1 files changed, 585 insertions, 0 deletions
diff --git a/src/math/ec_gfp/point_gfp.cpp b/src/math/ec_gfp/point_gfp.cpp
new file mode 100644
index 000000000..04805010d
--- /dev/null
+++ b/src/math/ec_gfp/point_gfp.cpp
@@ -0,0 +1,585 @@
+/*
+* Point arithmetic on elliptic curves over GF(p)
+*
+* (C) 2007 Martin Doering, Christoph Ludwig, Falko Strenzke
+*     2008-2011 Jack Lloyd
+*
+* Distributed under the terms of the Botan license
+*/
+
+#include <botan/point_gfp.h>
+#include <botan/numthry.h>
+#include <botan/reducer.h>
+#include <botan/internal/mp_core.h>
+
+namespace Botan {
+
+PointGFp::PointGFp(const CurveGFp& curve) :
+   curve(curve), ws(2 * (curve.get_p_words() + 2))
+   {
+   coord_x = 0;
+   coord_y = monty_mult(1, curve.get_r2());
+   coord_z = 0;
+   }
+
+PointGFp::PointGFp(const CurveGFp& curve, const BigInt& x, const BigInt& y) :
+   curve(curve), ws(2 * (curve.get_p_words() + 2))
+   {
+   coord_x = monty_mult(x, curve.get_r2());
+   coord_y = monty_mult(y, curve.get_r2());
+   coord_z = monty_mult(1, curve.get_r2());
+   }
+
+// Montgomery multiplication
+void PointGFp::monty_mult(BigInt& z, const BigInt& x, const BigInt& y) const
+   {
+   //assert(&z != &x && &z != &y);
+
+   if(x.is_zero() || y.is_zero())
+      {
+      z = 0;
+      return;
+      }
+
+   const BigInt& p = curve.get_p();
+   const size_t p_size = curve.get_p_words();
+   const word p_dash = curve.get_p_dash();
+
+   SecureVector<word>& z_reg = z.get_reg();
+   z_reg.resize(2*p_size+1);
+   zeroise(z_reg);
+
+   bigint_mul(&z_reg[0], z_reg.size(),
+              &ws[0],
+              x.data(), x.size(), x.sig_words(),
+              y.data(), y.size(), y.sig_words());
+
+   bigint_monty_redc(&z[0], z.size(),
+                     &ws[0],
+                     p.data(), p_size, p_dash);
+   }
+
+// Montgomery squaring
+void PointGFp::monty_sqr(BigInt& z, const BigInt& x) const
+   {
+   //assert(&z != &x);
+
+   if(x.is_zero())
+      {
+      z = 0;
+      return;
+      }
+
+   const BigInt& p = curve.get_p();
+   const size_t p_size = curve.get_p_words();
+   const word p_dash = curve.get_p_dash();
+
+   SecureVector<word>& z_reg = z.get_reg();
+   z_reg.resize(2*p_size+1);
+   zeroise(z_reg);
+
+   bigint_sqr(&z[0], z.size(),
+              &ws[0],
+              x.data(), x.size(), x.sig_words());
+
+   bigint_monty_redc(&z[0], z.size(),
+                     &ws[0],
+                     p.data(), p_size, p_dash);
+   }
+
+// Point addition
+void PointGFp::add(const PointGFp& rhs, std::vector<BigInt>& ws_bn)
+   {
+   if(is_zero())
+      {
+      coord_x = rhs.coord_x;
+      coord_y = rhs.coord_y;
+      coord_z = rhs.coord_z;
+      return;
+      }
+   else if(rhs.is_zero())
+      return;
+
+   const BigInt& p = curve.get_p();
+
+   BigInt& rhs_z2 = ws_bn[0];
+   BigInt& U1 = ws_bn[1];
+   BigInt& S1 = ws_bn[2];
+
+   BigInt& lhs_z2 = ws_bn[3];
+   BigInt& U2 = ws_bn[4];
+   BigInt& S2 = ws_bn[5];
+
+   BigInt& H = ws_bn[6];
+   BigInt& r = ws_bn[7];
+
+   BigInt& x = ws_bn[8];
+   BigInt& y = ws_bn[9];
+   BigInt& z = ws_bn[10];
+
+   monty_sqr(rhs_z2, rhs.coord_z);
+   monty_mult(U1, coord_x, rhs_z2);
+   monty_mult(S1, coord_y, monty_mult(rhs.coord_z, rhs_z2));
+
+   monty_sqr(lhs_z2, coord_z);
+   monty_mult(U2, rhs.coord_x, lhs_z2);
+   monty_mult(S2, rhs.coord_y, monty_mult(coord_z, lhs_z2));
+
+   H = U2;
+   H -= U1;
+   if(H.is_negative())
+      H += p;
+
+   r = S2;
+   r -= S1;
+   if(r.is_negative())
+      r += p;
+
+   if(H.is_zero())
+      {
+      if(r.is_zero())
+         {
+         mult2(ws_bn);
+         return;
+         }
+
+      *this = PointGFp(curve); // setting myself to zero
+      return;
+      }
+
+   monty_sqr(U2, H);
+
+   monty_mult(S2, U2, H);
+
+   U2 = monty_mult(U1, U2);
+
+   monty_sqr(x, r);
+   x -= S2;
+   x -= (U2 << 1);
+   while(x.is_negative())
+      x += p;
+
+   U2 -= x;
+   if(U2.is_negative())
+      U2 += p;
+
+   monty_mult(y, r, U2);
+   y -= monty_mult(S1, S2);
+   if(y.is_negative())
+      y += p;
+
+   monty_mult(z, monty_mult(coord_z, rhs.coord_z), H);
+
+   coord_x = x;
+   coord_y = y;
+   coord_z = z;
+   }
+
+// *this *= 2
+void PointGFp::mult2(std::vector<BigInt>& ws_bn)
+   {
+   if(is_zero())
