mirror of
https://github.com/bitcoin/bitcoin.git
synced 2025-01-12 04:42:36 -03:00
fix inversion, simplify, remove templates
This commit is contained in:
Pieter Wuille
Pieter Wuille
parent
37ca6dfaf3
commit
2b5d0102fa
1 changed files with 105 additions and 117 deletions
222
secp256k1.cpp
222
secp256k1.cpp
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@ -294,7 +294,7 @@ public:
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// calculate a^p, with p={45,63,1019,1023}
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FieldElem a2; a2.SetSquare(a);
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FieldElem a3; a3.SetMult(a2,a);
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FieldElem a4; a4.SetSquare(a);
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FieldElem a4; a4.SetSquare(a2);
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FieldElem a5; a5.SetMult(a4,a);
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FieldElem a10; a10.SetSquare(a5);
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FieldElem a11; a11.SetMult(a10,a);
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@ -361,118 +361,114 @@ public:
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}
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};
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template<typename F> class GroupElemJac;
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template<typename F> class GroupElem {
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class GroupElem {
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protected:
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bool fInfinity;
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F x;
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F y;
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FieldElem x;
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FieldElem y;
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public:
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void SetXY(const F &xin, const F &yin) {
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fInfinity = false;
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this->x = xin;
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this->y = yin;
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}
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/** Creates the point at infinity */
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GroupElem() {
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this->fInfinity = true;
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fInfinity = true;
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}
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/** Creates the point with given affine coordinates */
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GroupElem(const F &xin, const F &yin) {
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SetXY(xin,yin);
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GroupElem(const FieldElem &xin, const FieldElem &yin) {
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fInfinity = false;
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x = xin;
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y = yin;
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}
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/** Checks whether this is the point at infinity */
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bool IsInfinity() const {
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return this->fInfinity;
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return fInfinity;
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}
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void SetNeg(GroupElem<F> &p) {
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this->fInfinity = p.fInfinity;
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this->x = p.x;
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void SetNeg(GroupElem &p) {
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fInfinity = p.fInfinity;
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x = p.x;
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p.y.Normalize();
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this->y.SetNeg(p.y, 1);
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y.SetNeg(p.y, 1);
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}
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std::string ToString() {
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if (this->fInfinity)
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if (fInfinity)
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return "(inf)";
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return "(" + this->x.ToString() + "," + this->y.ToString() + ")";
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return "(" + x.ToString() + "," + y.ToString() + ")";
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}
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friend class GroupElemJac<F>;
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friend class GroupElemJac;
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};
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template<typename F> class GroupElemJac : public GroupElem<F> {
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class GroupElemJac : public GroupElem {
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protected:
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F z;
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FieldElem z;
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public:
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/** Creates the point at infinity */
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GroupElemJac() : GroupElem<F>(), z(1) {}
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GroupElemJac() : GroupElem(), z(1) {}
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/** Creates the point with given affine coordinates */
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GroupElemJac(const F &xin, const F &yin) : GroupElem<F>(xin,yin), z(1) {}
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GroupElemJac(const FieldElem &xin, const FieldElem &yin) : GroupElem(xin,yin), z(1) {}
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/** Checks whether this is a non-infinite point on the curve */
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bool IsValid() {
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if (this->IsInfinity())
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if (IsInfinity())
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return false;
