diff --git a/crypto/src/math/ec/Nat.cs b/crypto/src/math/ec/Nat.cs
new file mode 100644
index 000000000..cc8996dfc
--- /dev/null
+++ b/crypto/src/math/ec/Nat.cs
@@ -0,0 +1,495 @@
+using System;
+
+using Org.BouncyCastle.Crypto.Utilities;
+using Org.BouncyCastle.Math;
+
+namespace Org.BouncyCastle.Math.EC
+{
+ internal abstract class Nat
+ {
+ public static uint Add(int len, uint[] x, uint[] y, uint[] z)
+ {
+ ulong c = 0;
+ for (int i = 0; i < len; ++i)
+ {
+ c += (ulong)x[i] + y[i];
+ z[i] = (uint)c;
+ c >>= 32;
+ }
+ return (uint)c;
+ }
+
+ public static uint AddBothTo(int len, uint[] x, uint[] y, uint[] z)
+ {
+ ulong c = 0;
+ for (int i = 0; i < len; ++i)
+ {
+ c += (ulong)x[i] + y[i] + z[i];
+ z[i] = (uint)c;
+ c >>= 32;
+ }
+ return (uint)c;
+ }
+
+ public static uint AddDWord(int len, ulong x, uint[] z, int zOff)
+ {
+ // assert zOff < (len - 2);
+ 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(len, z, zOff + 2);
+ }
+
+ public static uint AddExt(int len, uint[] xx, uint[] yy, uint[] zz)
+ {
+ int extLen = len << 1;
+ ulong c = 0;
+ for (int i = 0; i < extLen; ++i)
+ {
+ c += (ulong)xx[i] + yy[i];
+ zz[i] = (uint)c;
+ c >>= 32;
+ }
+ return (uint)c;
+ }
+
+ public static uint AddToExt(int len, uint[] x, int xOff, uint[] zz, int zzOff)
+ {
+ // assert zzOff <= len;
+ ulong c = 0;
+ for (int i = 0; i < len; ++i)
+ {
+ c += (ulong)x[xOff + i] + zz[zzOff + i];
+ zz[zzOff + i] = (uint)c;
+ c >>= 32;
+ }
+ return (uint)c;
+ }
+
+ public static uint AddWordExt(int len, uint x, uint[] zz, int zzOff)
+ {
+ // assert zzOff < ((len << 1) - 1);
+ ulong c = (ulong)x + zz[zzOff];
+ zz[zzOff] = (uint)c;
+ c >>= 32;
+ return c == 0 ? 0 : IncExt(len, zz, zzOff + 1);
+ }
+
+ public static uint[] Copy(int len, uint[] x)
+ {
+ uint[] z = new uint[len];
+ Array.Copy(x, 0, z, 0, len);
+ return z;
+ }
+
+ public static uint[] Create(int len)
+ {
+ return new uint[len];
+ }
+
+ public static uint[] CreateExt(int len)
+ {
+ int extLen = len << 1;
+ return new uint[extLen];
+ }
+
+ public static int Dec(int len, uint[] z, int zOff)
+ {
+ // assert zOff < len;
+ int i = zOff;
+ do
+ {
+ if (--z[i] != uint.MaxValue)
+ {
+ return 0;
+ }
+ }
+ while (++i < len);
+ return -1;
+ }
+
+ public static uint[] FromBigInteger(int len, BigInteger x)
+ {
+ if (x.SignValue < 0 || x.BitLength > (len << 5))
+ throw new ArgumentException();
+
+ uint[] z = Create(len);
+ 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;
+ }
+ uint w = (uint)bit >> 5;
+ int b = bit & 31;
+ return (x[w] >> b) & 1;
+ }
+
+ public static bool Gte(int len, uint[] x, uint[] y)
+ {
+ for (int i = len - 1; 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(int len, uint[] xx, uint[] yy)
+ {
+ int extLen = len << 1;
+ for (int i = extLen - 1; 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(int len, uint[] z, int zOff)
+ {
+ // assert zOff < len;
+ for (int i = zOff; i < len; ++i)
+ {
+ if (++z[i] != 0)
+ {
+ return 0;
+ }
+ }
+ return 1;
+ }
+
+ public static uint IncExt(int len, uint[] zz, int zzOff)
+ {
+ int extLen = len;
+ // assert zzOff < extLen;
+ for (int i = zzOff; i < extLen; ++i)
+ {
+ if (++zz[i] != 0)
+ {
+ return 0;
+ }
+ }
+ return 1;
+ }
+
+ public static bool IsOne(int len, uint[] x)
+ {
+ if (x[0] != 1)
+ {
+ return false;
+ }
+ for (int i = 1; i < len; ++i)
+ {
+ if (x[i] != 0)
+ {
+ return false;
+ }
+ }
+ return true;
+ }
+
+ public static bool IsZero(int len, uint[] x)
+ {
+ if (x[0] != 0)
+ {
+ return false;
+ }
+ for (int i = 1; i < len; ++i)
+ {
+ if (x[i] != 0)
+ {
+ return false;
+ }
+ }
+ return true;
+ }
+
+ public static bool isZeroExt(int len, uint[] xx)
+ {
+ if (xx[0] != 0)
+ {
+ return false;
+ }
+ int extLen = len << 1;
+ for (int i = 1; i < extLen; ++i)
+ {
+ if (xx[i] != 0)
+ {
+ return false;
