diff --git a/crypto/src/crypto/ec/CustomNamedCurves.cs b/crypto/src/crypto/ec/CustomNamedCurves.cs
index ab609fdb9..16badbe97 100644
--- a/crypto/src/crypto/ec/CustomNamedCurves.cs
+++ b/crypto/src/crypto/ec/CustomNamedCurves.cs
@@ -2,10 +2,14 @@
using System.Collections;
using Org.BouncyCastle.Asn1;
+using Org.BouncyCastle.Asn1.Sec;
using Org.BouncyCastle.Asn1.X9;
+using Org.BouncyCastle.Math;
using Org.BouncyCastle.Math.EC;
+using Org.BouncyCastle.Math.EC.Custom.Sec;
using Org.BouncyCastle.Utilities;
using Org.BouncyCastle.Utilities.Collections;
+using Org.BouncyCastle.Utilities.Encoders;
namespace Org.BouncyCastle.Crypto.EC
{
@@ -15,19 +19,45 @@ namespace Org.BouncyCastle.Crypto.EC
{
}
+ private static BigInteger FromHex(string hex)
+ {
+ return new BigInteger(1, Hex.Decode(hex));
+ }
+
private static ECCurve ConfigureCurve(ECCurve curve)
{
return curve;
}
+ /*
+ * secp256k1
+ */
+ internal class Secp256k1Holder
+ : X9ECParametersHolder
+ {
+ private Secp256k1Holder() {}
+
+ internal static readonly X9ECParametersHolder Instance = new Secp256k1Holder();
+
+ protected override X9ECParameters CreateParameters()
+ {
+ byte[] S = null;
+ ECCurve curve = ConfigureCurve(new SecP256K1Curve());
+ ECPoint G = curve.DecodePoint(Hex.Decode("04"
+ + "79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798"
+ + "483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8"));
+ //return new X9ECParameters(curve, G, curve.getOrder(), curve.getCofactor(), S);
+ BigInteger n = FromHex("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141");
+ BigInteger h = BigInteger.ValueOf(1);
+ return new X9ECParameters(curve, G, n, h, S);
+ }
+ }
+
private static readonly IDictionary objIds = Platform.CreateHashtable();
private static readonly IDictionary curves = Platform.CreateHashtable();
private static readonly IDictionary names = Platform.CreateHashtable();
- private static void DefineCurve(
- string name,
- DerObjectIdentifier oid,
- X9ECParametersHolder holder)
+ private static void DefineCurve(string name, DerObjectIdentifier oid, X9ECParametersHolder holder)
{
objIds.Add(name, oid);
names.Add(oid, name);
@@ -36,26 +66,23 @@ namespace Org.BouncyCastle.Crypto.EC
static CustomNamedCurves()
{
+ DefineCurve("secp256k1", SecObjectIdentifiers.SecP256k1, Secp256k1Holder.Instance);
}
- public static X9ECParameters GetByName(
- string name)
+ public static X9ECParameters GetByName(string name)
{
- DerObjectIdentifier oid = (DerObjectIdentifier)
- objIds[Platform.ToLowerInvariant(name)];
+ DerObjectIdentifier oid = (DerObjectIdentifier)objIds[Platform.ToLowerInvariant(name)];
return oid == null ? null : GetByOid(oid);
}
-
/**
* return the X9ECParameters object for the named curve represented by
* the passed in object identifier. Null if the curve isn't present.
*
* @param oid an object identifier representing a named curve, if present.
*/
- public static X9ECParameters GetByOid(
- DerObjectIdentifier oid)
+ public static X9ECParameters GetByOid(DerObjectIdentifier oid)
{
X9ECParametersHolder holder = (X9ECParametersHolder)curves[oid];
@@ -68,8 +95,7 @@ namespace Org.BouncyCastle.Crypto.EC
*
* @return the object identifier associated with name, if present.
*/
- public static DerObjectIdentifier GetOid(
- string name)
+ public static DerObjectIdentifier GetOid(string name)
{
return (DerObjectIdentifier)objIds[Platform.ToLowerInvariant(name)];
}
@@ -77,8 +103,7 @@ namespace Org.BouncyCastle.Crypto.EC
/**
* return the named curve name represented by the given object identifier.
*/
- public static string GetName(
- DerObjectIdentifier oid)
+ public static string GetName(DerObjectIdentifier oid)
{
return (string)names[oid];
}
diff --git a/crypto/src/math/ec/custom/sec/Nat256.cs b/crypto/src/math/ec/custom/sec/Nat256.cs
new file mode 100644
index 000000000..a55e7bc0d
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/Nat256.cs
@@ -0,0 +1,767 @@
+using System;
+using System.Diagnostics;
+
+using Org.BouncyCastle.Crypto.Utilities;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+ internal abstract class Nat256
+ {
+ private const ulong M = 0xFFFFFFFFUL;
+
+ public static uint Add(uint[] x, uint[] y, uint[] z)
+ {
+ ulong c = 0;
+ c += (ulong)x[0] + y[0];
+ z[0] = (uint)c;
+ c >>= 32;
+ c += (ulong)x[1] + y[1];
+ z[1] = (uint)c;
+ c >>= 32;
+ c += (ulong)x[2] + y[2];
+ z[2] = (uint)c;
+ c >>= 32;
+ c += (ulong)x[3] + y[3];
+ z[3] = (uint)c;
+ c >>= 32;
+ c += (ulong)x[4] + y[4];
+ z[4] = (uint)c;
+ c >>= 32;
+ c += (ulong)x[5] + y[5];
+ z[5] = (uint)c;
+ c >>= 32;
+ c += (ulong)x[6] + y[6];
+ z[6] = (uint)c;
+ c >>= 32;
+ c += (ulong)x[7] + y[7];
+ z[7] = (uint)c;
+ c >>= 32;
+ return (uint)c;
+ }
+
+ public static uint AddBothTo(uint[] x, uint[] y, uint[] z)
+ {
+ ulong c = 0;
+ c += (ulong)x[0] + y[0] + z[0];
+ z[0] = (uint)c;
+ c >>= 32;
+ c += (ulong)x[1] + y[1] + z[1];
+ z[1] = (uint)c;
+ c >>= 32;
+ c += (ulong)x[2] + y[2] + z[2];
+ z[2] = (uint)c;
+ c >>= 32;
+ c += (ulong)x[3] + y[3] + z[3];
+ z[3] = (uint)c;
+ c >>= 32;
+ c += (ulong)x[4] + y[4] + z[4];
+ z[4] = (uint)c;
+ c >>= 32;
+ c += (ulong)x[5] + y[5] + z[5];
+ z[5] = (uint)c;
+ c >>= 32;
+ c += (ulong)x[6] + y[6] + z[6];
+ z[6] = (uint)c;
+ c >>= 32;
+ c += (ulong)x[7] + y[7] + z[7];
+ z[7] = (uint)c;
+ c >>= 32;
+ return (uint)c;
+ }
+
+ // TODO Re-write to allow full range for x?
