diff --git a/crypto/crypto.csproj b/crypto/crypto.csproj
index 1c2f6a7df..abc4f6050 100644
--- a/crypto/crypto.csproj
+++ b/crypto/crypto.csproj
@@ -4654,6 +4654,11 @@
BuildAction = "Compile"
/>
<File
+ RelPath = "src\math\ec\LongArray.cs"
+ SubType = "Code"
+ BuildAction = "Compile"
+ />
+ <File
RelPath = "src\math\ec\abc\SimpleBigDecimal.cs"
SubType = "Code"
BuildAction = "Compile"
diff --git a/crypto/src/math/ec/ECFieldElement.cs b/crypto/src/math/ec/ECFieldElement.cs
index fb0e8535b..9ebf6f41e 100644
--- a/crypto/src/math/ec/ECFieldElement.cs
+++ b/crypto/src/math/ec/ECFieldElement.cs
@@ -873,41 +873,38 @@ namespace Org.BouncyCastle.Math.EC
*/
private int m;
- /**
- * Tpb: The integer <code>k</code> where <code>x<sup>m</sup> +
- * x<sup>k</sup> + 1</code> represents the reduction polynomial
- * <code>f(z)</code>.<br/>
- * Ppb: The integer <code>k1</code> where <code>x<sup>m</sup> +
- * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
- * represents the reduction polynomial <code>f(z)</code>.<br/>
- */
- private int k1;
-
- /**
- * Tpb: Always set to <code>0</code><br/>
- * Ppb: The integer <code>k2</code> where <code>x<sup>m</sup> +
- * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
- * represents the reduction polynomial <code>f(z)</code>.<br/>
- */
- private int k2;
-
- /**
- * Tpb: Always set to <code>0</code><br/>
- * Ppb: The integer <code>k3</code> where <code>x<sup>m</sup> +
- * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
- * represents the reduction polynomial <code>f(z)</code>.<br/>
- */
- private int k3;
+ ///**
+ // * Tpb: The integer <code>k</code> where <code>x<sup>m</sup> +
+ // * x<sup>k</sup> + 1</code> represents the reduction polynomial
+ // * <code>f(z)</code>.<br/>
+ // * Ppb: The integer <code>k1</code> where <code>x<sup>m</sup> +
+ // * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
+ // * represents the reduction polynomial <code>f(z)</code>.<br/>
+ // */
+ //private int k1;
+
+ ///**
+ // * Tpb: Always set to <code>0</code><br/>
+ // * Ppb: The integer <code>k2</code> where <code>x<sup>m</sup> +
+ // * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
+ // * represents the reduction polynomial <code>f(z)</code>.<br/>
+ // */
+ //private int k2;
+
+ ///**
+ // * Tpb: Always set to <code>0</code><br/>
+ // * Ppb: The integer <code>k3</code> where <code>x<sup>m</sup> +
+ // * x<sup>k3</sup> + x<sup>k2</sup> + x<sup>k1</sup> + 1</code>
+ // * represents the reduction polynomial <code>f(z)</code>.<br/>
+ // */
+ //private int k3;
+
+ private int[] ks;
/**
- * The <code>IntArray</code> holding the bits.
+ * The <code>LongArray</code> holding the bits.
*/
- private IntArray x;
-
- /**
- * The number of <code>int</code>s required to hold <code>m</code> bits.
- */
- private readonly int t;
+ private LongArray x;
/**
* Constructor for Ppb.
@@ -931,13 +928,10 @@ namespace Org.BouncyCastle.Math.EC
int k3,
BigInteger x)
{
- // t = m / 32 rounded up to the next integer
- this.t = (m + 31) >> 5;
- this.x = new IntArray(x, t);
-
if ((k2 == 0) && (k3 == 0))
{
this.representation = Tpb;
+ this.ks = new int[] { k1 };
}
else
{
@@ -947,15 +941,11 @@ namespace Org.BouncyCastle.Math.EC
throw new ArgumentException("k2 must be larger than 0");
this.representation = Ppb;
+ this.ks = new int[] { k1, k2, k3 };
}
- if (x.SignValue < 0)
- throw new ArgumentException("x value cannot be negative");
-
this.m = m;
- this.k1 = k1;
- this.k2 = k2;
- this.k3 = k3;
+ this.x = new LongArray(x);
}
/**
@@ -976,23 +966,12 @@ namespace Org.BouncyCastle.Math.EC
// Set k1 to k, and set k2 and k3 to 0
}
- private F2mFieldElement(int m, int k1, int k2, int k3, IntArray x)
+ private F2mFieldElement(int m, int[] ks, LongArray x)
{
- t = (m + 31) >> 5;
- this.x = x;
this.m = m;
- this.k1 = k1;
- this.k2 = k2;
- this.k3 = k3;
-
- if ((k2 == 0) && (k3 == 0))
- {
- this.representation = Tpb;
- }
- else
- {
- this.representation = Ppb;
- }
+ this.representation = (ks.Length == 1) ? Tpb : Ppb;
+ this.ks = ks;
+ this.x = x;
}
public override BigInteger ToBigInteger()
@@ -1034,19 +1013,15 @@ namespace Org.BouncyCastle.Math.EC
F2mFieldElement aF2m = (F2mFieldElement)a;
F2mFieldElement bF2m = (F2mFieldElement)b;
- if ((aF2m.m != bF2m.m) || (aF2m.k1 != bF2m.k1)
- || (aF2m.k2 != bF2m.k2) || (aF2m.k3 != bF2m.k3))
+ if (aF2m.representation != bF2m.representation)
{
- throw new ArgumentException("Field elements are not "
- + "elements of the same field F2m");
+ // Should never occur
+ throw new ArgumentException("One of the F2m field elements has incorrect representation");
}
- if (aF2m.representation != bF2m.representation)
+ if ((aF2m.m != bF2m.m) || !Arrays.AreEqual(aF2m.ks, bF2m.ks))
{
- // Should never occur
- throw new ArgumentException(
- "One of the field "
- + "elements are not elements has incorrect representation");
+ throw new ArgumentException("Field elements are not elements of the same field F2m");
}
}
@@ -1056,10 +1031,10 @@ namespace Org.BouncyCastle.Math.EC
// No check performed here for performance reasons. Instead the
// elements involved are checked in ECPoint.F2m
// checkFieldElements(this, b);
- IntArray iarrClone = (IntArray) this.x.Copy();
- F2mFieldElement bF2m = (F2mFieldElement) b;
- iarrClone.AddShifted(bF2m.x, 0);
- return new F2mFieldElement(m, k1, k2, k3, iarrClone);
+ LongArray iarrClone = this.x.Copy();
+ F2mFieldElement bF2m = (F2mFieldElement)b;
+ iarrClone.AddShiftedByWords(bF2m.x, 0);
+ return new F2mFieldElement(m, ks, iarrClone);
}
public override ECFieldElement Subtract(
@@ -1079,10 +1054,7 @@ namespace Org.BouncyCastle.Math.EC
// No check performed here for performance reasons. Instead the
// elements involved are checked in ECPoint.F2m
// checkFieldElements(this, b);
- F2mFieldElement bF2m = (F2mFieldElement) b;
- IntArray mult = x.Multiply(bF2m.x, m);
- mult.Reduce(m, new int[]{k1, k2, k3});
- return new F2mFieldElement(m, k1, k2, k3, mult);
+ return new F2mFieldElement(m, ks, x.ModMultiply(((F2mFieldElement)b).x, m, ks));
}
public override ECFieldElement Divide(
@@ -1101,76 +1073,12 @@ namespace Org.BouncyCastle.Math.EC
public override ECFieldElement Square()
{
- IntArray squared = x.Square(m);
- squared.Reduce(m, new int[]{k1, k2, k3});
- return new F2mFieldElement(m, k1, k2, k3, squared);
+ return new F2mFieldElement(m, ks, x.ModSquare(m, ks));
}
public override ECFieldElement Invert()
{
- // Inversion in F2m using the extended Euclidean algorithm
- // Input: A nonzero polynomial a(z) of degree at most m-1
- // Output: a(z)^(-1) mod f(z)
-
- // u(z) := a(z)
- IntArray uz = (IntArray)this.x.Copy();
-
- // v(z) := f(z)
- IntArray vz = new IntArray(t);
- vz.SetBit(m);
- vz.SetBit(0);
- vz.SetBit(this.k1);
- if (this.representation == Ppb)
- {
- vz.SetBit(this.k2);
- vz.SetBit(this.k3);
- }
-
- // g1(z) := 1, g2(z) := 0
- IntArray g1z = new IntArray(t);
- g1z.SetBit(0);
- IntArray g2z = new IntArray(t);
-
- // while u != 0
- while (uz.GetUsedLength() > 0)
-// while (uz.bitLength() > 1)
- {
- // j := deg(u(z)) - deg(v(z))
- int j = uz.BitLength - vz.BitLength;
-
- // If j < 0 then: u(z) <-> v(z), g1(z) <-> g2(z), j := -j
- if (j < 0)
- {
- IntArray uzCopy = uz;
- uz = vz;
- vz = uzCopy;
-
- IntArray g1zCopy = g1z;
- g1z = g2z;
- g2z = g1zCopy;
-
- j = -j;
- }
-
- // u(z) := u(z) + z^j * v(z)
- // Note, that no reduction modulo f(z) is required, because
- // deg(u(z) + z^j * v(z)) <= max(deg(u(z)), j + deg(v(z)))
- // = max(deg(u(z)), deg(u(z)) - deg(v(z)) + deg(v(z))
- // = deg(u(z))
- // uz = uz.xor(vz.ShiftLeft(j));
- // jInt = n / 32
- int jInt = j >> 5;
- // jInt = n % 32
- int jBit = j & 0x1F;
- IntArray vzShift = vz.ShiftLeft(jBit);
- uz.AddShifted(vzShift, jInt);
-
- // g1(z) := g1(z) + z^j * g2(z)
-// g1z = g1z.xor(g2z.ShiftLeft(j));
- IntArray g2zShift = g2z.ShiftLeft(jBit);
- g1z.AddShifted(g2zShift, jInt);
- }
- return new F2mFieldElement(this.m, this.k1, this.k2, this.k3, g2z);
+ return new F2mFieldElement(this.m, this.ks, this.x.ModInverse(m, ks));
}
public override ECFieldElement Sqrt()
@@ -1210,7 +1118,7 @@ namespace Org.BouncyCastle.Math.EC
*/
public int K1
{
- get { return this.k1; }
+ get { return this.ks[0]; }
}
/**
@@ -1221,7 +1129,7 @@ namespace Org.BouncyCastle.Math.EC
*/
public int K2
{
- get { return this.k2; }
+ get { return this.ks.Length >= 2 ? this.ks[1] : 0; }
}
/**
@@ -1232,7 +1140,7 @@ namespace Org.BouncyCastle.Math.EC
*/
public int K3
{
- get { return this.k3; }
+ get { return this.ks.Length >= 3 ? this.ks[2] : 0; }
}
public override bool Equals(
@@ -1252,22 +1160,15 @@ namespace Org.BouncyCastle.Math.EC
public virtual bool Equals(
F2mFieldElement other)
{
- return m == other.m
- && k1 == other.k1
- && k2 == other.k2
- && k3 == other.k3
- && representation == other.representation
- && base.Equals(other);
+ return ((this.m == other.m)
+ && (this.representation == other.representation)
+ && Arrays.AreEqual(this.ks, other.ks)
+ && (this.x.Equals(other.x)));
}
public override int GetHashCode()
{
- return m.GetHashCode()
- ^ k1.GetHashCode()
- ^ k2.GetHashCode()
- ^ k3.GetHashCode()
- ^ representation.GetHashCode()
- ^ base.GetHashCode();
+ return x.GetHashCode() ^ m ^ Arrays.GetHashCode(ks);
}
}
}
diff --git a/crypto/src/math/ec/LongArray.cs b/crypto/src/math/ec/LongArray.cs
new file mode 100644
index 000000000..d694f0cf0
--- /dev/null
+++ b/crypto/src/math/ec/LongArray.cs
@@ -0,0 +1,2023 @@
+using System;
+using System.Text;
+
+using Org.BouncyCastle.Utilities;
+
+namespace Org.BouncyCastle.Math.EC
+{
+ internal class LongArray
+ {
+ //private static long DEInterleave_MASK = 0x5555555555555555L;
+
+ /*
+ * This expands 8 bit indices into 16 bit contents (high bit 14), by inserting 0s between bits.
