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-rw-r--r--src/math/numbertheory/point_gfp.cpp149
-rw-r--r--src/math/numbertheory/point_gfp.h3
2 files changed, 78 insertions, 74 deletions
diff --git a/src/math/numbertheory/point_gfp.cpp b/src/math/numbertheory/point_gfp.cpp
index 062fd5c0f..4711988dc 100644
--- a/src/math/numbertheory/point_gfp.cpp
+++ b/src/math/numbertheory/point_gfp.cpp
@@ -11,6 +11,7 @@
#include <botan/numthry.h>
#include <botan/mp_asm.h>
#include <botan/mp_asmi.h>
+#include <botan/mp_core.h>
namespace Botan {
@@ -25,6 +26,7 @@ void inner_montg_mult_sos(word result[],
t.grow_to(2*s+1);
// t = a_bar * b_bar
+ //bigint_simple_mul(t, a_bar, s, b_bar, s);
for (u32bit i=0; i<s; i++)
{
word C = 0;
@@ -42,6 +44,7 @@ void inner_montg_mult_sos(word result[],
}
// ???
+#if 1
for (u32bit i=0; i<s; i++)
{
// word word_madd2(word a, word b, word c, word* carry)
@@ -105,36 +108,34 @@ void inner_montg_mult_sos(word result[],
result[i] = u[i];
}
}
- }
-
-void compute_montgomery_params(const BigInt& prime,
- BigInt& r,
- BigInt& r_inv,
- BigInt& p_dash)
- {
- if(!prime.is_odd())
- throw Internal_Error("PointGFp: Only operates with odd primes");
-
- r = 1;
- r <<= prime.sig_words() * BOTAN_MP_WORD_BITS;
+#else
- r_inv = inverse_mod(r, prime);
+ bigint_monty_redc(&t[0], t.size(),
+ n, s,
+ n_dash[0]);
- p_dash = ((r * r_inv) - 1) / prime;
+ copy_mem(&result[0], &t[0], s);
+#endif
}
}
PointGFp::PointGFp(const CurveGFp& curve) :
- curve(curve), coord_x(0), coord_y(1), coord_z(0)
+ curve(curve),
+ coord_x(0),
+ coord_y(curve.get_r()),
+ coord_z(0)
{
- compute_montgomery_params(curve.get_p(), r, r_inv, p_dash);
}
PointGFp::PointGFp(const CurveGFp& curve, const BigInt& x, const BigInt& y) :
- curve(curve), coord_x(x), coord_y(y), coord_z(1)
+ curve(curve)
{
- compute_montgomery_params(curve.get_p(), r, r_inv, p_dash);
+ const Modular_Reducer& mod_p = curve.mod_p();
+
+ coord_x = mod_p.multiply(curve.get_r(), x);
+ coord_y = mod_p.multiply(curve.get_r(), y);
+ coord_z = curve.get_r();
}
BigInt PointGFp::monty_mult(const BigInt& a, const BigInt& b)
@@ -147,22 +148,32 @@ BigInt PointGFp::monty_mult(const BigInt& a, const BigInt& b)
const BigInt& p = curve.get_p();
const u32bit s = p.sig_words();
+ const BigInt& p_dash = curve.get_p_dash();
+
result.grow_to(s);
- if(a.size() >= s && b.size() >= s)
+ if(a > 0 && b > 0 && a < p && b < p && a.size() >= s && b.size() >= s)
{
inner_montg_mult_sos(result.get_reg(), a.data(), b.data(),
p.data(), p_dash.data(), s);
}
else
{
+ const Modular_Reducer& mod_p = curve.mod_p();
+
BigInt a2 = a;
BigInt b2 = b;
a2.grow_to(s);
b2.grow_to(s);
+
+ a2 = mod_p.reduce(a2);
+ b2 = mod_p.reduce(b2);
+
inner_montg_mult_sos(result.get_reg(), a2.data(), b2.data(),
p.data(), p_dash.data(), s);
}
+
+ return result;
}
// arithmetic operators
@@ -179,15 +190,16 @@ PointGFp& PointGFp::operator+=(const PointGFp& rhs)
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 rhs_z2 = monty_mult(rhs.coord_z, rhs.coord_z);
+ BigInt U1 = monty_mult(coord_x, rhs_z2);
+ BigInt S1 = monty_mult(coord_y, monty_mult(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 lhs_z2 = monty_mult(coord_z, coord_z);
+ BigInt U2 = monty_mult(rhs.coord_x, lhs_z2);
+ BigInt S2 = monty_mult(rhs.coord_y, monty_mult(coord_z, lhs_z2));
BigInt H = mod_p.reduce(U2 - U1);
+
BigInt r = mod_p.reduce(S2 - S1);
if(H.is_zero())
@@ -202,15 +214,18 @@ PointGFp& PointGFp::operator+=(const PointGFp& rhs)
return *this;
}
- U2 = mod_p.square(H);
+ U2 = monty_mult(H, H);
+
+ S2 = monty_mult(U2, H);
- S2 = mod_p.multiply(U2, H);