+ public static uint AddDWord(ulong x, uint[] z, int zOff)
+ {
+ Debug.Assert(zOff < 6);
+ ulong c = x;
+ c += (ulong)z[zOff + 0];
+ z[zOff + 0] = (uint)c;
+ c >>= 32;
+ c += (ulong)z[zOff + 1];
+ z[zOff + 1] = (uint)c;
+ c >>= 32;
+ return c == 0 ? 0 : Inc(z, zOff + 2);
+ }
+
+ public static uint AddExt(uint[] xx, uint[] yy, uint[] zz)
+ {
+ ulong c = 0;
+ for (int i = 0; i < 16; ++i)
+ {
+ c += (ulong)xx[i] + yy[i];
+ zz[i] = (uint)c;
+ c >>= 32;
+ }
+ return (uint)c;
+ }
+
+ public static uint AddToExt(uint[] x, int xOff, uint[] zz, int zzOff)
+ {
+ Debug.Assert(zzOff <= 8);
+ ulong c = 0;
+ c += (ulong)x[xOff + 0] + zz[zzOff + 0];
+ zz[zzOff + 0] = (uint)c;
+ c >>= 32;
+ c += (ulong)x[xOff + 1] + zz[zzOff + 1];
+ zz[zzOff + 1] = (uint)c;
+ c >>= 32;
+ c += (ulong)x[xOff + 2] + zz[zzOff + 2];
+ zz[zzOff + 2] = (uint)c;
+ c >>= 32;
+ c += (ulong)x[xOff + 3] + zz[zzOff + 3];
+ zz[zzOff + 3] = (uint)c;
+ c >>= 32;
+ c += (ulong)x[xOff + 4] + zz[zzOff + 4];
+ zz[zzOff + 4] = (uint)c;
+ c >>= 32;
+ c += (ulong)x[xOff + 5] + zz[zzOff + 5];
+ zz[zzOff + 5] = (uint)c;
+ c >>= 32;
+ c += (ulong)x[xOff + 6] + zz[zzOff + 6];
+ zz[zzOff + 6] = (uint)c;
+ c >>= 32;
+ c += (ulong)x[xOff + 7] + zz[zzOff + 7];
+ zz[zzOff + 7] = (uint)c;
+ c >>= 32;
+ return (uint)c;
+ }
+
+ public static uint AddWordExt(uint x, uint[] zz, int zzOff)
+ {
+ Debug.Assert(zzOff < 15);
+ ulong c = (ulong)x + zz[zzOff + 0];
+ zz[zzOff + 0] = (uint)c;
+ c >>= 32;
+ return c == 0 ? 0 : IncExt(zz, zzOff + 1);
+ }
+
+ public static uint[] Create()
+ {
+ return new uint[8];
+ }
+
+ public static uint[] CreateExt()
+ {
+ return new uint[16];
+ }
+
+ public static int Dec(uint[] z, int zOff)
+ {
+ Debug.Assert(zOff < 8);
+ int i = zOff;
+ do
+ {
+ if (--z[i] != uint.MaxValue)
+ {
+ return 0;
+ }
+ }
+ while (++i < 8);
+ return -1;
+ }
+
+ public static uint[] FromBigInteger(BigInteger x)
+ {
+ if (x.SignValue < 0 || x.BitLength > 256)
+ throw new ArgumentException();
+
+ uint[] z = Create();
+ int i = 0;
+ while (x.SignValue != 0)
+ {
+ z[i++] = (uint)x.IntValue;
+ x = x.ShiftRight(32);
+ }
+ return z;
+ }
+
+ public static uint GetBit(uint[] x, int bit)
+ {
+ if (bit == 0)
+ {
+ return x[0] & 1;
+ }
+ if ((bit & 255) != bit)
+ {
+ return 0;
+ }
+ int w = bit >> 5;
+ int b = bit & 31;
+ return (x[w] >> b) & 1;
+ }
+
+ public static bool Gte(uint[] x, uint[] y)
+ {
+ for (int i = 7; i >= 0; --i)
+ {
+ uint x_i = x[i], y_i = y[i];
+ if (x_i < y_i)
+ return false;
+ if (x_i > y_i)
+ return true;
+ }
+ return false;
+ }
+
+ public static bool GteExt(uint[] xx, uint[] yy)
+ {
+ for (int i = 15; i >= 0; --i)
+ {
+ uint xx_i = xx[i], yy_i = yy[i];
+ if (xx_i < yy_i)
+ return false;
+ if (xx_i > yy_i)
+ return true;
+ }
+ return false;
+ }
+
+ public static uint Inc(uint[] z, int zOff)
+ {
+ Debug.Assert(zOff < 8);
+ for (int i = zOff; i < 8; ++i)
+ {
+ if (++z[i] != 0)
+ {
+ return 0;
+ }
+ }
+ return 1;
+ }
+
+ public static uint IncExt(uint[] zz, int zzOff)
+ {
+ Debug.Assert(zzOff < 16);
+ for (int i = zzOff; i < 16; ++i)
+ {
+ if (++zz[i] != 0)
+ {
+ return 0;
+ }
+ }
+ return 1;
+ }
+
+ public static bool IsOne(uint[] x)
+ {
+ if (x[0] != 1)
+ {
+ return false;
+ }
+ for (int i = 1; i < 8; ++i)
+ {
+ if (x[i] != 0)
+ {
+ return false;
+ }
+ }
+ return true;
+ }
+
+ public static bool IsZero(uint[] x)
+ {
+ for (int i = 0; i < 8; ++i)
+ {
+ if (x[i] != 0)
+ {
+ return false;
+ }
+ }
+ return true;
+ }
+
+ public static bool IsZeroExt(uint[] xx)
+ {
+ for (int i = 0; i < 16; ++i)
+ {
+ if (xx[i] != 0)
+ {
+ return false;
+ }
+ }
+ return true;
+ }
+
+ public static void Mul(uint[] x, uint[] y, uint[] zz)
+ {
+ ulong y_0 = y[0];
+ ulong y_1 = y[1];
+ ulong y_2 = y[2];