+ * In a binary field, this operation is the same as squaring an 8 bit number.
+ */
+ private static readonly int[] INTERLEAVE2_TABLE = new int[]
+ {
+ 0x0000, 0x0001, 0x0004, 0x0005, 0x0010, 0x0011, 0x0014, 0x0015,
+ 0x0040, 0x0041, 0x0044, 0x0045, 0x0050, 0x0051, 0x0054, 0x0055,
+ 0x0100, 0x0101, 0x0104, 0x0105, 0x0110, 0x0111, 0x0114, 0x0115,
+ 0x0140, 0x0141, 0x0144, 0x0145, 0x0150, 0x0151, 0x0154, 0x0155,
+ 0x0400, 0x0401, 0x0404, 0x0405, 0x0410, 0x0411, 0x0414, 0x0415,
+ 0x0440, 0x0441, 0x0444, 0x0445, 0x0450, 0x0451, 0x0454, 0x0455,
+ 0x0500, 0x0501, 0x0504, 0x0505, 0x0510, 0x0511, 0x0514, 0x0515,
+ 0x0540, 0x0541, 0x0544, 0x0545, 0x0550, 0x0551, 0x0554, 0x0555,
+ 0x1000, 0x1001, 0x1004, 0x1005, 0x1010, 0x1011, 0x1014, 0x1015,
+ 0x1040, 0x1041, 0x1044, 0x1045, 0x1050, 0x1051, 0x1054, 0x1055,
+ 0x1100, 0x1101, 0x1104, 0x1105, 0x1110, 0x1111, 0x1114, 0x1115,
+ 0x1140, 0x1141, 0x1144, 0x1145, 0x1150, 0x1151, 0x1154, 0x1155,
+ 0x1400, 0x1401, 0x1404, 0x1405, 0x1410, 0x1411, 0x1414, 0x1415,
+ 0x1440, 0x1441, 0x1444, 0x1445, 0x1450, 0x1451, 0x1454, 0x1455,
+ 0x1500, 0x1501, 0x1504, 0x1505, 0x1510, 0x1511, 0x1514, 0x1515,
+ 0x1540, 0x1541, 0x1544, 0x1545, 0x1550, 0x1551, 0x1554, 0x1555,
+ 0x4000, 0x4001, 0x4004, 0x4005, 0x4010, 0x4011, 0x4014, 0x4015,
+ 0x4040, 0x4041, 0x4044, 0x4045, 0x4050, 0x4051, 0x4054, 0x4055,
+ 0x4100, 0x4101, 0x4104, 0x4105, 0x4110, 0x4111, 0x4114, 0x4115,
+ 0x4140, 0x4141, 0x4144, 0x4145, 0x4150, 0x4151, 0x4154, 0x4155,
+ 0x4400, 0x4401, 0x4404, 0x4405, 0x4410, 0x4411, 0x4414, 0x4415,
+ 0x4440, 0x4441, 0x4444, 0x4445, 0x4450, 0x4451, 0x4454, 0x4455,
+ 0x4500, 0x4501, 0x4504, 0x4505, 0x4510, 0x4511, 0x4514, 0x4515,
+ 0x4540, 0x4541, 0x4544, 0x4545, 0x4550, 0x4551, 0x4554, 0x4555,
+ 0x5000, 0x5001, 0x5004, 0x5005, 0x5010, 0x5011, 0x5014, 0x5015,
+ 0x5040, 0x5041, 0x5044, 0x5045, 0x5050, 0x5051, 0x5054, 0x5055,
+ 0x5100, 0x5101, 0x5104, 0x5105, 0x5110, 0x5111, 0x5114, 0x5115,
+ 0x5140, 0x5141, 0x5144, 0x5145, 0x5150, 0x5151, 0x5154, 0x5155,
+ 0x5400, 0x5401, 0x5404, 0x5405, 0x5410, 0x5411, 0x5414, 0x5415,
+ 0x5440, 0x5441, 0x5444, 0x5445, 0x5450, 0x5451, 0x5454, 0x5455,
+ 0x5500, 0x5501, 0x5504, 0x5505, 0x5510, 0x5511, 0x5514, 0x5515,
+ 0x5540, 0x5541, 0x5544, 0x5545, 0x5550, 0x5551, 0x5554, 0x5555
+ };
+
+ /*
+ * This expands 7 bit indices into 21 bit contents (high bit 18), by inserting 0s between bits.
+ */
+ private static readonly int[] INTERLEAVE3_TABLE = new int[]
+ {
+ 0x00000, 0x00001, 0x00008, 0x00009, 0x00040, 0x00041, 0x00048, 0x00049,
+ 0x00200, 0x00201, 0x00208, 0x00209, 0x00240, 0x00241, 0x00248, 0x00249,
+ 0x01000, 0x01001, 0x01008, 0x01009, 0x01040, 0x01041, 0x01048, 0x01049,
+ 0x01200, 0x01201, 0x01208, 0x01209, 0x01240, 0x01241, 0x01248, 0x01249,
+ 0x08000, 0x08001, 0x08008, 0x08009, 0x08040, 0x08041, 0x08048, 0x08049,
+ 0x08200, 0x08201, 0x08208, 0x08209, 0x08240, 0x08241, 0x08248, 0x08249,
+ 0x09000, 0x09001, 0x09008, 0x09009, 0x09040, 0x09041, 0x09048, 0x09049,
+ 0x09200, 0x09201, 0x09208, 0x09209, 0x09240, 0x09241, 0x09248, 0x09249,
+ 0x40000, 0x40001, 0x40008, 0x40009, 0x40040, 0x40041, 0x40048, 0x40049,
+ 0x40200, 0x40201, 0x40208, 0x40209, 0x40240, 0x40241, 0x40248, 0x40249,
+ 0x41000, 0x41001, 0x41008, 0x41009, 0x41040, 0x41041, 0x41048, 0x41049,
+ 0x41200, 0x41201, 0x41208, 0x41209, 0x41240, 0x41241, 0x41248, 0x41249,
+ 0x48000, 0x48001, 0x48008, 0x48009, 0x48040, 0x48041, 0x48048, 0x48049,
+ 0x48200, 0x48201, 0x48208, 0x48209, 0x48240, 0x48241, 0x48248, 0x48249,
+ 0x49000, 0x49001, 0x49008, 0x49009, 0x49040, 0x49041, 0x49048, 0x49049,
+ 0x49200, 0x49201, 0x49208, 0x49209, 0x49240, 0x49241, 0x49248, 0x49249
+ };
+
+ /*
+ * This expands 8 bit indices into 32 bit contents (high bit 28), by inserting 0s between bits.