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// y^2 = x^3 + 7
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// (Y/Z^3)^2 = (X/Z^2)^3 + 7
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// Y^2 / Z^6 = X^3 / Z^6 + 7
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// Y^2 = X^3 + 7*Z^6
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F y2; y2.SetSquare(this->y);
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F x3; x3.SetSquare(this->x); x3.SetMult(x3,this->x);
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F z2; z2.SetSquare(this->z);
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F z6; z6.SetSquare(z2); z6.SetMult(z6,z2);
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FieldElem y2; y2.SetSquare(y);
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FieldElem x3; x3.SetSquare(x); x3.SetMult(x3,x);
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FieldElem z2; z2.SetSquare(z);
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FieldElem z6; z6.SetSquare(z2); z6.SetMult(z6,z2);
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z6 *= 7;
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x3 += z6;
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return y2 == x3;
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}
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/** Returns the affine coordinates of this point */
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void GetAffine(GroupElem<F> &aff) {
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void GetAffine(GroupElem &aff) {
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z.SetInverse(z);
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F z2;
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FieldElem z2;
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z2.SetSquare(z);
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F z3;
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FieldElem z3;
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z3.SetMult(z,z2);
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this->x.SetMult(this->x,z2);
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this->y.SetMult(this->y,z3);
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this->z = F(1);
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aff.SetXY(this->x,this->y);
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x.SetMult(x,z2);
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y.SetMult(y,z3);
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z = FieldElem(1);
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aff.fInfinity = false;
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aff.x = x;
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aff.y = y;
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}
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/** Sets this point to have a given X coordinate & given Y oddness */
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void SetCompressed(const F &xin, bool fOdd) {
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this->x = xin;
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F x2; x2.SetSquare(this->x);
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F x3; x3.SetMult(this->x,x2);
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this->fInfinity = false;
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F c(7);
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void SetCompressed(const FieldElem &xin, bool fOdd) {
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x = xin;
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FieldElem x2; x2.SetSquare(x);
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FieldElem x3; x3.SetMult(x,x2);
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fInfinity = false;
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FieldElem c(7);
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c += x3;
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this->y.SetSquareRoot(c);
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this->z = F(1);
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if (this->y.IsOdd() != fOdd)
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this->y.SetNeg(this->y,1);
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y.SetSquareRoot(c);
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z = FieldElem(1);
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if (y.IsOdd() != fOdd)
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y.SetNeg(y,1);
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}
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/** Sets this point to be the EC double of another */
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void SetDouble(const GroupElemJac<F> &p) {
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if (p.fInfinity || this->y.IsZero()) {
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this->fInfinity = true;
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void SetDouble(const GroupElemJac &p) {
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if (p.fInfinity || y.IsZero()) {
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fInfinity = true;
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return;
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}
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F t1,t2,t3,t4,t5;
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this->z.SetMult(p.y,p.z);
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this->z *= 2; // Z' = 2*Y*Z (2)
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FieldElem t1,t2,t3,t4,t5;
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z.SetMult(p.y,p.z);
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z *= 2; // Z' = 2*Y*Z (2)
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t1.SetSquare(p.x);
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t1 *= 3; // T1 = 3*X^2 (3)
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t2.SetSquare(t1); // T2 = 9*X^4 (1)
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@ -481,20 +477,20 @@ public:
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t4.SetSquare(t3);
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t4 *= 2; // T4 = 8*Y^4 (2)
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t3.SetMult(p.x,t3); // T3 = 2*X*Y^2 (1)
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this->x = t3;
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this->x *= 4; // X' = 8*X*Y^2 (4)
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this->x.SetNeg(this->x,4); // X' = -8*X*Y^2 (5)
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this->x += t2; // X' = 9*X^4 - 8*X*Y^2 (6)
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x = t3;