+ ulong y_3 = y[3];
+ ulong y_4 = y[4];
+ ulong y_5 = y[5];
+ ulong y_6 = y[6];
+ ulong y_7 = y[7];
+
+ {
+ ulong c = 0, x_0 = x[0];
+ c += x_0 * y_0;
+ zz[0] = (uint)c;
+ c >>= 32;
+ c += x_0 * y_1;
+ zz[1] = (uint)c;
+ c >>= 32;
+ c += x_0 * y_2;
+ zz[2] = (uint)c;
+ c >>= 32;
+ c += x_0 * y_3;
+ zz[3] = (uint)c;
+ c >>= 32;
+ c += x_0 * y_4;
+ zz[4] = (uint)c;
+ c >>= 32;
+ c += x_0 * y_5;
+ zz[5] = (uint)c;
+ c >>= 32;
+ c += x_0 * y_6;
+ zz[6] = (uint)c;
+ c >>= 32;
+ c += x_0 * y_7;
+ zz[7] = (uint)c;
+ c >>= 32;
+ zz[8] = (uint)c;
+ }
+
+ for (int i = 1; i < 8; ++i)
+ {
+ ulong c = 0, x_i = x[i];
+ c += x_i * y_0 + zz[i + 0];
+ zz[i + 0] = (uint)c;
+ c >>= 32;
+ c += x_i * y_1 + zz[i + 1];
+ zz[i + 1] = (uint)c;
+ c >>= 32;
+ c += x_i * y_2 + zz[i + 2];
+ zz[i + 2] = (uint)c;
+ c >>= 32;
+ c += x_i * y_3 + zz[i + 3];
+ zz[i + 3] = (uint)c;
+ c >>= 32;
+ c += x_i * y_4 + zz[i + 4];
+ zz[i + 4] = (uint)c;
+ c >>= 32;
+ c += x_i * y_5 + zz[i + 5];
+ zz[i + 5] = (uint)c;
+ c >>= 32;
+ c += x_i * y_6 + zz[i + 6];
+ zz[i + 6] = (uint)c;
+ c >>= 32;
+ c += x_i * y_7 + zz[i + 7];
+ zz[i + 7] = (uint)c;
+ c >>= 32;
+ zz[i + 8] = (uint)c;
+ }
+ }
+
+ public static uint MulWordAddExt(uint x, uint[] yy, int yyOff, uint[] zz, int zzOff)
+ {
+ Debug.Assert(yyOff <= 8);
+ Debug.Assert(zzOff <= 8);
+ ulong c = 0, xVal = x;
+ int i = 0;
+ do
+ {
+ c += xVal * yy[yyOff + i] + zz[zzOff + i];
+ zz[zzOff + i] = (uint)c;
+ c >>= 32;
+ }
+ while (++i < 8);
+ return (uint)c;
+ }
+
+ public static uint MulWordDwordAdd(uint x, ulong y, uint[] z, int zOff)
+ {
+ Debug.Assert(zOff < 5);
+ ulong c = 0, xVal = x;
+ c += xVal * y + z[zOff + 0];
+ z[zOff + 0] = (uint)c;
+ c >>= 32;
+ c += xVal * (y >> 32) + z[zOff + 1];
+ z[zOff + 1] = (uint)c;
+ c >>= 32;
+ c += z[zOff + 2];
+ z[zOff + 2] = (uint)c;
+ c >>= 32;
+ return c == 0 ? 0 : Inc(z, zOff + 3);
+ }
+
+ public static uint MulWordExt(uint x, uint[] y, uint[] zz, int zzOff)
+ {
+ Debug.Assert(zzOff <= 8);
+ ulong c = 0, xVal = x;
+ int i = 0;
+ do
+ {
+ c += xVal * y[i];
+ zz[zzOff + i] = (uint)c;
+ c >>= 32;
+ }
+ while (++i < 8);
+ return (uint)c;
+ }
+
+ public static uint ShiftDownBit(uint[] x, int xLen, uint c)
+ {
+ int i = xLen;
+ while (--i >= 0)
+ {
+ uint next = x[i];
+ x[i] = (next >> 1) | (c << 31);
+ c = next;
+ }
+ return c << 31;
+ }
+
+ public static uint ShiftDownBit(uint[] x, uint c, uint[] z)
+ {
+ int i = 8;
+ while (--i >= 0)
+ {
+ uint next = x[i];
+ z[i] = (next >> 1) | (c << 31);
+ c = next;
+ }
+ return c << 31;
+ }
+
+ public static uint ShiftDownBits(uint[] x, int xLen, int bits, uint c)
+ {
+ Debug.Assert(bits > 0 && bits < 32);
+ int i = xLen;
+ while (--i >= 0)
+ {
+ uint next = x[i];
+ x[i] = (next >> bits) | (c << -bits);
+ c = next;
+ }
+ return c << -bits;
+ }
+
+ public static uint ShiftDownWord(uint[] x, int xLen, uint c)
+ {
+ int i = xLen;
+ while (--i >= 0)
+ {
+ uint next = x[i];
+ x[i] = c;
+ c = next;
+ }
+ return c;
+ }
+
+ public static uint ShiftUpBit(uint[] x, int xLen, uint c)
+ {
+ for (int i = 0; i < xLen; ++i)
+ {
+ uint next = x[i];
+ x[i] = (next << 1) | (c >> 31);
+ c = next;
+ }
+ return c >> 31;
+ }
+
+ public static uint ShiftUpBit(uint[] x, uint c, uint[] z)
+ {
+ for (int i = 0; i < 8; ++i)
+ {
+ uint next = x[i];
+ z[i] = (next << 1) | (c >> 31);
+ c = next;
+ }
+ return c >> 31;
+ }
+
+ public static void Square(uint[] x, uint[] zz)
+ {
+ ulong x_0 = x[0];
+ ulong zz_1;
+
+ {
+ uint c = 0;
+ int i = 7, j = 16;
+ do
+ {
+ ulong xVal = x[i--];
+ ulong p = xVal * xVal;
+ zz[--j] = (c << 31) | (uint)(p >> 33);
+ zz[--j] = (uint)(p >> 1);
+ c = (uint)p;
+ }
+ while (i > 0);
+
+ {
+ ulong p = x_0 * x_0;
+ zz_1 = (ulong)(c << 31) | (p >> 33);