+ */
+ private static readonly int[] INTERLEAVE4_TABLE = new int[]
+ {
+ 0x00000000, 0x00000001, 0x00000010, 0x00000011, 0x00000100, 0x00000101, 0x00000110, 0x00000111,
+ 0x00001000, 0x00001001, 0x00001010, 0x00001011, 0x00001100, 0x00001101, 0x00001110, 0x00001111,
+ 0x00010000, 0x00010001, 0x00010010, 0x00010011, 0x00010100, 0x00010101, 0x00010110, 0x00010111,
+ 0x00011000, 0x00011001, 0x00011010, 0x00011011, 0x00011100, 0x00011101, 0x00011110, 0x00011111,
+ 0x00100000, 0x00100001, 0x00100010, 0x00100011, 0x00100100, 0x00100101, 0x00100110, 0x00100111,
+ 0x00101000, 0x00101001, 0x00101010, 0x00101011, 0x00101100, 0x00101101, 0x00101110, 0x00101111,
+ 0x00110000, 0x00110001, 0x00110010, 0x00110011, 0x00110100, 0x00110101, 0x00110110, 0x00110111,
+ 0x00111000, 0x00111001, 0x00111010, 0x00111011, 0x00111100, 0x00111101, 0x00111110, 0x00111111,
+ 0x01000000, 0x01000001, 0x01000010, 0x01000011, 0x01000100, 0x01000101, 0x01000110, 0x01000111,
+ 0x01001000, 0x01001001, 0x01001010, 0x01001011, 0x01001100, 0x01001101, 0x01001110, 0x01001111,
+ 0x01010000, 0x01010001, 0x01010010, 0x01010011, 0x01010100, 0x01010101, 0x01010110, 0x01010111,
+ 0x01011000, 0x01011001, 0x01011010, 0x01011011, 0x01011100, 0x01011101, 0x01011110, 0x01011111,
+ 0x01100000, 0x01100001, 0x01100010, 0x01100011, 0x01100100, 0x01100101, 0x01100110, 0x01100111,
+ 0x01101000, 0x01101001, 0x01101010, 0x01101011, 0x01101100, 0x01101101, 0x01101110, 0x01101111,
+ 0x01110000, 0x01110001, 0x01110010, 0x01110011, 0x01110100, 0x01110101, 0x01110110, 0x01110111,
+ 0x01111000, 0x01111001, 0x01111010, 0x01111011, 0x01111100, 0x01111101, 0x01111110, 0x01111111,
+ 0x10000000, 0x10000001, 0x10000010, 0x10000011, 0x10000100, 0x10000101, 0x10000110, 0x10000111,
+ 0x10001000, 0x10001001, 0x10001010, 0x10001011, 0x10001100, 0x10001101, 0x10001110, 0x10001111,
+ 0x10010000, 0x10010001, 0x10010010, 0x10010011, 0x10010100, 0x10010101, 0x10010110, 0x10010111,
+ 0x10011000, 0x10011001, 0x10011010, 0x10011011, 0x10011100, 0x10011101, 0x10011110, 0x10011111,
+ 0x10100000, 0x10100001, 0x10100010, 0x10100011, 0x10100100, 0x10100101, 0x10100110, 0x10100111,
+ 0x10101000, 0x10101001, 0x10101010, 0x10101011, 0x10101100, 0x10101101, 0x10101110, 0x10101111,
+ 0x10110000, 0x10110001, 0x10110010, 0x10110011, 0x10110100, 0x10110101, 0x10110110, 0x10110111,
+ 0x10111000, 0x10111001, 0x10111010, 0x10111011, 0x10111100, 0x10111101, 0x10111110, 0x10111111,
+ 0x11000000, 0x11000001, 0x11000010, 0x11000011, 0x11000100, 0x11000101, 0x11000110, 0x11000111,
+ 0x11001000, 0x11001001, 0x11001010, 0x11001011, 0x11001100, 0x11001101, 0x11001110, 0x11001111,
+ 0x11010000, 0x11010001, 0x11010010, 0x11010011, 0x11010100, 0x11010101, 0x11010110, 0x11010111,
+ 0x11011000, 0x11011001, 0x11011010, 0x11011011, 0x11011100, 0x11011101, 0x11011110, 0x11011111,
+ 0x11100000, 0x11100001, 0x11100010, 0x11100011, 0x11100100, 0x11100101, 0x11100110, 0x11100111,
+ 0x11101000, 0x11101001, 0x11101010, 0x11101011, 0x11101100, 0x11101101, 0x11101110, 0x11101111,
+ 0x11110000, 0x11110001, 0x11110010, 0x11110011, 0x11110100, 0x11110101, 0x11110110, 0x11110111,
+ 0x11111000, 0x11111001, 0x11111010, 0x11111011, 0x11111100, 0x11111101, 0x11111110, 0x11111111
+ };
+
+ /*
+ * This expands 7 bit indices into 35 bit contents (high bit 30), by inserting 0s between bits.
+ */
+ private static readonly int[] INTERLEAVE5_TABLE = new int[] {
+ 0x00000000, 0x00000001, 0x00000020, 0x00000021, 0x00000400, 0x00000401, 0x00000420, 0x00000421,
+ 0x00008000, 0x00008001, 0x00008020, 0x00008021, 0x00008400, 0x00008401, 0x00008420, 0x00008421,
+ 0x00100000, 0x00100001, 0x00100020, 0x00100021, 0x00100400, 0x00100401, 0x00100420, 0x00100421,
+ 0x00108000, 0x00108001, 0x00108020, 0x00108021, 0x00108400, 0x00108401, 0x00108420, 0x00108421,
+ 0x02000000, 0x02000001, 0x02000020, 0x02000021, 0x02000400, 0x02000401, 0x02000420, 0x02000421,
+ 0x02008000, 0x02008001, 0x02008020, 0x02008021, 0x02008400, 0x02008401, 0x02008420, 0x02008421,
+ 0x02100000, 0x02100001, 0x02100020, 0x02100021, 0x02100400, 0x02100401, 0x02100420, 0x02100421,
+ 0x02108000, 0x02108001, 0x02108020, 0x02108021, 0x02108400, 0x02108401, 0x02108420, 0x02108421,
+ 0x40000000, 0x40000001, 0x40000020, 0x40000021, 0x40000400, 0x40000401, 0x40000420, 0x40000421,
+ 0x40008000, 0x40008001, 0x40008020, 0x40008021, 0x40008400, 0x40008401, 0x40008420, 0x40008421,
+ 0x40100000, 0x40100001, 0x40100020, 0x40100021, 0x40100400, 0x40100401, 0x40100420, 0x40100421,
+ 0x40108000, 0x40108001, 0x40108020, 0x40108021, 0x40108400, 0x40108401, 0x40108420, 0x40108421,
+ 0x42000000, 0x42000001, 0x42000020, 0x42000021, 0x42000400, 0x42000401, 0x42000420, 0x42000421,
+ 0x42008000, 0x42008001, 0x42008020, 0x42008021, 0x42008400, 0x42008401, 0x42008420, 0x42008421,
+ 0x42100000, 0x42100001, 0x42100020, 0x42100021, 0x42100400, 0x42100401, 0x42100420, 0x42100421,
+ 0x42108000, 0x42108001, 0x42108020, 0x42108021, 0x42108400, 0x42108401, 0x42108420, 0x42108421
+ };
+
+ /*
+ * This expands 9 bit indices into 63 bit (long) contents (high bit 56), by inserting 0s between bits.
+ */
+ private static readonly long[] INTERLEAVE7_TABLE = new long[]
+ {
+ 0x0000000000000000L, 0x0000000000000001L, 0x0000000000000080L, 0x0000000000000081L,
+ 0x0000000000004000L, 0x0000000000004001L, 0x0000000000004080L, 0x0000000000004081L,
+ 0x0000000000200000L, 0x0000000000200001L, 0x0000000000200080L, 0x0000000000200081L,
+ 0x0000000000204000L, 0x0000000000204001L, 0x0000000000204080L, 0x0000000000204081L,
+ 0x0000000010000000L, 0x0000000010000001L, 0x0000000010000080L, 0x0000000010000081L,
+ 0x0000000010004000L, 0x0000000010004001L, 0x0000000010004080L, 0x0000000010004081L,
+ 0x0000000010200000L, 0x0000000010200001L, 0x0000000010200080L, 0x0000000010200081L,
+ 0x0000000010204000L, 0x0000000010204001L, 0x0000000010204080L, 0x0000000010204081L,
+ 0x0000000800000000L, 0x0000000800000001L, 0x0000000800000080L, 0x0000000800000081L,
+ 0x0000000800004000L, 0x0000000800004001L, 0x0000000800004080L, 0x0000000800004081L,
+ 0x0000000800200000L, 0x0000000800200001L, 0x0000000800200080L, 0x0000000800200081L,
+ 0x0000000800204000L, 0x0000000800204001L, 0x0000000800204080L, 0x0000000800204081L,
+ 0x0000000810000000L, 0x0000000810000001L, 0x0000000810000080L, 0x0000000810000081L,
+ 0x0000000810004000L, 0x0000000810004001L, 0x0000000810004080L, 0x0000000810004081L,
+ 0x0000000810200000L, 0x0000000810200001L, 0x0000000810200080L, 0x0000000810200081L,
+ 0x0000000810204000L, 0x0000000810204001L, 0x0000000810204080L, 0x0000000810204081L,
+ 0x0000040000000000L, 0x0000040000000001L, 0x0000040000000080L, 0x0000040000000081L,
+ 0x0000040000004000L, 0x0000040000004001L, 0x0000040000004080L, 0x0000040000004081L,
+ 0x0000040000200000L, 0x0000040000200001L, 0x0000040000200080L, 0x0000040000200081L,
+ 0x0000040000204000L, 0x0000040000204001L, 0x0000040000204080L, 0x0000040000204081L,
+ 0x0000040010000000L, 0x0000040010000001L, 0x0000040010000080L, 0x0000040010000081L,
+ 0x0000040010004000L, 0x0000040010004001L, 0x0000040010004080L, 0x0000040010004081L,
+ 0x0000040010200000L, 0x0000040010200001L, 0x0000040010200080L, 0x0000040010200081L,
+ 0x0000040010204000L, 0x0000040010204001L, 0x0000040010204080L, 0x0000040010204081L,
+ 0x0000040800000000L, 0x0000040800000001L, 0x0000040800000080L, 0x0000040800000081L,
+ 0x0000040800004000L, 0x0000040800004001L, 0x0000040800004080L, 0x0000040800004081L,
+ 0x0000040800200000L, 0x0000040800200001L, 0x0000040800200080L, 0x0000040800200081L,
+ 0x0000040800204000L, 0x0000040800204001L, 0x0000040800204080L, 0x0000040800204081L,
+ 0x0000040810000000L, 0x0000040810000001L, 0x0000040810000080L, 0x0000040810000081L,
+ 0x0000040810004000L, 0x0000040810004001L, 0x0000040810004080L, 0x0000040810004081L,
+ 0x0000040810200000L, 0x0000040810200001L, 0x0000040810200080L, 0x0000040810200081L,
+ 0x0000040810204000L, 0x0000040810204001L, 0x0000040810204080L, 0x0000040810204081L,
+ 0x0002000000000000L, 0x0002000000000001L, 0x0002000000000080L, 0x0002000000000081L,
+ 0x0002000000004000L, 0x0002000000004001L, 0x0002000000004080L, 0x0002000000004081L,
+ 0x0002000000200000L, 0x0002000000200001L, 0x0002000000200080L, 0x0002000000200081L,
+ 0x0002000000204000L, 0x0002000000204001L, 0x0002000000204080L, 0x0002000000204081L,
+ 0x0002000010000000L, 0x0002000010000001L, 0x0002000010000080L, 0x0002000010000081L,
+ 0x0002000010004000L, 0x0002000010004001L, 0x0002000010004080L, 0x0002000010004081L,
+ 0x0002000010200000L, 0x0002000010200001L, 0x0002000010200080L, 0x0002000010200081L,
+ 0x0002000010204000L, 0x0002000010204001L, 0x0002000010204080L, 0x0002000010204081L,
+ 0x0002000800000000L, 0x0002000800000001L, 0x0002000800000080L, 0x0002000800000081L,
+ 0x0002000800004000L, 0x0002000800004001L, 0x0002000800004080L, 0x0002000800004081L,
+ 0x0002000800200000L, 0x0002000800200001L, 0x0002000800200080L, 0x0002000800200081L,
+ 0x0002000800204000L, 0x0002000800204001L, 0x0002000800204080L, 0x0002000800204081L,
+ 0x0002000810000000L, 0x0002000810000001L, 0x0002000810000080L, 0x0002000810000081L,
+ 0x0002000810004000L, 0x0002000810004001L, 0x0002000810004080L, 0x0002000810004081L,
