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-rw-r--r--src/math/gfpmath/point_gfp.cpp423
1 files changed, 0 insertions, 423 deletions
diff --git a/src/math/gfpmath/point_gfp.cpp b/src/math/gfpmath/point_gfp.cpp
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--- a/src/math/gfpmath/point_gfp.cpp
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-/*
-* Arithmetic for point groups of elliptic curves over GF(p)
-*
-* (C) 2007 Martin Doering, Christoph Ludwig, Falko Strenzke
-* 2008-2010 Jack Lloyd
-*
-* Distributed under the terms of the Botan license
-*/
-
-#include <botan/point_gfp.h>
-#include <botan/numthry.h>
-
-namespace Botan {
-
-namespace {
-
-BigInt decompress_point(bool yMod2,
- const BigInt& x,
- const CurveGFp& curve)
- {
- BigInt xpow3 = x * x * x;
-
- BigInt g = curve.get_a() * x;
- g += xpow3;
- g += curve.get_b();
- g = g % curve.get_p();
-
- BigInt z = ressol(g, curve.get_p());
-
- if(z < 0)
- throw Illegal_Point("error during decompression");
-
- if(z.get_bit(0) != yMod2)
- z = curve.get_p() - z;
-
- return z;
- }
-
-}
-
-// arithmetic operators
-PointGFp& PointGFp::operator+=(const PointGFp& rhs)
- {
- if(rhs.is_zero())
- return *this;
-
- if(is_zero())
- {
- *this = rhs;
- return *this;
- }
-
- const Modular_Reducer& mod_p = curve.mod_p();
-
- BigInt rhs_z2 = mod_p.square(rhs.coord_z);
- BigInt U1 = mod_p.multiply(coord_x, rhs_z2);
- BigInt S1 = mod_p.multiply(coord_y, mod_p.multiply(rhs.coord_z, rhs_z2));
-
- BigInt lhs_z2 = mod_p.square(coord_z);
- BigInt U2 = mod_p.multiply(rhs.coord_x, lhs_z2);
- BigInt S2 = mod_p.multiply(rhs.coord_y, mod_p.multiply(coord_z, lhs_z2));
-
- BigInt H = mod_p.reduce(U2 - U1);
- BigInt r = mod_p.reduce(S2 - S1);
-
- if(H.is_zero())
- {
- if(r.is_zero())
- {
- mult2_in_place();
- return *this;
- }
-
- *this = PointGFp(curve); // setting myself to zero
- return *this;
- }
-
- U2 = mod_p.square(H);
-
- S2 = mod_p.multiply(U2, H);
-
- U2 = mod_p.multiply(U1, U2);
-
- BigInt x = mod_p.reduce(mod_p.square(r) - S2 - mod_p.multiply(2, U2));
- BigInt y = mod_p.reduce(mod_p.multiply(r, (U2-x)) - mod_p.multiply(S1, S2));
- BigInt z = mod_p.multiply(mod_p.multiply(coord_z, rhs.coord_z), H);
-
- coord_x = x;
- coord_y = y;
- coord_z = z;
-
- return *this;
- }
-
-PointGFp& PointGFp::operator-=(const PointGFp& rhs)
- {
- PointGFp minus_rhs = PointGFp(rhs).negate();
-
- if(is_zero())
- *this = minus_rhs;
- else
- *this += minus_rhs;
-
- return *this;
- }
-
-PointGFp& PointGFp::operator*=(const BigInt& scalar)
- {
- if(scalar.abs() <= 2) // special cases for small values
- {
- u32bit value = scalar.abs().to_u32bit();
-
- if(value == 0)
- *this = PointGFp(curve); // set to zero point
- else if(value == 1)
- {
- if(scalar.is_negative())
- this->negate();
- }
- else if(value == 2)
- {
- this->mult2_in_place();
- if(scalar.is_negative())
- this->negate();
- }
-
- return *this;
- }
-
- PointGFp H(this->curve); // create as zero
- PointGFp P(*this);
-
- if(scalar.is_negative())
- P.negate();
-
- for(int i = scalar.bits() - 1; i >= 0; --i)
- {
- H.mult2_in_place();
- if(scalar.get_bit(i))
- H += P;
- }
-
- if(!H.is_zero()) // cannot convert if H == O
- {