+ zz[0] = (uint)(p >> 1);
+ }
+ }
+
+ ulong x_1 = x[1];
+ ulong zz_2 = zz[2];
+
+ {
+ zz_1 += x_1 * x_0;
+ zz[1] = (uint)zz_1;
+ zz_2 += zz_1 >> 32;
+ }
+
+ ulong x_2 = x[2];
+ ulong zz_3 = zz[3];
+ ulong zz_4 = zz[4];
+ {
+ zz_2 += x_2 * x_0;
+ zz[2] = (uint)zz_2;
+ zz_3 += (zz_2 >> 32) + x_2 * x_1;
+ zz_4 += zz_3 >> 32;
+ zz_3 &= M;
+ }
+
+ ulong x_3 = x[3];
+ ulong zz_5 = zz[5];
+ ulong zz_6 = zz[6];
+ {
+ zz_3 += x_3 * x_0;
+ zz[3] = (uint)zz_3;
+ zz_4 += (zz_3 >> 32) + x_3 * x_1;
+ zz_5 += (zz_4 >> 32) + x_3 * x_2;
+ zz_4 &= M;
+ zz_6 += zz_5 >> 32;
+ zz_5 &= M;
+ }
+
+ ulong x_4 = x[4];
+ ulong zz_7 = zz[7];
+ ulong zz_8 = zz[8];
+ {
+ zz_4 += x_4 * x_0;
+ zz[4] = (uint)zz_4;
+ zz_5 += (zz_4 >> 32) + x_4 * x_1;
+ zz_6 += (zz_5 >> 32) + x_4 * x_2;
+ zz_5 &= M;
+ zz_7 += (zz_6 >> 32) + x_4 * x_3;
+ zz_6 &= M;
+ zz_8 += zz_7 >> 32;
+ zz_7 &= M;
+ }
+
+ ulong x_5 = x[5];
+ ulong zz_9 = zz[9];
+ ulong zz_10 = zz[10];
+ {
+ zz_5 += x_5 * x_0;
+ zz[5] = (uint)zz_5;
+ zz_6 += (zz_5 >> 32) + x_5 * x_1;
+ zz_7 += (zz_6 >> 32) + x_5 * x_2;
+ zz_6 &= M;
+ zz_8 += (zz_7 >> 32) + x_5 * x_3;
+ zz_7 &= M;
+ zz_9 += (zz_8 >> 32) + x_5 * x_4;
+ zz_8 &= M;
+ zz_10 += zz_9 >> 32;
+ zz_9 &= M;
+ }
+
+ ulong x_6 = x[6];
+ ulong zz_11 = zz[11];
+ ulong zz_12 = zz[12];
+ {
+ zz_6 += x_6 * x_0;
+ zz[6] = (uint)zz_6;
+ zz_7 += (zz_6 >> 32) + x_6 * x_1;
+ zz_8 += (zz_7 >> 32) + x_6 * x_2;
+ zz_7 &= M;
+ zz_9 += (zz_8 >> 32) + x_6 * x_3;
+ zz_8 &= M;
+ zz_10 += (zz_9 >> 32) + x_6 * x_4;
+ zz_9 &= M;
+ zz_11 += (zz_10 >> 32) + x_6 * x_5;
+ zz_10 &= M;
+ zz_12 += zz_11 >> 32;
+ zz_11 &= M;
+ }
+
+ ulong x_7 = x[7];
+ ulong zz_13 = zz[13];
+ ulong zz_14 = zz[14];
+ {
+ zz_7 += x_7 * x_0;
+ zz[7] = (uint)zz_7;
+ zz_8 += (zz_7 >> 32) + x_7 * x_1;
+ zz_9 += (zz_8 >> 32) + x_7 * x_2;
+ zz_10 += (zz_9 >> 32) + x_7 * x_3;
+ zz_11 += (zz_10 >> 32) + x_7 * x_4;
+ zz_12 += (zz_11 >> 32) + x_7 * x_5;
+ zz_13 += (zz_12 >> 32) + x_7 * x_6;
+ zz_14 += zz_13 >> 32;
+ }
+
+ zz[8] = (uint)zz_8;
+ zz[9] = (uint)zz_9;
+ zz[10] = (uint)zz_10;
+ zz[11] = (uint)zz_11;
+ zz[12] = (uint)zz_12;
+ zz[13] = (uint)zz_13;
+ zz[14] = (uint)zz_14;
+ zz[15] += (uint)(zz_14 >> 32);
+
+ ShiftUpBit(zz, 16, (uint)x_0 << 31);
+ }
+
+ public static uint SquareWordAddExt(uint[] x, int xPos, uint[] zz)
+ {
+ Debug.Assert(xPos > 0 && xPos < 8);
+ ulong c = 0, xVal = x[xPos];
+ int i = 0;
+ do
+ {
+ c += xVal * x[i] + zz[xPos + i];
+ zz[xPos + i] = (uint)c;
+ c >>= 32;
+ }
+ while (++i < xPos);
+ return (uint)c;
+ }
+
+ public static int Sub(uint[] x, uint[] y, uint[] z)
+ {
+ long c = 0;
+ c += (long)x[0] - y[0];
+ z[0] = (uint)c;
+ c >>= 32;
+ c += (long)x[1] - y[1];
+ z[1] = (uint)c;
+ c >>= 32;
+ c += (long)x[2] - y[2];
+ z[2] = (uint)c;
+ c >>= 32;
+ c += (long)x[3] - y[3];
+ z[3] = (uint)c;
+ c >>= 32;
+ c += (long)x[4] - y[4];
+ z[4] = (uint)c;
+ c >>= 32;
+ c += (long)x[5] - y[5];
+ z[5] = (uint)c;
+ c >>= 32;
+ c += (long)x[6] - y[6];
+ z[6] = (uint)c;
+ c >>= 32;
+ c += (long)x[7] - y[7];
+ z[7] = (uint)c;
+ c >>= 32;
+ return (int)c;
+ }
+
+ public static int SubBothFrom(uint[] x, uint[] y, uint[] z)
+ {
+ long c = 0;
+ c += (long)z[0] - x[0] - y[0];
+ z[0] = (uint)c;
+ c >>= 32;
+ c += (long)z[1] - x[1] - y[1];
+ z[1] = (uint)c;
+ c >>= 32;
+ c += (long)z[2] - x[2] - y[2];
+ z[2] = (uint)c;
+ c >>= 32;
+ c += (long)z[3] - x[3] - y[3];
+ z[3] = (uint)c;
+ c >>= 32;
+ c += (long)z[4] - x[4] - y[4];
+ z[4] = (uint)c;
+ c >>= 32;
+ c += (long)z[5] - x[5] - y[5];
+ z[5] = (uint)c;
+ c >>= 32;
+ c += (long)z[6] - x[6] - y[6];
+ z[6] = (uint)c;
+ c >>= 32;
+ c += (long)z[7] - x[7] - y[7];
+ z[7] = (uint)c;
+ c >>= 32;
+ return (int)c;
+ }
+
+ // TODO Re-write to allow full range for x?