+ 0x0002000810200000L, 0x0002000810200001L, 0x0002000810200080L, 0x0002000810200081L,
+ 0x0002000810204000L, 0x0002000810204001L, 0x0002000810204080L, 0x0002000810204081L,
+ 0x0002040000000000L, 0x0002040000000001L, 0x0002040000000080L, 0x0002040000000081L,
+ 0x0002040000004000L, 0x0002040000004001L, 0x0002040000004080L, 0x0002040000004081L,
+ 0x0002040000200000L, 0x0002040000200001L, 0x0002040000200080L, 0x0002040000200081L,
+ 0x0002040000204000L, 0x0002040000204001L, 0x0002040000204080L, 0x0002040000204081L,
+ 0x0002040010000000L, 0x0002040010000001L, 0x0002040010000080L, 0x0002040010000081L,
+ 0x0002040010004000L, 0x0002040010004001L, 0x0002040010004080L, 0x0002040010004081L,
+ 0x0002040010200000L, 0x0002040010200001L, 0x0002040010200080L, 0x0002040010200081L,
+ 0x0002040010204000L, 0x0002040010204001L, 0x0002040010204080L, 0x0002040010204081L,
+ 0x0002040800000000L, 0x0002040800000001L, 0x0002040800000080L, 0x0002040800000081L,
+ 0x0002040800004000L, 0x0002040800004001L, 0x0002040800004080L, 0x0002040800004081L,
+ 0x0002040800200000L, 0x0002040800200001L, 0x0002040800200080L, 0x0002040800200081L,
+ 0x0002040800204000L, 0x0002040800204001L, 0x0002040800204080L, 0x0002040800204081L,
+ 0x0002040810000000L, 0x0002040810000001L, 0x0002040810000080L, 0x0002040810000081L,
+ 0x0002040810004000L, 0x0002040810004001L, 0x0002040810004080L, 0x0002040810004081L,
+ 0x0002040810200000L, 0x0002040810200001L, 0x0002040810200080L, 0x0002040810200081L,
+ 0x0002040810204000L, 0x0002040810204001L, 0x0002040810204080L, 0x0002040810204081L,
+ 0x0100000000000000L, 0x0100000000000001L, 0x0100000000000080L, 0x0100000000000081L,
+ 0x0100000000004000L, 0x0100000000004001L, 0x0100000000004080L, 0x0100000000004081L,
+ 0x0100000000200000L, 0x0100000000200001L, 0x0100000000200080L, 0x0100000000200081L,
+ 0x0100000000204000L, 0x0100000000204001L, 0x0100000000204080L, 0x0100000000204081L,
+ 0x0100000010000000L, 0x0100000010000001L, 0x0100000010000080L, 0x0100000010000081L,
+ 0x0100000010004000L, 0x0100000010004001L, 0x0100000010004080L, 0x0100000010004081L,
+ 0x0100000010200000L, 0x0100000010200001L, 0x0100000010200080L, 0x0100000010200081L,
+ 0x0100000010204000L, 0x0100000010204001L, 0x0100000010204080L, 0x0100000010204081L,
+ 0x0100000800000000L, 0x0100000800000001L, 0x0100000800000080L, 0x0100000800000081L,
+ 0x0100000800004000L, 0x0100000800004001L, 0x0100000800004080L, 0x0100000800004081L,
+ 0x0100000800200000L, 0x0100000800200001L, 0x0100000800200080L, 0x0100000800200081L,
+ 0x0100000800204000L, 0x0100000800204001L, 0x0100000800204080L, 0x0100000800204081L,
+ 0x0100000810000000L, 0x0100000810000001L, 0x0100000810000080L, 0x0100000810000081L,
+ 0x0100000810004000L, 0x0100000810004001L, 0x0100000810004080L, 0x0100000810004081L,
+ 0x0100000810200000L, 0x0100000810200001L, 0x0100000810200080L, 0x0100000810200081L,
+ 0x0100000810204000L, 0x0100000810204001L, 0x0100000810204080L, 0x0100000810204081L,
+ 0x0100040000000000L, 0x0100040000000001L, 0x0100040000000080L, 0x0100040000000081L,
+ 0x0100040000004000L, 0x0100040000004001L, 0x0100040000004080L, 0x0100040000004081L,
+ 0x0100040000200000L, 0x0100040000200001L, 0x0100040000200080L, 0x0100040000200081L,
+ 0x0100040000204000L, 0x0100040000204001L, 0x0100040000204080L, 0x0100040000204081L,
+ 0x0100040010000000L, 0x0100040010000001L, 0x0100040010000080L, 0x0100040010000081L,
+ 0x0100040010004000L, 0x0100040010004001L, 0x0100040010004080L, 0x0100040010004081L,
+ 0x0100040010200000L, 0x0100040010200001L, 0x0100040010200080L, 0x0100040010200081L,
+ 0x0100040010204000L, 0x0100040010204001L, 0x0100040010204080L, 0x0100040010204081L,
+ 0x0100040800000000L, 0x0100040800000001L, 0x0100040800000080L, 0x0100040800000081L,
+ 0x0100040800004000L, 0x0100040800004001L, 0x0100040800004080L, 0x0100040800004081L,
+ 0x0100040800200000L, 0x0100040800200001L, 0x0100040800200080L, 0x0100040800200081L,
+ 0x0100040800204000L, 0x0100040800204001L, 0x0100040800204080L, 0x0100040800204081L,
+ 0x0100040810000000L, 0x0100040810000001L, 0x0100040810000080L, 0x0100040810000081L,
+ 0x0100040810004000L, 0x0100040810004001L, 0x0100040810004080L, 0x0100040810004081L,
+ 0x0100040810200000L, 0x0100040810200001L, 0x0100040810200080L, 0x0100040810200081L,
+ 0x0100040810204000L, 0x0100040810204001L, 0x0100040810204080L, 0x0100040810204081L,
+ 0x0102000000000000L, 0x0102000000000001L, 0x0102000000000080L, 0x0102000000000081L,
+ 0x0102000000004000L, 0x0102000000004001L, 0x0102000000004080L, 0x0102000000004081L,
+ 0x0102000000200000L, 0x0102000000200001L, 0x0102000000200080L, 0x0102000000200081L,
+ 0x0102000000204000L, 0x0102000000204001L, 0x0102000000204080L, 0x0102000000204081L,
+ 0x0102000010000000L, 0x0102000010000001L, 0x0102000010000080L, 0x0102000010000081L,
+ 0x0102000010004000L, 0x0102000010004001L, 0x0102000010004080L, 0x0102000010004081L,
+ 0x0102000010200000L, 0x0102000010200001L, 0x0102000010200080L, 0x0102000010200081L,
+ 0x0102000010204000L, 0x0102000010204001L, 0x0102000010204080L, 0x0102000010204081L,
+ 0x0102000800000000L, 0x0102000800000001L, 0x0102000800000080L, 0x0102000800000081L,
+ 0x0102000800004000L, 0x0102000800004001L, 0x0102000800004080L, 0x0102000800004081L,
+ 0x0102000800200000L, 0x0102000800200001L, 0x0102000800200080L, 0x0102000800200081L,
+ 0x0102000800204000L, 0x0102000800204001L, 0x0102000800204080L, 0x0102000800204081L,
+ 0x0102000810000000L, 0x0102000810000001L, 0x0102000810000080L, 0x0102000810000081L,
+ 0x0102000810004000L, 0x0102000810004001L, 0x0102000810004080L, 0x0102000810004081L,
+ 0x0102000810200000L, 0x0102000810200001L, 0x0102000810200080L, 0x0102000810200081L,
+ 0x0102000810204000L, 0x0102000810204001L, 0x0102000810204080L, 0x0102000810204081L,
+ 0x0102040000000000L, 0x0102040000000001L, 0x0102040000000080L, 0x0102040000000081L,
+ 0x0102040000004000L, 0x0102040000004001L, 0x0102040000004080L, 0x0102040000004081L,
+ 0x0102040000200000L, 0x0102040000200001L, 0x0102040000200080L, 0x0102040000200081L,
+ 0x0102040000204000L, 0x0102040000204001L, 0x0102040000204080L, 0x0102040000204081L,
+ 0x0102040010000000L, 0x0102040010000001L, 0x0102040010000080L, 0x0102040010000081L,
+ 0x0102040010004000L, 0x0102040010004001L, 0x0102040010004080L, 0x0102040010004081L,
+ 0x0102040010200000L, 0x0102040010200001L, 0x0102040010200080L, 0x0102040010200081L,
+ 0x0102040010204000L, 0x0102040010204001L, 0x0102040010204080L, 0x0102040010204081L,
+ 0x0102040800000000L, 0x0102040800000001L, 0x0102040800000080L, 0x0102040800000081L,
+ 0x0102040800004000L, 0x0102040800004001L, 0x0102040800004080L, 0x0102040800004081L,
+ 0x0102040800200000L, 0x0102040800200001L, 0x0102040800200080L, 0x0102040800200081L,
+ 0x0102040800204000L, 0x0102040800204001L, 0x0102040800204080L, 0x0102040800204081L,
+ 0x0102040810000000L, 0x0102040810000001L, 0x0102040810000080L, 0x0102040810000081L,
+ 0x0102040810004000L, 0x0102040810004001L, 0x0102040810004080L, 0x0102040810004081L,
+ 0x0102040810200000L, 0x0102040810200001L, 0x0102040810200080L, 0x0102040810200081L,
+ 0x0102040810204000L, 0x0102040810204001L, 0x0102040810204080L, 0x0102040810204081L
+ };
+
+ // For toString(); must have length 64
+ private const string ZEROES = "0000000000000000000000000000000000000000000000000000000000000000";
+
+ internal static readonly byte[] BitLengths =
+ {
+ 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4,
+ 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,
+ 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
+ 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6,
+ 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
+ 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
+ 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
+ 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
+ 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
+ 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
+ 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
+ 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
+ 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
+ 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
+ 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
+ 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8
+ };
+
+ // TODO make m fixed for the LongArray, and hence compute T once and for all
+
+ private long[] m_ints;
+
+ public LongArray(int intLen)
+ {
+ m_ints = new long[intLen];
+ }
+
+ public LongArray(long[] ints)
+ {
+ m_ints = ints;
+ }
+
+ public LongArray(long[] ints, int off, int len)
+ {
+ if (off == 0 && len == ints.Length)
+ {
+ m_ints = ints;
+ }
+ else
+ {
+ m_ints = new long[len];
+ Array.Copy(ints, off, m_ints, 0, len);
+ }
+ }
+
+ public LongArray(BigInteger bigInt)
+ {
+ if (bigInt == null || bigInt.SignValue < 0)
+ {
+ throw new ArgumentException("invalid F2m field value", "bigInt");
+ }
+
+ if (bigInt.SignValue == 0)
+ {
+ m_ints = new long[] { 0L };
+ return;
+ }
+
+ byte[] barr = bigInt.ToByteArray();
+ int barrLen = barr.Length;
+ int barrStart = 0;
+ if (barr[0] == 0)
+ {
+ // First byte is 0 to enforce highest (=sign) bit is zero.