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x *= 4; // X' = 8*X*Y^2 (4)
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x.SetNeg(x,4); // X' = -8*X*Y^2 (5)
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x += t2; // X' = 9*X^4 - 8*X*Y^2 (6)
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t2.SetNeg(t2,1); // T2 = -9*X^4 (2)
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t3 *= 6; // T3 = 12*X*Y^2 (6)
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t3 += t2; // T3 = 12*X*Y^2 - 9*X^4 (8)
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this->y.SetMult(t1,t3); // Y' = 36*X^3*Y^2 - 27*X^6 (1)
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y.SetMult(t1,t3); // Y' = 36*X^3*Y^2 - 27*X^6 (1)
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t2.SetNeg(t4,2); // T2 = -8*Y^4 (3)
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this->y += t2; // Y' = 36*X^3*Y^2 - 27*X^6 - 8*Y^4 (4)
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y += t2; // Y' = 36*X^3*Y^2 - 27*X^6 - 8*Y^4 (4)
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}
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/** Sets this point to be the EC addition of two others */
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void SetAdd(const GroupElemJac<F> &p, const GroupElemJac<F> &q) {
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void SetAdd(const GroupElemJac &p, const GroupElemJac &q) {
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if (p.fInfinity) {
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*this = q;
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return;
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@ -503,79 +499,79 @@ public:
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*this = p;
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return;
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}
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this->fInfinity = false;
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const F &x1 = p.x, &y1 = p.y, &z1 = p.z, &x2 = q.x, &y2 = q.y, &z2 = q.z;
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F z22; z22.SetSquare(z2);
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F z12; z12.SetSquare(z1);
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F u1; u1.SetMult(x1, z22);
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F u2; u2.SetMult(x2, z12);
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F s1; s1.SetMult(y1, z22); s1.SetMult(s1, z2);
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F s2; s2.SetMult(y2, z12); s2.SetMult(s2, z1);
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fInfinity = false;
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const FieldElem &x1 = p.x, &y1 = p.y, &z1 = p.z, &x2 = q.x, &y2 = q.y, &z2 = q.z;
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FieldElem z22; z22.SetSquare(z2);
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FieldElem z12; z12.SetSquare(z1);
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FieldElem u1; u1.SetMult(x1, z22);
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FieldElem u2; u2.SetMult(x2, z12);
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FieldElem s1; s1.SetMult(y1, z22); s1.SetMult(s1, z2);
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FieldElem s2; s2.SetMult(y2, z12); s2.SetMult(s2, z1);
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if (u1 == u2) {
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if (s1 == s2) {
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SetDouble(p);
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} else {
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this->fInfinity = true;
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fInfinity = true;
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}
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return;
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}
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F h; h.SetNeg(u1,1); h += u2;
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F r; r.SetNeg(s1,1); r += s2;
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F r2; r2.SetSquare(r);
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F h2; h2.SetSquare(h);
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F h3; h3.SetMult(h,h2);
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this->z.SetMult(z1,z2); this->z.SetMult(z, h);
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F t; t.SetMult(u1,h2);
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this->x = t; this->x *= 2; this->x += h3; this->x.SetNeg(this->x,3); this->x += r2;
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this->y.SetNeg(this->x,5); this->y += t; this->y.SetMult(this->y,r);
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FieldElem h; h.SetNeg(u1,1); h += u2;
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FieldElem r; r.SetNeg(s1,1); r += s2;
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FieldElem r2; r2.SetSquare(r);
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FieldElem h2; h2.SetSquare(h);
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FieldElem h3; h3.SetMult(h,h2);
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z.SetMult(z1,z2); z.SetMult(z, h);
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FieldElem t; t.SetMult(u1,h2);
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x = t; x *= 2; x += h3; x.SetNeg(x,3); x += r2;
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y.SetNeg(x,5); y += t; y.SetMult(y,r);
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h3.SetMult(h3,s1); h3.SetNeg(h3,1);
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this->y += h3;
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y += h3;
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}
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/** Sets this point to be the EC addition of two others (one of which is in affine coordinates) */
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void SetAdd(const GroupElemJac<F> &p, const GroupElem<F> &q) {
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void SetAdd(const GroupElemJac &p, const GroupElem &q) {
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if (p.fInfinity) {
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this->x = q.x;
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this->y = q.y;
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this->fInfinity = q.fInfinity;
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this->z = F(1);
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x = q.x;
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y = q.y;