+ public static int SubDWord(ulong x, uint[] z)
+ {
+ long c = -(long)x;
+ c += (long)z[0];
+ z[0] = (uint)c;
+ c >>= 32;
+ c += (long)z[1];
+ z[1] = (uint)c;
+ c >>= 32;
+ return c == 0 ? 0 : Dec(z, 2);
+ }
+
+ public static int SubExt(uint[] xx, uint[] yy, uint[] zz)
+ {
+ long c = 0;
+ for (int i = 0; i < 16; ++i)
+ {
+ c += (long)xx[i] - yy[i];
+ zz[i] = (uint)c;
+ c >>= 32;
+ }
+ return (int)c;
+ }
+
+ public static int SubFromExt(uint[] x, int xOff, uint[] zz, int zzOff)
+ {
+ Debug.Assert(zzOff <= 8);
+ long c = 0;
+ c += (long)zz[zzOff + 0] - x[xOff + 0];
+ zz[zzOff + 0] = (uint)c;
+ c >>= 32;
+ c += (long)zz[zzOff + 1] - x[xOff + 1];
+ zz[zzOff + 1] = (uint)c;
+ c >>= 32;
+ c += (long)zz[zzOff + 2] - x[xOff + 2];
+ zz[zzOff + 2] = (uint)c;
+ c >>= 32;
+ c += (long)zz[zzOff + 3] - x[xOff + 3];
+ zz[zzOff + 3] = (uint)c;
+ c >>= 32;
+ c += (long)zz[zzOff + 4] - x[xOff + 4];
+ zz[zzOff + 4] = (uint)c;
+ c >>= 32;
+ c += (long)zz[zzOff + 5] - x[xOff + 5];
+ zz[zzOff + 5] = (uint)c;
+ c >>= 32;
+ c += (long)zz[zzOff + 6] - x[xOff + 6];
+ zz[zzOff + 6] = (uint)c;
+ c >>= 32;
+ c += (long)zz[zzOff + 7] - x[xOff + 7];
+ zz[zzOff + 7] = (uint)c;
+ c >>= 32;
+ return (int)c;
+ }
+
+ public static BigInteger ToBigInteger(uint[] x)
+ {
+ byte[] bs = new byte[32];
+ for (int i = 0; i < 8; ++i)
+ {
+ uint x_i = x[i];
+ if (x_i != 0)
+ {
+ Pack.UInt32_To_BE(x_i, bs, (7 - i) << 2);
+ }
+ }
+ return new BigInteger(1, bs);
+ }
+
+ public static void Zero(uint[] z)
+ {
+ z[0] = 0;
+ z[1] = 0;
+ z[2] = 0;
+ z[3] = 0;
+ z[4] = 0;
+ z[5] = 0;
+ z[6] = 0;
+ z[7] = 0;
+ }
+ }
+}
diff --git a/crypto/src/math/ec/custom/sec/SecP256K1Curve.cs b/crypto/src/math/ec/custom/sec/SecP256K1Curve.cs
new file mode 100644
index 000000000..2e0a4a5e4
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/SecP256K1Curve.cs
@@ -0,0 +1,93 @@
+using System;
+
+using Org.BouncyCastle.Math.Field;
+using Org.BouncyCastle.Utilities.Encoders;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+ internal class SecP256K1Curve
+ : ECCurve
+ {
+ public static readonly BigInteger q = new BigInteger(1,
+ Hex.Decode("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F"));
+
+ private const int SECP256K1_DEFAULT_COORDS = COORD_JACOBIAN;
+
+ protected readonly SecP256K1Point m_infinity;
+
+ public SecP256K1Curve()
+ : base(FiniteFields.GetPrimeField(q))
+ {
+ this.m_infinity = new SecP256K1Point(this, null, null);
+
+ this.m_a = FromBigInteger(BigInteger.Zero);
+ this.m_b = FromBigInteger(BigInteger.ValueOf(7));
+ //this.order = new BigInteger(1, Hex.decode("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141"));
+ //this.cofactor = BigInteger.valueOf(1);
+ this.m_coord = SECP256K1_DEFAULT_COORDS;
+ }
+
+ protected override ECCurve CloneCurve()
+ {
+ return new SecP256K1Curve();
+ }
+
+ public override bool SupportsCoordinateSystem(int coord)
+ {
+ switch (coord)
+ {
+ case COORD_JACOBIAN:
+ return true;
+ default:
+ return false;
+ }
+ }
+
+ public virtual BigInteger Q
+ {
+ get { return q; }
+ }
+
+ public override ECPoint Infinity
+ {
+ get { return m_infinity; }
+ }
+
+ public override int FieldSize
+ {
+ get { return q.BitLength; }
+ }
+
+ public override ECFieldElement FromBigInteger(BigInteger x)
+ {
+ return new SecP256K1FieldElement(x);
+ }
+
+ protected internal override ECPoint CreateRawPoint(ECFieldElement x, ECFieldElement y, bool withCompression)
+ {
+ return new SecP256K1Point(this, x, y, withCompression);
+ }
+
+ protected override ECPoint DecompressPoint(int yTilde, BigInteger X1)
+ {
+ ECFieldElement x = FromBigInteger(X1);
+ ECFieldElement alpha = x.Square().Add(m_a).Multiply(x).Add(m_b);
+ ECFieldElement beta = alpha.Sqrt();
+
+ //
+ // if we can't find a sqrt we haven't got a point on the
+ // curve - run!