+ // In this case ignore barr[0].
+ barrLen--;
+ barrStart = 1;
+ }
+ int intLen = (barrLen + 7) / 8;
+ m_ints = new long[intLen];
+
+ int iarrJ = intLen - 1;
+ int rem = barrLen % 8 + barrStart;
+ long temp = 0;
+ int barrI = barrStart;
+ if (barrStart < rem)
+ {
+ for (; barrI < rem; barrI++)
+ {
+ temp <<= 8;
+ uint barrBarrI = barr[barrI];
+ temp |= barrBarrI;
+ }
+ m_ints[iarrJ--] = temp;
+ }
+
+ for (; iarrJ >= 0; iarrJ--)
+ {
+ temp = 0;
+ for (int i = 0; i < 8; i++)
+ {
+ temp <<= 8;
+ uint barrBarrI = barr[barrI++];
+ temp |= barrBarrI;
+ }
+ m_ints[iarrJ] = temp;
+ }
+ }
+
+ public bool IsOne()
+ {
+ long[] a = m_ints;
+ if (a[0] != 1L)
+ {
+ return false;
+ }
+ for (int i = 1; i < a.Length; ++i)
+ {
+ if (a[i] != 0L)
+ {
+ return false;
+ }
+ }
+ return true;
+ }
+
+ public bool IsZero()
+ {
+ long[] a = m_ints;
+ for (int i = 0; i < a.Length; ++i)
+ {
+ if (a[i] != 0L)
+ {
+ return false;
+ }
+ }
+ return true;
+ }
+
+ public int GetUsedLength()
+ {
+ return GetUsedLengthFrom(m_ints.Length);
+ }
+
+ public int GetUsedLengthFrom(int from)
+ {
+ long[] a = m_ints;
+ from = System.Math.Min(from, a.Length);
+
+ if (from < 1)
+ {
+ return 0;
+ }
+
+ // Check if first element will act as sentinel
+ if (a[0] != 0)
+ {
+ while (a[--from] == 0)
+ {
+ }
+ return from + 1;
+ }
+
+ do
+ {
+ if (a[--from] != 0)
+ {
+ return from + 1;
+ }
+ }
+ while (from > 0);
+
+ return 0;
+ }
+
+ public int Degree()
+ {
+ int i = m_ints.Length;
+ long w;
+ do
+ {
+ if (i == 0)
+ {
+ return 0;
+ }
+ w = m_ints[--i];
+ }
+ while (w == 0);
+
+ return (i << 6) + BitLength(w);
+ }
+
+ private int DegreeFrom(int limit)
+ {
+ int i = (int)(((uint)limit + 62) >> 6);
+ long w;
+ do
+ {
+ if (i == 0)
+ {
+ return 0;
+ }
+ w = m_ints[--i];
+ }
+ while (w == 0);
+
+ return (i << 6) + BitLength(w);
+ }
+
+ // private int lowestCoefficient()
+ // {
+ // for (int i = 0; i < m_ints.Length; ++i)
+ // {
+ // long mi = m_ints[i];
+ // if (mi != 0)
+ // {
+ // int j = 0;
+ // while ((mi & 0xFFL) == 0)
+ // {
+ // j += 8;
+ // mi >>>= 8;
+ // }
+ // while ((mi & 1L) == 0)
+ // {
+ // ++j;
+ // mi >>>= 1;
+ // }
+ // return (i << 6) + j;
+ // }
+ // }
+ // return -1;
+ // }
+
+ private static int BitLength(long w)
+ {
+ int u = (int)((ulong)w >> 32), b;
+ if (u == 0)
+ {
+ u = (int)w;
+ b = 0;
+ }
+ else
+ {
+ b = 32;
+ }
+
+ int t = (int)((uint)u >> 16), k;
+ if (t == 0)
+ {
+ t = (int)((uint)u >> 8);
+ k = (t == 0) ? BitLengths[u] : 8 + BitLengths[t];
+ }
+ else
+ {
+ int v = (int)((uint)t >> 8);
+ k = (v == 0) ? 16 + BitLengths[t] : 24 + BitLengths[v];
+ }
+
+ return b + k;
+ }
+
+ private long[] ResizedInts(int newLen)
+ {
+ long[] newInts = new long[newLen];
+ Array.Copy(m_ints, 0, newInts, 0, System.Math.Min(m_ints.Length, newLen));
+ return newInts;
+ }
+
+ public BigInteger ToBigInteger()
+ {
+ int usedLen = GetUsedLength();
+ if (usedLen == 0)
+ {
+ return BigInteger.Zero;
+ }
+
+ long highestInt = m_ints[usedLen - 1];
+ byte[] temp = new byte[8];
+ int barrI = 0;
+ bool trailingZeroBytesDone = false;
+ for (int j = 7; j >= 0; j--)
+ {
+ byte thisByte = (byte)((ulong)highestInt >> (8 * j));
+ if (trailingZeroBytesDone || (thisByte != 0))
+ {
+ trailingZeroBytesDone = true;
+ temp[barrI++] = thisByte;
+ }
+ }
+
+ int barrLen = 8 * (usedLen - 1) + barrI;
+ byte[] barr = new byte[barrLen];
+ for (int j = 0; j < barrI; j++)
+ {
+ barr[j] = temp[j];
+ }
+ // Highest value int is done now
+
+ for (int iarrJ = usedLen - 2; iarrJ >= 0; iarrJ--)
+ {
+ long mi = m_ints[iarrJ];
+ for (int j = 7; j >= 0; j--)
+ {
+ barr[barrI++] = (byte)((ulong)mi >> (8 * j));
+ }
+ }
+ return new BigInteger(1, barr);
+ }
+
+ // private static long shiftUp(long[] x, int xOff, int count)
+ // {
+ // long prev = 0;
+ // for (int i = 0; i < count; ++i)
+ // {
+ // long next = x[xOff + i];
+ // x[xOff + i] = (next << 1) | prev;
+ // prev = next >>> 63;
+ // }
+ // return prev;
+ // }
+
+ private static long ShiftUp(long[] x, int xOff, int count, int shift)
+ {
+ int shiftInv = 64 - shift;
+ long prev = 0;
+ for (int i = 0; i < count; ++i)
+ {
+ long next = x[xOff + i];
+ x[xOff + i] = (next << shift) | prev;
+ prev = (long)((ulong)next >> shiftInv);
+ }
+ return prev;
+ }
+
+ private static long ShiftUp(long[] x, int xOff, long[] z, int zOff, int count, int shift)
+ {
+ int shiftInv = 64 - shift;
+ long prev = 0;
+ for (int i = 0; i < count; ++i)
+ {
+ long next = x[xOff + i];
+ z[zOff + i] = (next << shift) | prev;
+ prev = (long)((ulong)next >> shiftInv);
+ }
+ return prev;
+ }
+
+ public LongArray AddOne()
+ {
+ if (m_ints.Length == 0)
+ {
+ return new LongArray(new long[]{ 1L });
+ }
+
+ int resultLen = System.Math.Max(1, GetUsedLength());
+ long[] ints = ResizedInts(resultLen);
+ ints[0] ^= 1L;
+ return new LongArray(ints);
+ }
+
+ // private void addShiftedByBits(LongArray other, int bits)
+ // {
+ // int words = bits >>> 6;
+ // int shift = bits & 0x3F;
+ //
+ // if (shift == 0)
+ // {
+ // addShiftedByWords(other, words);
+ // return;
+ // }
+ //
+ // int otherUsedLen = other.GetUsedLength();
+ // if (otherUsedLen == 0)
+ // {
+ // return;
+ // }
+ //
+ // int minLen = otherUsedLen + words + 1;
+ // if (minLen > m_ints.Length)
+ // {
+ // m_ints = resizedInts(minLen);
+ // }
+ //
+ // long carry = addShiftedByBits(m_ints, words, other.m_ints, 0, otherUsedLen, shift);
+ // m_ints[otherUsedLen + words] ^= carry;
+ // }
+
+ private void AddShiftedByBitsSafe(LongArray other, int otherDegree, int bits)
+ {
+ int otherLen = (int)((uint)(otherDegree + 63) >> 6);
+
+ int words = (int)((uint)bits >> 6);
+ int shift = bits & 0x3F;
+
+ if (shift == 0)
+ {
+ Add(m_ints, words, other.m_ints, 0, otherLen);
+ return;
+ }
+
+ long carry = AddShiftedUp(m_ints, words, other.m_ints, 0, otherLen, shift);
+ if (carry != 0L)
+ {
+ m_ints[otherLen + words] ^= carry;
+ }
+ }
+
+ private static long AddShiftedUp(long[] x, int xOff, long[] y, int yOff, int count, int shift)
+ {
+ int shiftInv = 64 - shift;
+ long prev = 0;
+ for (int i = 0; i < count; ++i)
+ {
+ long next = y[yOff + i];
+ x[xOff + i] ^= (next << shift) | prev;
+ prev = (long)((ulong)next >> shiftInv);
+ }
+ return prev;
+ }
+
+ private static long AddShiftedDown(long[] x, int xOff, long[] y, int yOff, int count, int shift)