+ }
+ }
+ return true;
+ }
+
+ public static void Mul(int len, uint[] x, uint[] y, uint[] zz)
+ {
+ zz[len] = (uint)MulWordExt(len, x[0], y, zz, 0);
+
+ for (int i = 1; i < len; ++i)
+ {
+ zz[i + len] = (uint)MulWordAddExt(len, x[i], y, 0, zz, i);
+ }
+ }
+
+ public static uint MulWordAddExt(int len, uint x, uint[] yy, int yyOff, uint[] zz, int zzOff)
+ {
+ // assert yyOff <= len;
+ // assert zzOff <= len;
+ ulong c = 0, xVal = (ulong)x;
+ int i = 0;
+ do
+ {
+ c += xVal * yy[yyOff + i] + zz[zzOff + i];
+ zz[zzOff + i] = (uint)c;
+ c >>= 32;
+ }
+ while (++i < len);
+ return (uint)c;
+ }
+
+ public static uint SquareWordAddExt(int len, uint[] x, int xPos, uint[] zz)
+ {
+ // assert xPos > 0 && xPos < len;
+ ulong c = 0, xVal = (ulong)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 uint MulWordDwordAdd(int len, uint x, ulong y, uint[] z, int zOff)
+ {
+ // assert zOff < (len - 3);
+ ulong c = 0, xVal = (ulong)x;
+ c += xVal * (uint)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 += (ulong)z[zOff + 2];
+ z[zOff + 2] = (uint)c;
+ c >>= 32;
+ return c == 0 ? 0 : Inc(len, z, zOff + 3);
+ }
+
+ public static uint MulWordExt(int len, uint x, uint[] y, uint[] zz, int zzOff)
+ {
+ // assert zzOff <= len;
+ ulong c = 0, xVal = (ulong)x;
+ int i = 0;
+ do
+ {
+ c += xVal * y[i];
+ zz[zzOff + i] = (uint)c;
+ c >>= 32;
+ }
+ while (++i < len);
+ 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(int len, uint[] x, uint c, uint[] z)
+ {
+ int i = len;
+ 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)
+ {
+ //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 << 32 - 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(int len, uint[] x, uint c, uint[] z)
+ {
+ for (int i = 0; i < len; ++i)
+ {
+ uint next = x[i];
+ z[i] = (next << 1) | (c >> 31);
+ c = next;
+ }
+ return c >> 31;
+ }
+
+ public static void Square(int len, uint[] x, uint[] zz)
+ {
+ int extLen = len << 1;
+ uint c = 0;
+ int j = len, k = extLen;
+ do
+ {
+ ulong xVal = (ulong)x[--j];
+ ulong p = xVal * xVal;
+ zz[--k] = (c << 31) | (uint)(p >> 33);
+ zz[--k] = (uint)(p >> 1);
+ c = (uint)p;
+ }
+ while (j > 0);
+
+ for (int i = 1; i < len; ++i)
+ {
+ c = SquareWordAddExt(len, x, i, zz);
+ AddWordExt(len, c, zz, i << 1);
+ }
+
+ ShiftUpBit(zz, extLen, x[0] << 31);
+ }
+
+ public static int Sub(int len, uint[] x, uint[] y, uint[] z)
+ {
+ long c = 0;
+ for (int i = 0; i < len; ++i)
+ {
+ c += (long)x[i] - y[i];
+ z[i] = (uint)c;
+ c >>= 32;
+ }
+ return (int)c;
+ }
+
+ public static int SubBothFrom(int len, uint[] x, uint[] y, uint[] z)
+ {
+ long c = 0;
+ for (int i = 0; i < len; ++i)
+ {
+ c += (long)z[i] - x[i] - y[i];
+ z[i] = (uint)c;
+ c >>= 32;
+ }
+ return (int)c;
+ }
+
+ public static int SubDWord(int len, 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(len, z, 2);
+ }
+
+ public static int SubExt(int len, uint[] xx, uint[] yy, uint[] zz)
+ {
+ int extLen = len << 1;
+ long c = 0;
+ for (int i = 0; i < extLen; ++i)
+ {
+ c += (long)xx[i] - yy[i];
+ zz[i] = (uint)c;
+ c >>= 32;
+ }
+ return (int)c;
+ }
+
+ public static uint SubFromExt(int len, uint[] x, int xOff, uint[] zz, int zzOff)
+ {
+ // assert zzOff <= len;
+ ulong c = 0;
+ for (int i = 0; i < len; ++i)
+ {
+ c += (ulong)zz[zzOff + i] - x[xOff + i];
+ zz[zzOff + i] = (uint)c;
+ c >>= 32;
+ }
+ return (uint)c;
+ }
+
+ public static BigInteger ToBigInteger(int len, uint[] x)
+ {
+ byte[] bs = new byte[len << 2];
+ for (int i = 0; i < len; ++i)
+ {
+ uint x_i = x[i];
+ if (x_i != 0)
+ {
+ Pack.UInt32_To_BE(x_i, bs, (len - 1 - i) << 2);
+ }
+ }
+ return new BigInteger(1, bs);
+ }
+
+ public static void Zero(int len, uint[] z)
+ {
+ for (int i = 0; i < len; ++i)
+ {
+ z[i] = 0;
+ }
+ }
+ }
+}
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