+ //
+ if (beta == null)
+ throw new ArithmeticException("Invalid point compression");
+
+ if (beta.TestBitZero() != (yTilde == 1))
+ {
+ // Use the other root
+ beta = beta.Negate();
+ }
+
+ return new SecP256K1Point(this, x, beta, true);
+ }
+ }
+}
diff --git a/crypto/src/math/ec/custom/sec/SecP256K1Field.cs b/crypto/src/math/ec/custom/sec/SecP256K1Field.cs
new file mode 100644
index 000000000..ec2c36e9f
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/SecP256K1Field.cs
@@ -0,0 +1,142 @@
+using System;
+using System.Diagnostics;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+ internal class SecP256K1Field
+ {
+ // 2^256 - 2^32 - 2^9 - 2^8 - 2^7 - 2^6 - 2^4 - 1
+ internal static readonly uint[] P = new uint[]{ 0xFFFFFC2F, 0xFFFFFFFE, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
+ 0xFFFFFFFF, 0xFFFFFFFF };
+ private const uint P7 = 0xFFFFFFFF;
+ private static readonly uint[] PExt = new uint[]{ 0x000E90A1, 0x000007A2, 0x00000001, 0x00000000, 0x00000000,
+ 0x00000000, 0x00000000, 0x00000000, 0xFFFFF85E, 0xFFFFFFFD, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF,
+ 0xFFFFFFFF, 0xFFFFFFFF };
+ private const uint PExt15 = 0xFFFFFFFF;
+ private static readonly ulong PInv = 0x00000001000003D1UL;
+
+ public static void Add(uint[] x, uint[] y, uint[] z)
+ {
+ uint c = Nat256.Add(x, y, z);
+ if (c != 0 || (z[7] == P7 && Nat256.Gte(z, P)))
+ {
+ Nat256.AddDWord(PInv, z, 0);
+ }
+ }
+
+ public static void AddExt(uint[] xx, uint[] yy, uint[] zz)
+ {
+ uint c = Nat256.AddExt(xx, yy, zz);
+ if (c != 0 || (zz[15] == PExt15 && Nat256.GteExt(zz, PExt)))
+ {
+ Nat256.SubExt(zz, PExt, zz);
+ }
+ }
+
+ public static void AddOne(uint[] x, uint[] z)
+ {
+ Array.Copy(x, 0, z, 0, 8);
+ uint c = Nat256.Inc(z, 0);
+ if (c != 0 || (z[7] == P7 && Nat256.Gte(z, P)))
+ {
+ Nat256.AddDWord(PInv, z, 0);
+ }
+ }
+
+ public static uint[] FromBigInteger(BigInteger x)
+ {
+ uint[] z = Nat256.FromBigInteger(x);
+ if (z[7] == P7 && Nat256.Gte(z, P))
+ {
+ Nat256.AddDWord(PInv, z, 0);
+ }
+ return z;
+ }
+
+ public static void Half(uint[] x, uint[] z)
+ {
+ if ((x[0] & 1) == 0)
+ {
+ Nat256.ShiftDownBit(x, 0, z);
+ }
+ else
+ {
+ uint c = Nat256.Add(x, P, z);
+ Nat256.ShiftDownBit(z, c, z);
+ }
+ }
+
+ public static void Multiply(uint[] x, uint[] y, uint[] z)
+ {
+ uint[] tt = Nat256.CreateExt();
+ Nat256.Mul(x, y, tt);
+ Reduce(tt, z);
+ }
+
+ public static void Negate(uint[] x, uint[] z)
+ {
+ if (Nat256.IsZero(x))
+ {
+ Nat256.Zero(z);
+ }
+ else
+ {
+ Nat256.Sub(P, x, z);
+ }
+ }
+
+ public static void Reduce(uint[] tt, uint[] z)
+ {
+ long extra = -(long)tt[8];
+ extra += (long)Nat256.MulWordAddExt((uint)PInv, tt, 8, tt, 0);
+ extra += (long)Nat256.AddToExt(tt, 8, tt, 1) << 32;
+ extra += (long)tt[8];
+
+ ulong c = Nat256.MulWordDwordAdd((uint)PInv, (ulong)extra, tt, 0);
+ c += Nat256.AddDWord((ulong)extra, tt, 1);
+
+ Debug.Assert(c == 0 || c == 1);
+
+ if (c != 0 || (tt[7] == P7 && Nat256.Gte(tt, P)))
+ {
+ Nat256.AddDWord(PInv, tt, 0);
+ }
+
+ Array.Copy(tt, 0, z, 0, 8);
+ }
+
+ public static void Square(uint[] x, uint[] z)
+ {
+ uint[] tt = Nat256.CreateExt();
+ Nat256.Square(x, tt);
+ Reduce(tt, z);
+ }
+
+ public static void Subtract(uint[] x, uint[] y, uint[] z)
+ {
+ int c = Nat256.Sub(x, y, z);
+ if (c != 0)
+ {
+ Nat256.SubDWord(PInv, z);
+ }
+ }
+
+ public static void SubtractExt(uint[] xx, uint[] yy, uint[] zz)
+ {
+ int c = Nat256.SubExt(xx, yy, zz);
+ if (c != 0)
+ {
+ Nat256.AddExt(zz, PExt, zz);
+ }
+ }
+
+ public static void Twice(uint[] x, uint[] z)
+ {
+ uint c = Nat256.ShiftUpBit(x, 0, z);
+ if (c != 0 || (z[7] == P7 && Nat256.Gte(z, P)))
+ {
+ Nat256.AddDWord(PInv, z, 0);
+ }
+ }
+ }
+}
diff --git a/crypto/src/math/ec/custom/sec/SecP256K1FieldElement.cs b/crypto/src/math/ec/custom/sec/SecP256K1FieldElement.cs
new file mode 100644
index 000000000..4da1013d1
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/SecP256K1FieldElement.cs
@@ -0,0 +1,157 @@
+using System;
+using System.Diagnostics;
+
+using Org.BouncyCastle.Utilities;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+ internal class SecP256K1FieldElement
+ : ECFieldElement
+ {
+ public static readonly BigInteger Q = SecP256K1Curve.q;
+
+ protected internal readonly uint[] x;
+
+ public SecP256K1FieldElement(BigInteger x)
+ {
+ if (x == null || x.SignValue < 0 || x.CompareTo(Q) >= 0)
+ throw new ArgumentException("value invalid for SecP256K1FieldElement", "x");
+
+ this.x = SecP256K1Field.FromBigInteger(x);
+ }
+
+ public SecP256K1FieldElement()
+ {
+ this.x = Nat256.Create();
+ }
+
+ protected internal SecP256K1FieldElement(uint[] x)
+ {
+ this.x = x;
+ }
+
+ public override bool IsZero
+ {
+ get { return Nat256.IsZero(x); }
+ }
+
+ public override bool IsOne