+ {
+ int shiftInv = 64 - shift;
+ long prev = 0;
+ int i = count;
+ while (--i >= 0)
+ {
+ long next = y[yOff + i];
+ x[xOff + i] ^= (long)((ulong)next >> shift) | prev;
+ prev = next << shiftInv;
+ }
+ return prev;
+ }
+
+ public void AddShiftedByWords(LongArray other, int words)
+ {
+ int otherUsedLen = other.GetUsedLength();
+ if (otherUsedLen == 0)
+ {
+ return;
+ }
+
+ int minLen = otherUsedLen + words;
+ if (minLen > m_ints.Length)
+ {
+ m_ints = ResizedInts(minLen);
+ }
+
+ Add(m_ints, words, other.m_ints, 0, otherUsedLen);
+ }
+
+ private static void Add(long[] x, int xOff, long[] y, int yOff, int count)
+ {
+ for (int i = 0; i < count; ++i)
+ {
+ x[xOff + i] ^= y[yOff + i];
+ }
+ }
+
+ private static void Add(long[] x, int xOff, long[] y, int yOff, long[] z, int zOff, int count)
+ {
+ for (int i = 0; i < count; ++i)
+ {
+ z[zOff + i] = x[xOff + i] ^ y[yOff + i];
+ }
+ }
+
+ private static void AddBoth(long[] x, int xOff, long[] y1, int y1Off, long[] y2, int y2Off, int count)
+ {
+ for (int i = 0; i < count; ++i)
+ {
+ x[xOff + i] ^= y1[y1Off + i] ^ y2[y2Off + i];
+ }
+ }
+
+ private static void Distribute(long[] x, int src, int dst1, int dst2, int count)
+ {
+ for (int i = 0; i < count; ++i)
+ {
+ long v = x[src + i];
+ x[dst1 + i] ^= v;
+ x[dst2 + i] ^= v;
+ }
+ }
+
+ public int Length
+ {
+ get { return m_ints.Length; }
+ }
+
+ private static void FlipWord(long[] buf, int off, int bit, long word)
+ {
+ int n = off + (int)((uint)bit >> 6);
+ int shift = bit & 0x3F;
+ if (shift == 0)
+ {
+ buf[n] ^= word;
+ }
+ else
+ {
+ buf[n] ^= word << shift;
+ word = (long)((ulong)word >> (64 - shift));
+ if (word != 0)
+ {
+ buf[++n] ^= word;
+ }
+ }
+ }
+
+ // private static long getWord(long[] buf, int off, int len, int bit)
+ // {
+ // int n = off + (bit >>> 6);
+ // int shift = bit & 0x3F;
+ // if (shift == 0)
+ // {
+ // return buf[n];
+ // }
+ // long result = buf[n] >>> shift;
+ // if (++n < len)
+ // {
+ // result |= buf[n] << (64 - shift);
+ // }
+ // return result;
+ // }
+
+ public bool TestBitZero()
+ {
+ return m_ints.Length > 0 && (m_ints[0] & 1L) != 0;
+ }
+
+ private static bool TestBit(long[] buf, int off, int n)
+ {
+ // theInt = n / 64
+ int theInt = (int)((uint)n >> 6);
+ // theBit = n % 64
+ int theBit = n & 0x3F;
+ long tester = 1L << theBit;
+ return (buf[off + theInt] & tester) != 0;
+ }
+
+ private static void FlipBit(long[] buf, int off, int n)
+ {
+ // theInt = n / 64
+ int theInt = (int)((uint)n >> 6);
+ // theBit = n % 64
+ int theBit = n & 0x3F;
+ long flipper = 1L << theBit;
+ buf[off + theInt] ^= flipper;
+ }
+
+ // private static void SetBit(long[] buf, int off, int n)
+ // {
+ // // theInt = n / 64
+ // int theInt = n >>> 6;
+ // // theBit = n % 64
+ // int theBit = n & 0x3F;
+ // long setter = 1L << theBit;
+ // buf[off + theInt] |= setter;
+ // }
+ //
+ // private static void ClearBit(long[] buf, int off, int n)
+ // {
+ // // theInt = n / 64
+ // int theInt = n >>> 6;
+ // // theBit = n % 64
+ // int theBit = n & 0x3F;
+ // long setter = 1L << theBit;
+ // buf[off + theInt] &= ~setter;
+ // }
+
+ private static void MultiplyWord(long a, long[] b, int bLen, long[] c, int cOff)
+ {
+ if ((a & 1L) != 0L)
+ {
+ Add(c, cOff, b, 0, bLen);
+ }
+ int k = 1;
+ while ((a = (long)((ulong)a >> 1)) != 0L)
+ {
+ if ((a & 1L) != 0L)
+ {
+ long carry = AddShiftedUp(c, cOff, b, 0, bLen, k);
+ if (carry != 0L)
+ {
+ c[cOff + bLen] ^= carry;
+ }
+ }
+ ++k;
+ }
+ }
+
+ public LongArray ModMultiplyLD(LongArray other, int m, int[] ks)
+ {
+ /*
+ * Find out the degree of each argument and handle the zero cases
+ */
+ int aDeg = Degree();
+ if (aDeg == 0)
+ {
+ return this;
+ }
+ int bDeg = other.Degree();
+ if (bDeg == 0)
+ {
+ return other;
+ }
+
+ /*
+ * Swap if necessary so that A is the smaller argument
+ */
+ LongArray A = this, B = other;
+ if (aDeg > bDeg)
+ {
+ A = other; B = this;
+ int tmp = aDeg; aDeg = bDeg; bDeg = tmp;
+ }
+
+ /*
+ * Establish the word lengths of the arguments and result
+ */
+ int aLen = (int)((uint)(aDeg + 63) >> 6);
+ int bLen = (int)((uint)(bDeg + 63) >> 6);
+ int cLen = (int)((uint)(aDeg + bDeg + 62) >> 6);
+
+ if (aLen == 1)
+ {
+ long a0 = A.m_ints[0];
+ if (a0 == 1L)
+ {
+ return B;
+ }
+
+ /*
+ * Fast path for small A, with performance dependent only on the number of set bits
+ */
+ long[] c0 = new long[cLen];
+ MultiplyWord(a0, B.m_ints, bLen, c0, 0);
+
+ /*
+ * Reduce the raw answer against the reduction coefficients
+ */
+ return ReduceResult(c0, 0, cLen, m, ks);
+ }
+
+ /*
+ * Determine if B will get bigger during shifting
+ */
+ int bMax = (int)((uint)(bDeg + 7 + 63) >> 6);
+
+ /*
+ * Lookup table for the offset of each B in the tables
+ */
+ int[] ti = new int[16];
+
+ /*
+ * Precompute table of all 4-bit products of B
+ */
+ long[] T0 = new long[bMax << 4];
+ int tOff = bMax;
+ ti[1] = tOff;
+ Array.Copy(B.m_ints, 0, T0, tOff, bLen);
+ for (int i = 2; i < 16; ++i)
+ {
+ ti[i] = (tOff += bMax);
+ if ((i & 1) == 0)
+ {
+ ShiftUp(T0, (int)((uint)tOff >> 1), T0, tOff, bMax, 1);
+ }
+ else
+ {
+ Add(T0, bMax, T0, tOff - bMax, T0, tOff, bMax);
+ }
+ }
+
+ /*
+ * Second table with all 4-bit products of B shifted 4 bits
+ */
+ long[] T1 = new long[T0.Length];
+ ShiftUp(T0, 0, T1, 0, T0.Length, 4);
+ // shiftUp(T0, bMax, T1, bMax, tOff, 4);
+
+ long[] a = A.m_ints;
+ long[] c = new long[cLen];
+
+ int MASK = 0xF;
+
+ /*
+ * Lopez-Dahab algorithm
+ */
+
+ for (int k = 56; k >= 0; k -= 8)
+ {
+ for (int j = 1; j < aLen; j += 2)
+ {
+ int aVal = (int)((ulong)a[j] >> k);
+ int u = aVal & MASK;
+ int v = (int)((uint)aVal >> 4) & MASK;
+ AddBoth(c, j - 1, T0, ti[u], T1, ti[v], bMax);
+ }
+ ShiftUp(c, 0, cLen, 8);
+ }
+
+ for (int k = 56; k >= 0; k -= 8)
+ {
+ for (int j = 0; j < aLen; j += 2)
+ {
+ int aVal = (int)((ulong)a[j] >> k);
+ int u = aVal & MASK;
+ int v = (int)((uint)aVal >> 4) & MASK;
+ AddBoth(c, j, T0, ti[u], T1, ti[v], bMax);
+ }
+ if (k > 0)
+ {
+ ShiftUp(c, 0, cLen, 8);
+ }
+ }
+
+ /*
+ * Finally the raw answer is collected, reduce it against the reduction coefficients
+ */
+ return ReduceResult(c, 0, cLen, m, ks);
+ }
+
+ public LongArray ModMultiply(LongArray other, int m, int[] ks)
+ {
+ /*
+ * Find out the degree of each argument and handle the zero cases