- /**
- * Convert H to an equivalent point with z == 1, thus x and y
- * correspond to their affine coordinates
- */
- if(H.coord_z != 1)
- {
- const Modular_Reducer& mod_p = curve.mod_p();
-
- BigInt z_inv = inverse_mod(H.coord_z, curve.get_p());
-
- BigInt z_inv_2 = mod_p.square(z_inv);
-
- H.coord_x = mod_p.multiply(H.coord_x, z_inv_2);
- H.coord_y = mod_p.multiply(H.coord_y, mod_p.multiply(z_inv, z_inv_2));
- H.coord_z = 1;
- }
- }
-
- *this = H;
- return *this;
- }
-
-PointGFp& PointGFp::negate()
- {
- if(!is_zero())
- coord_y = curve.get_p() - coord_y;
-
- return *this;
- }
-
-// *this *= 2
-void PointGFp::mult2_in_place()
- {
- if(is_zero())
- return;
- else if(coord_y.is_zero())
- {
- *this = PointGFp(curve); // setting myself to zero
- return;
- }
-
- const Modular_Reducer& mod_p = curve.mod_p();
-
- BigInt y_2 = mod_p.square(coord_y);
-
- BigInt S = mod_p.multiply(4, mod_p.multiply(coord_x, y_2));
-
- BigInt a_z4 = mod_p.multiply(curve.get_a(),
- mod_p.square(mod_p.square(coord_z)));
-
- BigInt M = mod_p.reduce(a_z4 + 3 * mod_p.square(coord_x));
-
- BigInt x = mod_p.reduce(mod_p.square(M) - mod_p.multiply(2, S));
-
- BigInt y = mod_p.square(y_2);
-
- BigInt z = mod_p.multiply(2, mod_p.reduce(y + y));
-
- BigInt U = mod_p.reduce(z + z);
-
- y = mod_p.reduce(mod_p.multiply(M, S - x) - U);
-
- z = mod_p.multiply(2, mod_p.multiply(coord_y, coord_z));
-
- coord_x = x;
- coord_y = y;
- coord_z = z;
- }
-
-BigInt PointGFp::get_affine_x() const
- {
- if(is_zero())
- throw Illegal_Transformation("cannot convert to affine");
-
- const Modular_Reducer& mod_p = curve.mod_p();
-
- BigInt z2 = mod_p.square(coord_z);
- return mod_p.multiply(coord_x, inverse_mod(z2, curve.get_p()));
- }
-
-BigInt PointGFp::get_affine_y() const
- {
- if(is_zero())
- throw Illegal_Transformation("cannot convert to affine");
-
- const Modular_Reducer& mod_p = curve.mod_p();
-
- BigInt z3 = mod_p.cube(coord_z);
- return mod_p.multiply(coord_y, inverse_mod(z3, curve.get_p()));
- }
-
-// Is this the point at infinity?
-bool PointGFp::is_zero() const
- {
- return(coord_x.is_zero() && coord_z.is_zero());
- }
-
-void PointGFp::check_invariants() const
- {
- /*
- Is the point still on the curve?? (If everything is correct, the
- point is always on its curve; then the function will return
- silently. If Oskar managed to corrupt this object's state, then it
- will throw an exception.)
- */
-
- if(is_zero())
- return;
-
- const Modular_Reducer& mod_p = curve.mod_p();
-
- BigInt y2 = mod_p.square(coord_y);
- BigInt x3 = mod_p.cube(coord_x);
-
- BigInt ax = mod_p.multiply(coord_x, curve.get_a());
-
- if(coord_z == 1)
- {
- if(mod_p.reduce(x3 + ax + curve.get_b()) != y2)
- throw Illegal_Point("Invalid ECP point: y^2 != x^3 + a*x + b");
- }
-
- BigInt z2 = mod_p.square(coord_z);
- BigInt z3 = mod_p.multiply(coord_z, z2);
-
- BigInt ax_z4 = mod_p.multiply(mod_p.multiply(z3, coord_z), ax);
-
- BigInt b_z6 = mod_p.multiply(curve.get_b(), mod_p.square(z3));
-
- if(y2 != mod_p.reduce(x3 + ax_z4 + b_z6))
- throw Illegal_Point("Invalid ECP point: y^2 != x^3 + a*x*z^4 + b*z^6");
- }
-
-// swaps the states of *this and other, does not throw!