+ {
+ get { return Nat256.IsOne(x); }
+ }
+
+ public override bool TestBitZero()
+ {
+ return Nat256.GetBit(x, 0) == 1;
+ }
+
+ public override BigInteger ToBigInteger()
+ {
+ return Nat256.ToBigInteger(x);
+ }
+
+ public override string FieldName
+ {
+ get { return "SecP256K1Field"; }
+ }
+
+ public override int FieldSize
+ {
+ get { return Q.BitLength; }
+ }
+
+ public override ECFieldElement Add(ECFieldElement b)
+ {
+ uint[] z = Nat256.Create();
+ SecP256K1Field.Add(x, ((SecP256K1FieldElement)b).x, z);
+ return new SecP256K1FieldElement(z);
+ }
+
+ public override ECFieldElement AddOne()
+ {
+ uint[] z = Nat256.Create();
+ SecP256K1Field.AddOne(x, z);
+ return new SecP256K1FieldElement(z);
+ }
+
+ public override ECFieldElement Subtract(ECFieldElement b)
+ {
+ uint[] z = Nat256.Create();
+ SecP256K1Field.Subtract(x, ((SecP256K1FieldElement)b).x, z);
+ return new SecP256K1FieldElement(z);
+ }
+
+ public override ECFieldElement Multiply(ECFieldElement b)
+ {
+ uint[] z = Nat256.Create();
+ SecP256K1Field.Multiply(x, ((SecP256K1FieldElement)b).x, z);
+ return new SecP256K1FieldElement(z);
+ }
+
+ public override ECFieldElement Divide(ECFieldElement b)
+ {
+ // return Multiply(b.Invert());
+ uint[] z = Nat256.Create();
+ Mod.Invert(SecP256K1Field.P, ((SecP256K1FieldElement)b).x, z);
+ SecP256K1Field.Multiply(z, x, z);
+ return new SecP256K1FieldElement(z);
+ }
+
+ public override ECFieldElement Negate()
+ {
+ uint[] z = Nat256.Create();
+ SecP256K1Field.Negate(x, z);
+ return new SecP256K1FieldElement(z);
+ }
+
+ public override ECFieldElement Square()
+ {
+ uint[] z = Nat256.Create();
+ SecP256K1Field.Square(x, z);
+ return new SecP256K1FieldElement(z);
+ }
+
+ public override ECFieldElement Invert()
+ {
+ // return new SecP256K1FieldElement(ToBigInteger().ModInverse(Q));
+ uint[] z = Nat256.Create();
+ Mod.Invert(SecP256K1Field.P, x, z);
+ return new SecP256K1FieldElement(z);
+ }
+
+ // D.1.4 91
+ /**
+ * return a sqrt root - the routine verifies that the calculation returns the right value - if
+ * none exists it returns null.
+ */
+ public override ECFieldElement Sqrt()
+ {
+ ECFieldElement root = new FpFieldElement(Q, ToBigInteger()).Sqrt();
+ return root == null ? null : new SecP256K1FieldElement(root.ToBigInteger());
+ }
+
+ public override bool Equals(object obj)
+ {
+ return Equals(obj as SecP256K1FieldElement);
+ }
+
+ public override bool Equals(ECFieldElement other)
+ {
+ return Equals(other as SecP256K1FieldElement);
+ }
+
+ public virtual bool Equals(SecP256K1FieldElement other)
+ {
+ if (this == other)
+ return true;
+ if (null == other)
+ return false;
+ return Arrays.AreEqual(x, other.x);
+ }
+
+ public override int GetHashCode()
+ {
+ return Q.GetHashCode() ^ Arrays.GetHashCode(x);
+ }
+ }
+}
diff --git a/crypto/src/math/ec/custom/sec/SecP256K1Point.cs b/crypto/src/math/ec/custom/sec/SecP256K1Point.cs
new file mode 100644
index 000000000..e2a22fbe7
--- /dev/null
+++ b/crypto/src/math/ec/custom/sec/SecP256K1Point.cs
@@ -0,0 +1,275 @@
+using System;
+
+namespace Org.BouncyCastle.Math.EC.Custom.Sec
+{
+ internal class SecP256K1Point
+ : ECPointBase
+ {
+ /**
+ * Create a point which encodes with point compression.
+ *
+ * @param curve
+ * the curve to use
+ * @param x
+ * affine x co-ordinate
+ * @param y
+ * affine y co-ordinate
+ *
+ * @deprecated Use ECCurve.createPoint to construct points
+ */
+ public SecP256K1Point(ECCurve curve, ECFieldElement x, ECFieldElement y)
+ : this(curve, x, y, false)
+ {
+ }
+
+ /**
+ * Create a point that encodes with or without point compresion.
+ *
+ * @param curve
+ * the curve to use
+ * @param x
+ * affine x co-ordinate
+ * @param y
+ * affine y co-ordinate
+ * @param withCompression
+ * if true encode with point compression
+ *
+ * @deprecated per-point compression property will be removed, refer
+ * {@link #getEncoded(bool)}
+ */
+ public SecP256K1Point(ECCurve curve, ECFieldElement x, ECFieldElement y, bool withCompression)
+ : base(curve, x, y, withCompression)
+ {
+ if ((x == null) != (y == null))
+ throw new ArgumentException("Exactly one of the field elements is null");
+ }
+
+ internal SecP256K1Point(ECCurve curve, ECFieldElement x, ECFieldElement y, ECFieldElement[] zs,
+ bool withCompression)
+ : base(curve, x, y, zs, withCompression)
+ {
+ }
+
+ protected internal override bool CompressionYTilde
+ {
+ get { return this.AffineYCoord.TestBitZero(); }
+ }
+
+ // B.3 pg 62
+ public override ECPoint Add(ECPoint b)
+ {
+ if (this.IsInfinity)
+ return b;
+ if (b.IsInfinity)
+ return this;
+ if (this == b)
+ return Twice();
+
+ ECCurve curve = this.Curve;
+
+ SecP256K1FieldElement X1 = (SecP256K1FieldElement)this.RawXCoord, Y1 = (SecP256K1FieldElement)this.RawYCoord;