+      return;
+   else if(coord_y.is_zero())
+      {
+      *this = PointGFp(curve); // setting myself to zero
+      return;
+      }
+
+   const BigInt& p = curve.get_p();
+
+   BigInt& y_2 = ws_bn[0];
+   BigInt& S = ws_bn[1];
+   BigInt& z4 = ws_bn[2];
+   BigInt& a_z4 = ws_bn[3];
+   BigInt& M = ws_bn[4];
+   BigInt& U = ws_bn[5];
+   BigInt& x = ws_bn[6];
+   BigInt& y = ws_bn[7];
+   BigInt& z = ws_bn[8];
+
+   monty_sqr(y_2, coord_y);
+
+   monty_mult(S, coord_x, y_2);
+   S <<= 2; // * 4
+   while(S >= p)
+      S -= p;
+
+   monty_sqr(z4, monty_sqr(coord_z));
+   monty_mult(a_z4, curve.get_a_r(), z4);
+
+   M = 3 * monty_sqr(coord_x);
+   M += a_z4;
+   while(M >= p)
+      M -= p;
+
+   monty_sqr(x, M);
+   x -= (S << 1);
+   while(x.is_negative())
+      x += p;
+
+   monty_sqr(U, y_2);
+   U <<= 3;
+   while(U >= p)
+      U -= p;
+
+   S -= x;
+   while(S.is_negative())
+      S += p;
+
+   monty_mult(y, M, S);
+   y -= U;
+   if(y.is_negative())
+      y += p;
+
+   monty_mult(z, coord_y, coord_z);
+   z <<= 1;
+   if(z >= p)
+      z -= p;
+
+   coord_x = x;
+   coord_y = y;
+   coord_z = z;
+   }
+
+// arithmetic operators
+PointGFp& PointGFp::operator+=(const PointGFp& rhs)
+   {
+   std::vector<BigInt> ws(11);
+   add(rhs, ws);
+   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)
+   {
+   *this = scalar * *this;
+   return *this;
+   }
+
+PointGFp operator*(const BigInt& scalar, const PointGFp& point)
+   {
+   const CurveGFp& curve = point.get_curve();
+
+   if(scalar.is_zero())
+      return PointGFp(curve); // zero point
+
+   std::vector<BigInt> ws(11);
+
+   if(scalar.abs() <= 2) // special cases for small values
+      {
+      byte value = scalar.abs().byte_at(0);
+
+      PointGFp result = point;
+
+      if(value == 2)
+         result.mult2(ws);
+
+      if(scalar.is_negative())
+         result.negate();
+
+      return result;
+      }
+
+   const size_t scalar_bits = scalar.bits();
+
+#if 0
+
+   PointGFp x1 = PointGFp(curve);
+   PointGFp x2 = point;
+
+   size_t bits_left = scalar_bits;
+
+   // Montgomery Ladder
+   while(bits_left)
+      {
+      const bool bit_set = scalar.get_bit(bits_left - 1);
+
+      if(bit_set)
+         {
+         x1.add(x2, ws);
+         x2.mult2(ws);
+         }
+      else
+         {
+         x2.add(x1, ws);
+         x1.mult2(ws);
+         }
+
+      --bits_left;
+      }
+
+   if(scalar.is_negative())
+      x1.negate();
+
+   return x1;
+
+#else
+   const size_t window_size = 4;
+
+   std::vector<PointGFp> Ps(1 << window_size);
+   Ps[0] = PointGFp(curve);
+   Ps[1] = point;
+
+   for(size_t i = 2; i != Ps.size(); ++i)
+      {
+      Ps[i] = Ps[i-1];
+      Ps[i].add(point, ws);
+      }
+
+   PointGFp H(curve); // create as zero
+   size_t bits_left = scalar_bits;
+
+   while(bits_left >= window_size)
+      {
+      for(size_t i = 0; i != window_size; ++i)
+         H.mult2(ws);
+
+      const u32bit nibble = scalar.get_substring(bits_left - window_size,
+                                                 window_size);
+
+      H.add(Ps[nibble], ws);
+
+      bits_left -= window_size;
+      }
+
+   while(bits_left)
+      {
+      H.mult2(ws);
+      if(scalar.get_bit(bits_left-1))
+         H.add(point, ws);
+
+      --bits_left;
+      }
+
+   if(scalar.is_negative())
+      H.negate();
+
+   return H;
+#endif
+   }
+
+BigInt PointGFp::get_affine_x() const
+   {
+   if(is_zero())
+      throw Illegal_Transformation("Cannot convert zero point to affine");
+
+   const BigInt& r2 = curve.get_r2();
+
+   BigInt z2 = monty_sqr(coord_z);
+   z2 = inverse_mod(z2, curve.get_p());
+
+   z2 = monty_mult(z2, r2);
+   return monty_mult(coord_x, z2);
+   }
+
+BigInt PointGFp::get_affine_y() const
+   {
+   if(is_zero())
+      throw Illegal_Transformation("Cannot convert zero point to affine");
+
+   const BigInt& r2 = curve.get_r2();
+
+   BigInt z3 = monty_mult(coord_z, monty_sqr(coord_z));
+   z3 = inverse_mod(z3, curve.get_p());
+   z3 = monty_mult(z3, r2);
+   return monty_mult(coord_y, z3);
+   }
+
+bool PointGFp::on_the_curve() const
+   {
+   /*
+   Is the point still on the curve?? (If everything is correct, the
+   point is always on its curve; then the function will return true.