+ U2 = monty_mult(U1, U2);
- U2 = mod_p.multiply(U1, U2);
+ BigInt x = mod_p.reduce(monty_mult(r, r) - S2 - U2*2);
- 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);
+ U2 = mod_p.reduce(U2 - x);
+
+ BigInt y = monty_mult(r, U2) - monty_mult(S1, S2);
+ BigInt z = monty_mult(monty_mult(coord_z, rhs.coord_z), H);
coord_x = x;
coord_y = y;
@@ -267,26 +282,6 @@ PointGFp& PointGFp::operator*=(const BigInt& scalar)
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;
}
@@ -304,22 +299,24 @@ void PointGFp::mult2()
const Modular_Reducer& mod_p = curve.mod_p();
- BigInt y_2 = mod_p.square(coord_y);
+ BigInt y_2 = monty_mult(coord_y, coord_y);
+
+ BigInt S = mod_p.reduce(4 * monty_mult(coord_x, y_2));
- BigInt S = mod_p.multiply(4, mod_p.multiply(coord_x, y_2));
+ BigInt z4 = monty_mult(coord_z, coord_z);
+ z4 = monty_mult(z4, z4);
- BigInt a_z4 = mod_p.multiply(curve.get_a(),
- mod_p.square(mod_p.square(coord_z)));
+ BigInt a_z4 = monty_mult(mod_p.multiply(curve.get_r(), curve.get_a()), z4);
- BigInt M = mod_p.reduce(a_z4 + 3 * mod_p.square(coord_x));
+ BigInt M = mod_p.reduce(a_z4 + 3 * monty_mult(coord_x, coord_x));
- BigInt x = mod_p.reduce(mod_p.square(M) - mod_p.multiply(2, S));
+ BigInt x = monty_mult(M, M) - 2*S;
- BigInt U = mod_p.multiply(8, mod_p.square(y_2));
+ BigInt U = 8 * monty_mult(y_2, y_2);
- BigInt y = mod_p.reduce(mod_p.multiply(M, S - x) - U);
+ BigInt y = monty_mult(M, S - x) - U;
- BigInt z = mod_p.multiply(2, mod_p.multiply(coord_y, coord_z));
+ BigInt z = 2 * monty_mult(coord_y, coord_z);
coord_x = x;
coord_y = y;
@@ -333,8 +330,11 @@ BigInt PointGFp::get_affine_x() const
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 x = mod_p.multiply(curve.get_r_inv(), coord_x);
+ BigInt z = mod_p.multiply(curve.get_r_inv(), coord_z);
+
+ BigInt z2 = mod_p.square(z);
+ return mod_p.multiply(x, inverse_mod(z2, curve.get_p()));
}
BigInt PointGFp::get_affine_y() const
@@ -344,8 +344,11 @@ BigInt PointGFp::get_affine_y() const
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()));
+ BigInt y = mod_p.multiply(curve.get_r_inv(), coord_y);
+ BigInt z = mod_p.multiply(curve.get_r_inv(), coord_z);
+
+ BigInt z3 = mod_p.cube(z);
+ return mod_p.multiply(y, inverse_mod(z3, curve.get_p()));
}
void PointGFp::check_invariants() const
@@ -362,21 +365,25 @@ void PointGFp::check_invariants() const
const Modular_Reducer& mod_p = curve.mod_p();
- BigInt y2 = mod_p.square(coord_y);
- BigInt x3 = mod_p.cube(coord_x);
+ BigInt x = mod_p.multiply(curve.get_r_inv(), coord_x);
+ BigInt y = mod_p.multiply(curve.get_r_inv(), coord_y);
+ BigInt z = mod_p.multiply(curve.get_r_inv(), coord_z);
+
+ BigInt y2 = mod_p.square(y);
+ BigInt x3 = mod_p.cube(x);
- BigInt ax = mod_p.multiply(coord_x, curve.get_a());
+ BigInt ax = mod_p.multiply(x, curve.get_a());
- if(coord_z == 1)
+ if(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 z2 = mod_p.square(z);
+ BigInt z3 = mod_p.multiply(z, z2);
- BigInt ax_z4 = mod_p.multiply(mod_p.multiply(z3, coord_z), ax);
+ BigInt ax_z4 = mod_p.multiply(mod_p.multiply(z3, z), ax);
BigInt b_z6 = mod_p.multiply(curve.get_b(), mod_p.square(z3));
diff --git a/src/math/numbertheory/point_gfp.h b/src/math/numbertheory/point_gfp.h
index 34f761cca..c86e61381 100644
--- a/src/math/numbertheory/point_gfp.h
+++ b/src/math/numbertheory/point_gfp.h
@@ -152,9 +152,6 @@ class BOTAN_DLL PointGFp
CurveGFp curve;
BigInt coord_x, coord_y, coord_z;
-
- // Values for Montgomery operations
- BigInt r, r_inv, p_dash;
};
// relational operators
generated by cgit v1.2.3 (git 2.39.1) at 2024-12-27 11:45:24 +0000