+ SecP256K1FieldElement X2 = (SecP256K1FieldElement)b.RawXCoord, Y2 = (SecP256K1FieldElement)b.RawYCoord;
+
+ SecP256K1FieldElement Z1 = (SecP256K1FieldElement)this.RawZCoords[0];
+ SecP256K1FieldElement Z2 = (SecP256K1FieldElement)b.RawZCoords[0];
+
+ uint[] tt1 = Nat256.CreateExt();
+ uint[] tt2 = Nat256.CreateExt();
+ uint[] t3 = Nat256.Create();
+ uint[] t4 = Nat256.Create();
+
+ bool Z1IsOne = Z1.IsOne;
+ uint[] U2, S2;
+ if (Z1IsOne)
+ {
+ U2 = X2.x;
+ S2 = Y2.x;
+ }
+ else
+ {
+ S2 = t3;
+ SecP256K1Field.Square(Z1.x, S2);
+
+ U2 = tt2;
+ SecP256K1Field.Multiply(S2, X2.x, U2);
+
+ SecP256K1Field.Multiply(S2, Z1.x, S2);
+ SecP256K1Field.Multiply(S2, Y2.x, S2);
+ }
+
+ bool Z2IsOne = Z2.IsOne;
+ uint[] U1, S1;
+ if (Z2IsOne)
+ {
+ U1 = X1.x;
+ S1 = Y1.x;
+ }
+ else
+ {
+ S1 = t4;
+ SecP256K1Field.Square(Z2.x, S1);
+
+ U1 = tt1;
+ SecP256K1Field.Multiply(S1, X1.x, U1);
+
+ SecP256K1Field.Multiply(S1, Z2.x, S1);
+ SecP256K1Field.Multiply(S1, Y1.x, S1);
+ }
+
+ uint[] H = Nat256.Create();
+ SecP256K1Field.Subtract(U1, U2, H);
+
+ uint[] R = tt2;
+ SecP256K1Field.Subtract(S1, S2, R);
+
+ // Check if b == this or b == -this
+ if (Nat256.IsZero(H))
+ {
+ if (Nat256.IsZero(R))
+ {
+ // this == b, i.e. this must be doubled
+ return this.Twice();
+ }
+
+ // this == -b, i.e. the result is the point at infinity
+ return curve.Infinity;
+ }
+
+ uint[] HSquared = t3;
+ SecP256K1Field.Square(H, HSquared);
+
+ uint[] G = Nat256.Create();
+ SecP256K1Field.Multiply(HSquared, H, G);
+
+ uint[] V = t3;
+ SecP256K1Field.Multiply(HSquared, U1, V);
+
+ Nat256.Mul(S1, G, tt1);
+
+ SecP256K1FieldElement X3 = new SecP256K1FieldElement(t4);
+ SecP256K1Field.Square(R, X3.x);
+ SecP256K1Field.Add(X3.x, G, X3.x);
+ SecP256K1Field.Subtract(X3.x, V, X3.x);
+ SecP256K1Field.Subtract(X3.x, V, X3.x);
+
+ SecP256K1FieldElement Y3 = new SecP256K1FieldElement(G);
+ SecP256K1Field.Subtract(V, X3.x, Y3.x);
+ Nat256.Mul(Y3.x, R, tt2);
+ SecP256K1Field.SubtractExt(tt2, tt1, tt2);
+ SecP256K1Field.Reduce(tt2, Y3.x);
+
+ SecP256K1FieldElement Z3 = new SecP256K1FieldElement(H);
+ if (!Z1IsOne)
+ {
+ SecP256K1Field.Multiply(Z3.x, Z1.x, Z3.x);
+ }
+ if (!Z2IsOne)
+ {
+ SecP256K1Field.Multiply(Z3.x, Z2.x, Z3.x);
+ }
+
+ ECFieldElement[] zs = new ECFieldElement[] { Z3 };
+
+ return new SecP256K1Point(curve, X3, Y3, zs, IsCompressed);
+ }
+
+ // B.3 pg 62
+ public override ECPoint Twice()
+ {
+ if (this.IsInfinity)
+ return this;
+
+ ECCurve curve = this.Curve;
+
+ SecP256K1FieldElement Y1 = (SecP256K1FieldElement)this.RawYCoord;
+ if (Y1.IsZero)
+ return curve.Infinity;
+
+ SecP256K1FieldElement X1 = (SecP256K1FieldElement)this.RawXCoord, Z1 = (SecP256K1FieldElement)this.RawZCoords[0];
+
+ uint[] Y1Squared = Nat256.Create();
+ SecP256K1Field.Square(Y1.x, Y1Squared);
+
+ uint[] T = Nat256.Create();
+ SecP256K1Field.Square(Y1Squared, T);
+
+ uint[] t1 = Nat256.Create();
+ SecP256K1Field.Square(X1.x, t1);
+
+ uint[] M = Nat256.Create();
+ SecP256K1Field.Twice(t1, M);
+ SecP256K1Field.Add(M, t1, M);
+
+ uint[] S = Y1Squared;
+ SecP256K1Field.Multiply(Y1Squared, X1.x, S);
+ SecP256K1Field.Twice(S, S);
+ SecP256K1Field.Twice(S, S);
+
+ SecP256K1Field.Twice(T, t1);
+ SecP256K1Field.Twice(t1, t1);
+ SecP256K1Field.Twice(t1, t1);
+
+ SecP256K1FieldElement X3 = new SecP256K1FieldElement(T);
+ SecP256K1Field.Square(M, X3.x);
+ SecP256K1Field.Subtract(X3.x, S, X3.x);
+ SecP256K1Field.Subtract(X3.x, S, X3.x);
+
+ SecP256K1FieldElement Y3 = new SecP256K1FieldElement(S);
+ SecP256K1Field.Subtract(S, X3.x, Y3.x);
+ SecP256K1Field.Multiply(Y3.x, M, Y3.x);
+ SecP256K1Field.Subtract(Y3.x, t1, Y3.x);
+
+ SecP256K1FieldElement Z3 = new SecP256K1FieldElement(M);
+ SecP256K1Field.Twice(Y1.x, Z3.x);
+ if (!Z1.IsOne)
+ {
+ SecP256K1Field.Multiply(Z3.x, Z1.x, Z3.x);
+ }
+
+ return new SecP256K1Point(curve, X3, Y3, new ECFieldElement[] { Z3 }, IsCompressed);
+ }
+
+ public override ECPoint TwicePlus(ECPoint b)
+ {
+ if (this == b)
+ return ThreeTimes();
+ if (this.IsInfinity)
+ return b;
+ if (b.IsInfinity)
+ return Twice();
+
+ ECFieldElement Y1 = this.RawYCoord;
+ if (Y1.IsZero)
+ return b;
+
+ return Twice().Add(b);
+ }
+
+ public override ECPoint ThreeTimes()
+ {
+ if (this.IsInfinity || this.RawYCoord.IsZero)
+ return this;
+
+ // NOTE: Be careful about recursions between TwicePlus and ThreeTimes
+ return Twice().Add(this);
+ }
+
+ // D.3.2 pg 102 (see Note:)
+ public override ECPoint Subtract(ECPoint b)
+ {
+ if (b.IsInfinity)
+ return this;
+
+ // Add -b
+ return Add(b.Negate());
+ }
+
+ public override ECPoint Negate()
+ {
+ if (IsInfinity)
+ return this;
+
+ return new SecP256K1Point(Curve, RawXCoord, RawYCoord.Negate(), RawZCoords, IsCompressed);
+ }
+ }
+}
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