+ */
+ int aDeg = Degree();
+ if (aDeg == 0)
+ {
+ return this;
+ }
+ int bDeg = other.Degree();
+ if (bDeg == 0)
+ {
+ return other;
+ }
+
+ /*
+ * Swap if necessary so that A is the smaller argument
+ */
+ LongArray A = this, B = other;
+ if (aDeg > bDeg)
+ {
+ A = other; B = this;
+ int tmp = aDeg; aDeg = bDeg; bDeg = tmp;
+ }
+
+ /*
+ * Establish the word lengths of the arguments and result
+ */
+ int aLen = (int)((uint)(aDeg + 63) >> 6);
+ int bLen = (int)((uint)(bDeg + 63) >> 6);
+ int cLen = (int)((uint)(aDeg + bDeg + 62) >> 6);
+
+ if (aLen == 1)
+ {
+ long a0 = A.m_ints[0];
+ if (a0 == 1L)
+ {
+ return B;
+ }
+
+ /*
+ * Fast path for small A, with performance dependent only on the number of set bits
+ */
+ long[] c0 = new long[cLen];
+ MultiplyWord(a0, B.m_ints, bLen, c0, 0);
+
+ /*
+ * Reduce the raw answer against the reduction coefficients
+ */
+ return ReduceResult(c0, 0, cLen, m, ks);
+ }
+
+ /*
+ * Determine if B will get bigger during shifting
+ */
+ int bMax = (int)((uint)(bDeg + 7 + 63) >> 6);
+
+ /*
+ * Lookup table for the offset of each B in the tables
+ */
+ int[] ti = new int[16];
+
+ /*
+ * Precompute table of all 4-bit products of B
+ */
+ long[] T0 = new long[bMax << 4];
+ int tOff = bMax;
+ ti[1] = tOff;
+ Array.Copy(B.m_ints, 0, T0, tOff, bLen);
+ for (int i = 2; i < 16; ++i)
+ {
+ ti[i] = (tOff += bMax);
+ if ((i & 1) == 0)
+ {
+ ShiftUp(T0, (int)((uint)tOff >> 1), T0, tOff, bMax, 1);
+ }
+ else
+ {
+ Add(T0, bMax, T0, tOff - bMax, T0, tOff, bMax);
+ }
+ }
+
+ /*
+ * Second table with all 4-bit products of B shifted 4 bits
+ */
+ long[] T1 = new long[T0.Length];
+ ShiftUp(T0, 0, T1, 0, T0.Length, 4);
+ // ShiftUp(T0, bMax, T1, bMax, tOff, 4);
+
+ long[] a = A.m_ints;
+ long[] c = new long[cLen << 3];
+
+ int MASK = 0xF;
+
+ /*
+ * Lopez-Dahab (Modified) algorithm
+ */
+
+ for (int aPos = 0; aPos < aLen; ++aPos)
+ {
+ long aVal = a[aPos];
+ int cOff = aPos;
+ for (;;)
+ {
+ int u = (int)aVal & MASK;
+ aVal = (long)((ulong)aVal >> 4);
+ int v = (int)aVal & MASK;
+ AddBoth(c, cOff, T0, ti[u], T1, ti[v], bMax);
+ aVal = (long)((ulong)aVal >> 4);
+ if (aVal == 0L)
+ {
+ break;
+ }
+ cOff += cLen;
+ }
+ }
+
+ {
+ int cOff = c.Length;
+ while ((cOff -= cLen) != 0)
+ {
+ AddShiftedUp(c, cOff - cLen, c, cOff, cLen, 8);
+ }
+ }
+
+ /*
+ * Finally the raw answer is collected, reduce it against the reduction coefficients
+ */
+ return ReduceResult(c, 0, cLen, m, ks);
+ }
+
+ public LongArray ModMultiplyAlt(LongArray other, int m, int[] ks)
+ {
+ /*
+ * Find out the degree of each argument and handle the zero cases
+ */
+ int aDeg = Degree();
+ if (aDeg == 0)
+ {
+ return this;
+ }
+ int bDeg = other.Degree();
+ if (bDeg == 0)
+ {
+ return other;
+ }
+
+ /*
+ * Swap if necessary so that A is the smaller argument
+ */
+ LongArray A = this, B = other;
+ if (aDeg > bDeg)
+ {
+ A = other; B = this;
+ int tmp = aDeg; aDeg = bDeg; bDeg = tmp;
+ }
+
+ /*
+ * Establish the word lengths of the arguments and result
+ */
+ int aLen = (int)((uint)(aDeg + 63) >> 6);
+ int bLen = (int)((uint)(bDeg + 63) >> 6);
+ int cLen = (int)((uint)(aDeg + bDeg + 62) >> 6);
+
+ if (aLen == 1)
+ {
+ long a0 = A.m_ints[0];
+ if (a0 == 1L)
+ {
+ return B;
+ }
+
+ /*
+ * Fast path for small A, with performance dependent only on the number of set bits
+ */
+ long[] c0 = new long[cLen];
+ MultiplyWord(a0, B.m_ints, bLen, c0, 0);
+
+ /*
+ * Reduce the raw answer against the reduction coefficients
+ */
+ return ReduceResult(c0, 0, cLen, m, ks);
+ }
+
+ // NOTE: This works, but is slower than width 4 processing
+ // if (aLen == 2)
+ // {
+ // /*
+ // * Use common-multiplicand optimization to save ~1/4 of the adds
+ // */
+ // long a1 = A.m_ints[0], a2 = A.m_ints[1];
+ // long aa = a1 & a2; a1 ^= aa; a2 ^= aa;
+ //
+ // long[] b = B.m_ints;
+ // long[] c = new long[cLen];
+ // multiplyWord(aa, b, bLen, c, 1);
+ // add(c, 0, c, 1, cLen - 1);
+ // multiplyWord(a1, b, bLen, c, 0);
+ // multiplyWord(a2, b, bLen, c, 1);
+ //
+ // /*
+ // * Reduce the raw answer against the reduction coefficients
+ // */
+ // return ReduceResult(c, 0, cLen, m, ks);
+ // }
+
+ /*
+ * Determine the parameters of the Interleaved window algorithm: the 'width' in bits to
+ * process together, the number of evaluation 'positions' implied by that width, and the
+ * 'top' position at which the regular window algorithm stops.
+ */
+ int width, positions, top, banks;
+
+ // NOTE: width 4 is the fastest over the entire range of sizes used in current crypto
+ // width = 1; positions = 64; top = 64; banks = 4;
+ // width = 2; positions = 32; top = 64; banks = 4;
+ // width = 3; positions = 21; top = 63; banks = 3;
+ width = 4; positions = 16; top = 64; banks = 8;
+ // width = 5; positions = 13; top = 65; banks = 7;
+ // width = 7; positions = 9; top = 63; banks = 9;
+ // width = 8; positions = 8; top = 64; banks = 8;
+
+ /*
+ * Determine if B will get bigger during shifting
+ */
+ int shifts = top < 64 ? positions : positions - 1;
+ int bMax = (int)((uint)(bDeg + shifts + 63) >> 6);
+
+ int bTotal = bMax * banks, stride = width * banks;
+
+ /*
+ * Create a single temporary buffer, with an offset table to find the positions of things in it
+ */
+ int[] ci = new int[1 << width];
+ int cTotal = aLen;
+ {
+ ci[0] = cTotal;
+ cTotal += bTotal;
+ ci[1] = cTotal;
+ for (int i = 2; i < ci.Length; ++i)
+ {
+ cTotal += cLen;
+ ci[i] = cTotal;
+ }
+ cTotal += cLen;
+ }
+ // NOTE: Provide a safe dump for "high zeroes" since we are adding 'bMax' and not 'bLen'
+ ++cTotal;
+
+ long[] c = new long[cTotal];
+
+ // Prepare A in Interleaved form, according to the chosen width
+ Interleave(A.m_ints, 0, c, 0, aLen, width);
+
+ // Make a working copy of B, since we will be shifting it
+ {
+ int bOff = aLen;
+ Array.Copy(B.m_ints, 0, c, bOff, bLen);
+ for (int bank = 1; bank < banks; ++bank)
+ {
+ ShiftUp(c, aLen, c, bOff += bMax, bMax, bank);
+ }
+ }
+
+ /*
+ * The main loop analyzes the Interleaved windows in A, and for each non-zero window
+ * a single word-array XOR is performed to a carefully selected slice of 'c'. The loop is
+ * breadth-first, checking the lowest window in each word, then looping again for the
+ * next higher window position.
