diff --git a/secp256k1.cpp b/secp256k1.cpp index 9c96f64c..9feed436 100644 --- a/secp256k1.cpp +++ b/secp256k1.cpp @@ -361,6 +361,8 @@ public: } }; +template class GroupElemJac; + template class GroupElem { protected: bool fInfinity; @@ -369,35 +371,41 @@ protected: public: + void SetXY(const F &xin, const F &yin) { + fInfinity = false; + this->x = xin; + this->y = yin; + } + /** Creates the point at infinity */ GroupElem() { - fInfinity = true; + this->fInfinity = true; } /** Creates the point with given affine coordinates */ GroupElem(const F &xin, const F &yin) { - fInfinity = false; - x = xin; - y = yin; + SetXY(xin,yin); } /** Checks whether this is the point at infinity */ bool IsInfinity() const { - return fInfinity; + return this->fInfinity; } void SetNeg(GroupElem &p) { - fInfinity = p.fInfinity; - x = p.x; + this->fInfinity = p.fInfinity; + this->x = p.x; p.y.Normalize(); - y.SetNeg(p.y, 1); + this->y.SetNeg(p.y, 1); } std::string ToString() { - if (fInfinity) + if (this->fInfinity) return "(inf)"; - return "(" + xt.ToString() + "," + yt.ToString() + ")"; + return "(" + this->x.ToString() + "," + this->y.ToString() + ")"; } + + friend class GroupElemJac; }; template class GroupElemJac : public GroupElem { @@ -413,15 +421,15 @@ public: /** Checks whether this is a non-infinite point on the curve */ bool IsValid() { - if (IsInfinity()) + if (this->IsInfinity()) 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 - F y2; y2.SetSquare(y); - F x3; x3.SetSquare(x); x3.SetMult(x3,x); - F z2; z2.SetSquare(z); + F y2; y2.SetSquare(this->y); + F x3; x3.SetSquare(this->x); x3.SetMult(x3,this->x); + F z2; z2.SetSquare(this->z); F z6; z6.SetSquare(z2); z6.SetMult(z6,z2); z6 *= 7; x3 += z6; @@ -435,55 +443,54 @@ public: z2.SetSquare(z); F z3; z3.SetMult(z,z2); - x.SetMult(x,z2); - y.SetMult(y,z3); - z = F(1); - aff.x = x; - aff.y = y; + this->x.SetMult(this->x,z2); + this->y.SetMult(this->y,z3); + this->z = F(1); + aff.SetXY(this->x,this->y); } /** Sets this point to have a given X coordinate & given Y oddness */ void SetCompressed(const F &xin, bool fOdd) { - x = xin; - F x2; x2.SetSquare(x); - F x3; x3.SetMult(x,x2); - fInfinity = false; + this->x = xin; + F x2; x2.SetSquare(this->x); + F x3; x3.SetMult(this->x,x2); + this->fInfinity = false; F c(7); c += x3; - y.SetSquareRoot(c); - z = F(1); - if (y.IsOdd() != fOdd) - y.SetNeg(y,1); + this->y.SetSquareRoot(c); + this->z = F(1); + if (this->y.IsOdd() != fOdd) + this->y.SetNeg(this->y,1); } /** Sets this point to be the EC double of another */ void SetDouble(const GroupElemJac &p) { - if (p.fInfinity || y.IsZero()) { - fInfinity = true; + if (p.fInfinity || this->y.IsZero()) { + this->fInfinity = true; return; } F t1,t2,t3,t4,t5; - z.SetMult(p.y,p.z); - z *= 2; // Z' = 2*Y*Z (2) + this->z.SetMult(p.y,p.z); + this->z *= 2; // Z' = 2*Y*Z (2) t1.SetSquare(p.x); t1 *= 3; // T1 = 3*X^2 (3) t2.SetSquare(t1); // T2 = 9*X^4 (1) - t3.SetSquare(y); + t3.SetSquare(p.y); t3 *= 2; // T3 = 2*Y^2 (2) t4.SetSquare(t3); t4 *= 2; // T4 = 8*Y^4 (2) - t3.SetMult(x,t3); // T3 = 2*X*Y^2 (1) - x = t3; - x *= 4; // X' = 8*X*Y^2 (4) - x.SetNeg(x,4); // X' = -8*X*Y^2 (5) - x += t2; // X' = 9*X^4 - 8*X*Y^2 (6) + t3.SetMult(p.x,t3); // T3 = 2*X*Y^2 (1) + this->x = t3; + this->x *= 4; // X' = 8*X*Y^2 (4) + this->x.SetNeg(this->x,4); // X' = -8*X*Y^2 (5) + this->x += t2; // X' = 9*X^4 - 8*X*Y^2 (6) t2.SetNeg(t2,1); // T2 = -9*X^4 (2) t3 *= 6; // T3 = 12*X*Y^2 (6) t3 += t2; // T3 = 12*X*Y^2 - 9*X^4 (8) - y.SetMult(t1,t3); // Y' = 36*X^3*Y^2 - 27*X^6 (1) + this->y.SetMult(t1,t3); // Y' = 36*X^3*Y^2 - 27*X^6 (1) t2.SetNeg(t4,2); // T2 = -8*Y^4 (3) - y += t2; // Y' = 36*X^3*Y^2 - 27*X^6 - 8*Y^4 (4) + this->y += t2; // Y' = 36*X^3*Y^2 - 27*X^6 - 8*Y^4 (4) } /** Sets this point to be the EC addition of two others */ @@ -496,7 +503,7 @@ public: *this = p; return; } - fInfinity = false; + this->fInfinity = false; const F &x1 = p.x, &y1 = p.y, &z1 = p.z, &x2 = q.x, &y2 = q.y, &z2 = q.z; F z22; z22.SetSquare(z2); F z12; z12.SetSquare(z1); @@ -508,7 +515,7 @@ public: if (s1 == s2) { SetDouble(p); } else { - fInfinity = true; + this->fInfinity = true; } return; } @@ -517,35 +524,39 @@ public: F r2; r2.SetSquare(r); F h2; h2.SetSquare(h); F h3; h3.SetMult(h,h2); - z.SetMult(p.z,q.z); z.SetMult(z, h); + this->z.SetMult(p.z,q.z); this->z.SetMult(z, h); F t; t.SetMult(u1,h2); - x = t; x *= 2; x += h3; x.SetNeg(x,3); x += r2; - y.SetNeg(x,5); y += t; y.SetMult(y,r); + this->x = t; this->x *= 2; this->x += h3; this->x.SetNeg(this->x,3); this->x += r2; + this->y.SetNeg(this->x,5); this->y += t; this->y.SetMult(this->y,r); h3.SetMult(h3,s1); h3.SetNeg(h3,1); - y += h3; + this->y += h3; } /** 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) { if (p.fInfinity) { - *this = q; - z = F(1); + this->x = q.x; + this->y = q.y; + this->fInfinity = q.fInfinity; + this->z = F(1); return; } if (q.fInfinity) { *this = p; return; } - fInfinity = false; - const F &u1 = p.x, &s1 = p.y, &z1 = p.z, &x2 = q.x, &y2 = q.y; + this->fInfinity = false; + const F &x1 = p.x, &y1 = p.y, &z1 = p.z, &x2 = q.x, &y2 = q.y; F z12; z12.SetSquare(z1); + F u1 = x1; F u2; u2.SetMult(x2, z12); + F s1 = y1; F s2; s2.SetMult(y2, z12); s2.SetMult(s2, z1); if (u1 == u2) { if (s1 == s2) { SetDouble(p); } else { - fInfinity = true; + this->fInfinity = true; } return; } @@ -554,17 +565,17 @@ public: F r2; r2.SetSquare(r); F h2; h2.SetSquare(h); F h3; h3.SetMult(h,h2); - z = p.z; z.SetMult(z, h); + this->z = p.z; this->z.SetMult(z, h); F t; t.SetMult(u1,h2); - x = t; x *= 2; x += h3; x.SetNeg(x,3); x += r2; - y.SetNeg(x,5); y += t; y.SetMult(y,r); + this->x = t; this->x *= 2; this->x += h3; this->x.SetNeg(this->x,3); this->x += r2; + this->y.SetNeg(this->x,5); this->y += t; this->y.SetMult(this->y,r); h3.SetMult(h3,s1); h3.SetNeg(h3,1); - y += h3; + this->y += h3; } std::string ToString() { GroupElem aff; - GetAffine(aff); + this->GetAffine(aff); return aff.ToString(); } }; @@ -576,10 +587,15 @@ using namespace secp256k1; int main() { FieldElem f1,f2; f1.SetHex("8b30bbe9ae2a990696b22f670709dff3727fd8bc04d3362c6c7bf458e2846004"); - f2.SetHex("a357ae915c4a65281309edf20504740f1eb3343990216b4f81063cb65f2f7e0f"); + f2.SetHex("a357ae915c4a65281309edf20504740f1eb3333990216b4f81063cb65f2f7e0f"); GroupElemJac g1; g1.SetCompressed(f1,false); GroupElemJac g2; g2.SetCompressed(f2,false); printf("g1: %s (%s)\n", g1.ToString().c_str(), g1.IsValid() ? "ok" : "fail"); - printf("g2: %s (%s)\n", g1.ToString().c_str(), g1.IsValid() ? "ok" : "fail"); + printf("g2: %s (%s)\n", g2.ToString().c_str(), g2.IsValid() ? "ok" : "fail"); + GroupElem g2a; g2.GetAffine(g2a); + printf("g2a:%s\n", g2a.ToString().c_str()); + for (int i=0; i<1000000; i++) + g1.SetAdd(g1,g2a); + printf("res:%s (%s)\n", g1.ToString().c_str(), g1.IsValid() ? "ok" : "fail"); return 0; }