+   If somehow the state is corrupted, which suggests a fault attack
+   (or internal computational error), then return false.
+   */
+
+   if(is_zero())
+      return true;
+
+   BigInt y2 = monty_mult(monty_sqr(coord_y), 1);
+   BigInt x3 = monty_mult(coord_x, monty_sqr(coord_x));
+
+   BigInt ax = monty_mult(coord_x, curve.get_a_r());
+
+   const BigInt& b_r = curve.get_b_r();
+
+   BigInt z2 = monty_sqr(coord_z);
+
+   if(coord_z == z2) // Is z equal to 1 (in Montgomery form)?
+      {
+      if(y2 != monty_mult(x3 + ax + b_r, 1))
+         return false;
+      }
+
+   BigInt z3 = monty_mult(coord_z, z2);
+
+   BigInt ax_z4 = monty_mult(ax, monty_sqr(z2));
+
+   BigInt b_z6 = monty_mult(b_r, monty_sqr(z3));
+
+   if(y2 != monty_mult(x3 + ax_z4 + b_z6, 1))
+      return false;
+
+   return true;
+   }
+
+// 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);
+   ws.swap(other.ws);
+   }
+
+bool PointGFp::operator==(const PointGFp& other) const
+   {
+   if(get_curve() != other.get_curve())
+      return false;
+
+   // If this is zero, only equal if other is also zero
+   if(is_zero())
+      return other.is_zero();
+
+   return (get_affine_x() == other.get_affine_x() &&
+           get_affine_y() == other.get_affine_y());
+   }
+
+// encoding and decoding
+SecureVector<byte> EC2OSP(const PointGFp& point, byte format)
+   {
+   if(point.is_zero())
+      return SecureVector<byte>(1); // single 0 byte
+
+   const size_t 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;
+      result.push_back(0x04);
+
+      result += bX;
+      result += bY;
+
+      return result;
+      }
+   else if(format == PointGFp::COMPRESSED)
+      {
+      SecureVector<byte> result;
+      result.push_back(0x02 | static_cast<byte>(y.get_bit(0)));
+
+      result += bX;
+
+      return result;
+      }
+   else if(format == PointGFp::HYBRID)
+      {
+      SecureVector<byte> result;
+      result.push_back(0x06 | static_cast<byte>(y.get_bit(0)));
+
+      result += bX;
+      result += bY;
+
+      return result;
+      }
+   else
+      throw Invalid_Argument("illegal point encoding format specification");
+   }
+
+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;
+   }
+
+}
+
+PointGFp OS2ECP(const byte data[], size_t data_len,
+                const CurveGFp& curve)
+   {
+   if(data_len <= 1)
+      return PointGFp(curve); // return zero
+
+   const byte pc = data[0];
+
+   BigInt x, y;
+
+   if(pc == 2 || pc == 3)
+      {
+      //compressed form
+      x = BigInt::decode(&data[1], data_len - 1);
+
+      const bool y_mod_2 = ((pc & 0x01) == 1);
+      y = decompress_point(y_mod_2, x, curve);
+      }
+   else if(pc == 4)
+      {
+      const size_t l = (data_len - 1) / 2;
+
+      // uncompressed form
+      x = BigInt::decode(&data[1], l);
+      y = BigInt::decode(&data[l+1], l);
+      }
+   else if(pc == 6 || pc == 7)
+      {
+      const size_t l = (data_len - 1) / 2;
+
+      // hybrid form
+      x = BigInt::decode(&data[1], l);
+      y = BigInt::decode(&data[l+1], l);
+
+      const bool y_mod_2 = ((pc & 0x01) == 1);
+
+      if(decompress_point(y_mod_2, 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);
+
+   if(!result.on_the_curve())
+      throw Illegal_Point("OS2ECP: Decoded point was not on the curve");
+
+   return result;
+   }
+
+}