-void PointGFp::swap(PointGFp& other)
- {
- curve.swap(other.curve);
- coord_x.swap(other.coord_x);
- coord_y.swap(other.coord_y);
- coord_z.swap(other.coord_z);
- }
-
-bool PointGFp::operator==(const PointGFp& other) const
- {
- return (coord_x == other.coord_x &&
- coord_y == other.coord_y &&
- coord_z == other.coord_z &&
- get_curve() == other.get_curve());
- }
-
-// arithmetic operators
-PointGFp operator+(const PointGFp& lhs, PointGFp const& rhs)
- {
- PointGFp tmp(lhs);
- return tmp += rhs;
- }
-
-PointGFp operator-(const PointGFp& lhs, PointGFp const& rhs)
- {
- PointGFp tmp(lhs);
- return tmp -= rhs;
- }
-
-PointGFp operator-(const PointGFp& lhs)
- {
- return PointGFp(lhs).negate();
- }
-
-PointGFp operator*(const BigInt& scalar, const PointGFp& point)
- {
- PointGFp result(point);
- return result *= scalar;
- }
-
-PointGFp operator*(const PointGFp& point, const BigInt& scalar)
- {
- PointGFp result(point);
- return result *= scalar;
- }
-
-// encoding and decoding
-SecureVector<byte> EC2OSP(const PointGFp& point, byte format)
- {
- if(point.is_zero())
- return SecureVector<byte>(1); // single 0 byte
-
- const u32bit p_bytes = point.get_curve().get_p().bytes();
-
- BigInt x = point.get_affine_x();
- BigInt y = point.get_affine_y();
-
- SecureVector<byte> bX = BigInt::encode_1363(x, p_bytes);
- SecureVector<byte> bY = BigInt::encode_1363(y, p_bytes);
-
- if(format == PointGFp::UNCOMPRESSED)
- {
- SecureVector<byte> result(2*p_bytes+1);
- result[0] = 4;
-
- result.copy(1, bX.begin(), p_bytes);
- result.copy(p_bytes+1, bY.begin(), p_bytes);
- return result;
- }
- else if(format == PointGFp::COMPRESSED)
- {
- SecureVector<byte> result(p_bytes+1);
- result[0] = 2;
-
- result.copy(1, bX.begin(), bX.size());
-
- if(y.get_bit(0))
- result[0] |= 1;
-
- return result;
- }
- else if(format == PointGFp::HYBRID)
- {
- SecureVector<byte> result(2*p_bytes+1);
- result[0] = 6;
-
- result.copy(1, bX.begin(), bX.size());
- result.copy(p_bytes+1, bY.begin(), bY.size());
-
- if(y.get_bit(0))
- result[0] |= 1;
-
- return result;
- }
- else
- throw Invalid_Argument("illegal point encoding format specification");
- }
-
-PointGFp OS2ECP(const MemoryRegion<byte>& os, const CurveGFp& curve)
- {
- if(os.size() == 1 && os[0] == 0)
- return PointGFp(curve); // return zero
-
- const byte pc = os[0];
-
- BigInt x, y;
-
- if(pc == 2 || pc == 3)
- {
- //compressed form
- x = BigInt::decode(&os[1], os.size() - 1);
-
- bool yMod2 = ((pc & 0x01) == 1);
- y = decompress_point(yMod2, x, curve);
- }
- else if(pc == 4)
- {
- // uncompressed form
- u32bit l = (os.size() - 1) / 2;
-
- x = BigInt::decode(&os[1], l);
- y = BigInt::decode(&os[l+1], l);
- }
- else if(pc == 6 || pc == 7)
- {
- // hybrid form
- u32bit l = (os.size() - 1) / 2;
-
- x = BigInt::decode(&os[1], l);
- y = BigInt::decode(&os[l+1], l);
-
- bool yMod2 = ((pc & 0x01) == 1);
-
- if(decompress_point(yMod2, x, curve) != y)
- throw Illegal_Point("OS2ECP: Decoding error in hybrid format");
- }
- else
- throw Invalid_Argument("OS2ECP: Unknown format type");
-
- PointGFp result(curve, x, y);
- result.check_invariants();
- return result;
- }
-
-}