp256k1_num_t *order = &secp256k1_ge_consts->order;
for (int i=0; i<200*COUNT; i++) { for (int i=0; i<200*COUNT; i++) {
// in each iteration, compute X = xn*X + gn*G; // in each iteration, compute X = xn*X + gn*G;
ECMult(x, x, xn, gn); ECMult(x, x, xn, gn);
// also compute ae and ge: the actual accumulated factors for A and G // 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) // 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(&ae, &ae, &xn, order);
secp256k1_num_mod_mul(&ge, &ge, &xn, &order); secp256k1_num_mod_mul(&ge, &ge, &xn, order);
secp256k1_num_add(&ge, &ge, &gn); secp256k1_num_add(&ge, &ge, &gn);
secp256k1_num_mod(&ge, &ge, &order); secp256k1_num_mod(&ge, &ge, order);
// modify xn and gn // modify xn and gn
secp256k1_num_mod_mul(&xn, &xn, &xf, &order); secp256k1_num_mod_mul(&xn, &xn, &xf, order);
secp256k1_num_mod_mul(&gn, &gn, &gf, &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) { 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: // redo the computation, but directly with the resulting ae and ge coefficients:
GroupElemJac x2; ECMult(x2, a, ae, ge); secp256k1_gej_t x2; ECMult(x2, a, ae, ge);
std::string res2 = x2.ToString(); char res2[132]; int resl2 = 132;
assert(res == res2); secp256k1_gej_get_hex(res2, &resl2, &x2);
assert(strcmp(res, res2) == 0);
assert(strlen(res) == 131);
secp256k1_num_free(&xn); secp256k1_num_free(&xn);
secp256k1_num_free(&gn); secp256k1_num_free(&gn);
secp256k1_num_free(&xf); secp256k1_num_free(&xf);
@ -69,25 +72,25 @@ void test_run_ecmult_chain() {
secp256k1_num_free(&ge); 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 // 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; return;
const GroupConstants &c = GetGroupConst(); const secp256k1_num_t *order = &secp256k1_ge_consts->order;
secp256k1_num_t zero; secp256k1_num_t zero;
secp256k1_num_init(&zero); secp256k1_num_init(&zero);
secp256k1_num_set_int(&zero, 0); secp256k1_num_set_int(&zero, 0);
GroupElemJac res; secp256k1_gej_t res;
ECMult(res, point, c.order, zero); // calc res = order * point + 0 * G; ECMult(res, point, *order, zero); // calc res = order * point + 0 * G;
assert(res.IsInfinity()); assert(secp256k1_gej_is_infinity(&res));
secp256k1_num_free(&zero); secp256k1_num_free(&zero);
} }
void test_run_point_times_order() { void test_run_point_times_order() {
secp256k1_fe_t x; secp256k1_fe_set_hex(&x, "02", 2); secp256k1_fe_t x; secp256k1_fe_set_hex(&x, "02", 2);
for (int i=0; i<500; i++) { 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); test_point_times_order(j);
secp256k1_fe_sqr(&x, &x); secp256k1_fe_sqr(&x, &x);
} }
@ -147,14 +150,14 @@ void test_run_wnaf() {
} }
void test_ecdsa_sign_verify() { 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_t msg, key, nonce;
secp256k1_num_init(&msg); secp256k1_num_init(&msg);
secp256k1_num_set_rand(&msg, &c.order); secp256k1_num_set_rand(&msg, &c.order);
secp256k1_num_init(&key); secp256k1_num_init(&key);
secp256k1_num_set_rand(&key, &c.order); secp256k1_num_set_rand(&key, &c.order);
secp256k1_num_init(&nonce); secp256k1_num_init(&nonce);
GroupElemJac pub; ECMultBase(pub, key); secp256k1_gej_t pub; ECMultBase(pub, key);
Signature sig; Signature sig;
do { do {
secp256k1_num_set_rand(&nonce, &c.order); secp256k1_num_set_rand(&nonce, &c.order);
@ -176,12 +179,15 @@ void test_run_ecdsa_sign_verify() {
int main(void) { int main(void) {
secp256k1_num_start(); secp256k1_num_start();
secp256k1_fe_start(); secp256k1_fe_start();
secp256k1_ge_start();
test_run_wnaf(); test_run_wnaf();
test_run_point_times_order(); test_run_point_times_order();
test_run_ecmult_chain(); test_run_ecmult_chain();
test_run_ecdsa_sign_verify(); test_run_ecdsa_sign_verify();
secp256k1_ge_stop();
secp256k1_fe_stop(); secp256k1_fe_stop();
secp256k1_num_stop();
return 0; return 0;
} }