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fInfinity = q.fInfinity;
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z = FieldElem(1);
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return;
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}
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if (q.fInfinity) {
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*this = p;
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return;
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}
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this->fInfinity = false;
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const F &x1 = p.x, &y1 = p.y, &z1 = p.z, &x2 = q.x, &y2 = q.y;
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F z12; z12.SetSquare(z1);
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F u1 = x1; u1.Normalize();
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F u2; u2.SetMult(x2, z12);
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F s1 = y1; s1.Normalize();
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F s2; s2.SetMult(y2, z12); s2.SetMult(s2, z1);
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fInfinity = false;
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const FieldElem &x1 = p.x, &y1 = p.y, &z1 = p.z, &x2 = q.x, &y2 = q.y;
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FieldElem z12; z12.SetSquare(z1);
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FieldElem u1 = x1; u1.Normalize();
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FieldElem u2; u2.SetMult(x2, z12);
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FieldElem s1 = y1; s1.Normalize();
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FieldElem s2; s2.SetMult(y2, z12); s2.SetMult(s2, z1);
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if (u1 == u2) {
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if (s1 == s2) {
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SetDouble(p);
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} else {
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this->fInfinity = true;
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fInfinity = true;
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}
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return;
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}
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F h; h.SetNeg(u1,1); h += u2;
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F r; r.SetNeg(s1,1); r += s2;
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F r2; r2.SetSquare(r);
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F h2; h2.SetSquare(h);
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F h3; h3.SetMult(h,h2);
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this->z = p.z; this->z.SetMult(z, h);
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F t; t.SetMult(u1,h2);
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this->x = t; this->x *= 2; this->x += h3; this->x.SetNeg(this->x,3); this->x += r2;
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this->y.SetNeg(this->x,5); this->y += t; this->y.SetMult(this->y,r);
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FieldElem h; h.SetNeg(u1,1); h += u2;
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FieldElem r; r.SetNeg(s1,1); r += s2;
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FieldElem r2; r2.SetSquare(r);
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FieldElem h2; h2.SetSquare(h);
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FieldElem h3; h3.SetMult(h,h2);
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z = p.z; z.SetMult(z, h);
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FieldElem t; t.SetMult(u1,h2);
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x = t; x *= 2; x += h3; x.SetNeg(x,3); x += r2;
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y.SetNeg(x,5); y += t; y.SetMult(y,r);
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h3.SetMult(h3,s1); h3.SetNeg(h3,1);
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this->y += h3;
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y += h3;
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}
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std::string ToString() {
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GroupElem<F> aff;
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this->GetAffine(aff);
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GroupElem aff;
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GetAffine(aff);
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return aff.ToString();
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}
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};
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@ -587,17 +583,9 @@ using namespace secp256k1;
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int main() {
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FieldElem f1,f2;
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f1.SetHex("8b30bbe9ae2a990696b22f670709dff3727fd8bc04d3362c6c7bf458e2846004");
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f2.SetHex("a357ae915c4a65281309edf20504740f1eb3333990216b4f81063cb65f2f7e0f");
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GroupElemJac<FieldElem> g1; g1.SetCompressed(f1,false);
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GroupElemJac<FieldElem> g2; g2.SetCompressed(f2,false);
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printf("g1: %s (%s)\n", g1.ToString().c_str(), g1.IsValid() ? "ok" : "fail");
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printf("g2: %s (%s)\n", g2.ToString().c_str(), g2.IsValid() ? "ok" : "fail");
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GroupElem<FieldElem> g2a; g2.GetAffine(g2a);
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printf("g2a:%s\n", g2a.ToString().c_str());
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GroupElemJac<FieldElem> x1 = g1, x2 = g1;
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for (int i=0; i<100000000; i++) {
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x1.SetAdd(x1,g2a);
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for (int i=0; i<1000000; i++) {
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f1.SetInverse(f1);
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f1 *= 2;
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}
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printf("res:%s (%s)\n", x1.ToString().c_str(), x1.IsValid() ? "ok" : "fail");
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return 0;
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}
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