+ */
+ int MASK = (1 << width) - 1;
+
+ int k = 0;
+ for (;;)
+ {
+ int aPos = 0;
+ do
+ {
+ long aVal = (long)((ulong)c[aPos] >> k);
+ int bank = 0, bOff = aLen;
+ for (;;)
+ {
+ int index = (int)(aVal) & MASK;
+ if (index != 0)
+ {
+ /*
+ * Add to a 'c' buffer based on the bit-pattern of 'index'. Since A is in
+ * Interleaved form, the bits represent the current B shifted by 0, 'positions',
+ * 'positions' * 2, ..., 'positions' * ('width' - 1)
+ */
+ Add(c, aPos + ci[index], c, bOff, bMax);
+ }
+ if (++bank == banks)
+ {
+ break;
+ }
+ bOff += bMax;
+ aVal = (long)((ulong)aVal >> width);
+ }
+ }
+ while (++aPos < aLen);
+
+ if ((k += stride) >= top)
+ {
+ if (k >= 64)
+ {
+ break;
+ }
+
+ /*
+ * Adjustment for window setups with top == 63, the final bit (if any) is processed
+ * as the top-bit of a window
+ */
+ k = 64 - width;
+ MASK &= MASK << (top - k);
+ }
+
+ /*
+ * After each position has been checked for all words of A, B is shifted up 1 place
+ */
+ ShiftUp(c, aLen, bTotal, banks);
+ }
+
+ int ciPos = ci.Length;
+ while (--ciPos > 1)
+ {
+ if ((ciPos & 1L) == 0L)
+ {
+ /*
+ * For even numbers, shift contents and add to the half-position
+ */
+ AddShiftedUp(c, ci[(uint)ciPos >> 1], c, ci[ciPos], cLen, positions);
+ }
+ else
+ {
+ /*
+ * For odd numbers, 'distribute' contents to the result and the next-lowest position
+ */
+ Distribute(c, ci[ciPos], ci[ciPos - 1], ci[1], cLen);
+ }
+ }
+
+ /*
+ * Finally the raw answer is collected, reduce it against the reduction coefficients
+ */
+ return ReduceResult(c, ci[1], cLen, m, ks);
+ }
+
+ private static LongArray ReduceResult(long[] buf, int off, int len, int m, int[] ks)
+ {
+ int rLen = ReduceInPlace(buf, off, len, m, ks);
+ return new LongArray(buf, off, rLen);
+ }
+
+ // private static void deInterleave(long[] x, int xOff, long[] z, int zOff, int count, int rounds)
+ // {
+ // for (int i = 0; i < count; ++i)
+ // {
+ // z[zOff + i] = deInterleave(x[zOff + i], rounds);
+ // }
+ // }
+ //
+ // private static long deInterleave(long x, int rounds)
+ // {
+ // while (--rounds >= 0)
+ // {
+ // x = deInterleave32(x & DEInterleave_MASK) | (deInterleave32((x >>> 1) & DEInterleave_MASK) << 32);
+ // }
+ // return x;
+ // }
+ //
+ // private static long deInterleave32(long x)
+ // {
+ // x = (x | (x >>> 1)) & 0x3333333333333333L;
+ // x = (x | (x >>> 2)) & 0x0F0F0F0F0F0F0F0FL;
+ // x = (x | (x >>> 4)) & 0x00FF00FF00FF00FFL;
+ // x = (x | (x >>> 8)) & 0x0000FFFF0000FFFFL;
+ // x = (x | (x >>> 16)) & 0x00000000FFFFFFFFL;
+ // return x;
+ // }
+
+ private static int ReduceInPlace(long[] buf, int off, int len, int m, int[] ks)
+ {
+ int mLen = (int)((uint)(m + 63) >> 6);
+ if (len < mLen)
+ {
+ return len;
+ }
+
+ int numBits = System.Math.Min(len << 6, (m << 1) - 1); // TODO use actual degree?
+ int excessBits = (len << 6) - numBits;
+ while (excessBits >= 64)
+ {
+ --len;
+ excessBits -= 64;
+ }
+
+ int kLen = ks.Length, kMax = ks[kLen - 1], kNext = kLen > 1 ? ks[kLen - 2] : 0;
+ int wordWiseLimit = System.Math.Max(m, kMax + 64);
+ int vectorableWords = (excessBits + System.Math.Min(numBits - wordWiseLimit, m - kNext)) >> 6;
+ if (vectorableWords > 1)
+ {
+ int vectorWiseWords = len - vectorableWords;
+ ReduceVectorWise(buf, off, len, vectorWiseWords, m, ks);
+ while (len > vectorWiseWords)
+ {
+ buf[off + --len] = 0L;
+ }
+ numBits = vectorWiseWords << 6;
+ }
+
+ if (numBits > wordWiseLimit)
+ {
+ ReduceWordWise(buf, off, len, wordWiseLimit, m, ks);
+ numBits = wordWiseLimit;
+ }
+
+ if (numBits > m)
+ {
+ ReduceBitWise(buf, off, numBits, m, ks);
+ }
+
+ return mLen;
+ }
+
+ private static void ReduceBitWise(long[] buf, int off, int BitLength, int m, int[] ks)
+ {
+ while (--BitLength >= m)
+ {
+ if (TestBit(buf, off, BitLength))
+ {
+ ReduceBit(buf, off, BitLength, m, ks);
+ }
+ }
+ }
+
+ private static void ReduceBit(long[] buf, int off, int bit, int m, int[] ks)
+ {
+ FlipBit(buf, off, bit);
+ int n = bit - m;
+ int j = ks.Length;
+ while (--j >= 0)
+ {
+ FlipBit(buf, off, ks[j] + n);
+ }
+ FlipBit(buf, off, n);
+ }
+
+ private static void ReduceWordWise(long[] buf, int off, int len, int toBit, int m, int[] ks)
+ {
+ int toPos = (int)((uint)toBit >> 6);
+
+ while (--len > toPos)
+ {
+ long word = buf[off + len];
+ if (word != 0)
+ {
+ buf[off + len] = 0;
+ ReduceWord(buf, off, (len << 6), word, m, ks);
+ }
+ }
+
+ {
+ int partial = toBit & 0x3F;
+ long word = (long)((ulong)buf[off + toPos] >> partial);
+ if (word != 0)
+ {
+ buf[off + toPos] ^= word << partial;
+ ReduceWord(buf, off, toBit, word, m, ks);
+ }
+ }
+ }
+
+ private static void ReduceWord(long[] buf, int off, int bit, long word, int m, int[] ks)
+ {
+ int offset = bit - m;
+ int j = ks.Length;
+ while (--j >= 0)
+ {
+ FlipWord(buf, off, offset + ks[j], word);
+ }
+ FlipWord(buf, off, offset, word);
+ }
+
+ private static void ReduceVectorWise(long[] buf, int off, int len, int words, int m, int[] ks)
+ {
+ /*
+ * NOTE: It's important we go from highest coefficient to lowest, because for the highest
+ * one (only) we allow the ranges to partially overlap, and therefore any changes must take
+ * effect for the subsequent lower coefficients.
+ */
+ int baseBit = (words << 6) - m;
+ int j = ks.Length;
+ while (--j >= 0)
+ {
+ FlipVector(buf, off, buf, off + words, len - words, baseBit + ks[j]);
+ }
+ FlipVector(buf, off, buf, off + words, len - words, baseBit);
+ }
+
+ private static void FlipVector(long[] x, int xOff, long[] y, int yOff, int yLen, int bits)
+ {
+ xOff += (int)((uint)bits >> 6);
+ bits &= 0x3F;
+
+ if (bits == 0)
+ {
+ Add(x, xOff, y, yOff, yLen);
+ }
+ else
+ {
+ long carry = AddShiftedDown(x, xOff + 1, y, yOff, yLen, 64 - bits);
+ x[xOff] ^= carry;
+ }
+ }
+
+ public LongArray ModSquare(int m, int[] ks)
+ {
+ int len = GetUsedLength();
+ if (len == 0)
+ {
+ return this;
+ }
+
+ int _2len = len << 1;
+ long[] r = new long[_2len];
+
+ int pos = 0;
+ while (pos < _2len)
+ {
+ long mi = m_ints[(uint)pos >> 1];
+ r[pos++] = Interleave2_32to64((int)mi);
+ r[pos++] = Interleave2_32to64((int)((ulong)mi >> 32));
+ }
+
+ return new LongArray(r, 0, ReduceInPlace(r, 0, r.Length, m, ks));
+ }
+
+ // private LongArray modSquareN(int n, int m, int[] ks)
+ // {
+ // int len = GetUsedLength();
+ // if (len == 0)
+ // {
+ // return this;
+ // }
+ //
+ // int mLen = (m + 63) >>> 6;
+ // long[] r = new long[mLen << 1];
+ // Array.Copy(m_ints, 0, r, 0, len);
+ //
+ // while (--n >= 0)
+ // {
+ // squareInPlace(r, len, m, ks);
+ // len = reduceInPlace(r, 0, r.Length, m, ks);
+ // }
+ //
+ // return new LongArray(r, 0, len);
+ // }
+ //
+ // private static void squareInPlace(long[] x, int xLen, int m, int[] ks)
+ // {
+ // int pos = xLen << 1;
+ // while (--xLen >= 0)
+ // {
+ // long xVal = x[xLen];
+ // x[--pos] = Interleave2_32to64((int)(xVal >>> 32));
+ // x[--pos] = Interleave2_32to64((int)xVal);
+ // }
+ // }
+
+ private static void Interleave(long[] x, int xOff, long[] z, int zOff, int count, int width)
+ {
+ switch (width)
+ {
+ case 3:
+ Interleave3(x, xOff, z, zOff, count);
+ break;
+ case 5:
+ Interleave5(x, xOff, z, zOff, count);
+ break;
+ case 7:
+ Interleave7(x, xOff, z, zOff, count);
+ break;
+ default:
+ Interleave2_n(x, xOff, z, zOff, count, BitLengths[width] - 1);
+ break;
+ }
+ }
+
+ private static void Interleave3(long[] x, int xOff, long[] z, int zOff, int count)
+ {
+ for (int i = 0; i < count; ++i)
+ {
+ z[zOff + i] = Interleave3(x[xOff + i]);
+ }
+ }
+
+ private static long Interleave3(long x)
+ {
+ long z = x & (1L << 63);
+ return z
+ | Interleave3_21to63((int)x & 0x1FFFFF)
+ | Interleave3_21to63((int)((ulong)x >> 21) & 0x1FFFFF) << 1
+ | Interleave3_21to63((int)((ulong)x >> 42) & 0x1FFFFF) << 2;
+
+ // int zPos = 0, wPos = 0, xPos = 0;
+ // for (;;)
+ // {
+ // z |= ((x >>> xPos) & 1L) << zPos;
+ // if (++zPos == 63)
+ // {
+ // String sz2 = Long.toBinaryString(z);
+ // return z;
+ // }
+ // if ((xPos += 21) >= 63)
+ // {
+ // xPos = ++wPos;
+ // }
+ // }
+ }
+
+ private static long Interleave3_21to63(int x)
+ {
+ int r00 = INTERLEAVE3_TABLE[x & 0x7F];
+ int r21 = INTERLEAVE3_TABLE[((uint)x >> 7) & 0x7F];
+ int r42 = INTERLEAVE3_TABLE[(uint)x >> 14];
+ return (r42 & 0xFFFFFFFFL) << 42 | (r21 & 0xFFFFFFFFL) << 21 | (r00 & 0xFFFFFFFFL);
+ }
+
+ private static void Interleave5(long[] x, int xOff, long[] z, int zOff, int count)
+ {
+ for (int i = 0; i < count; ++i)
+ {
+ z[zOff + i] = Interleave5(x[xOff + i]);
+ }
+ }
+
+ private static long Interleave5(long x)
+ {
+ return Interleave3_13to65((int)x & 0x1FFF)
+ | Interleave3_13to65((int)((ulong)x >> 13) & 0x1FFF) << 1
+ | Interleave3_13to65((int)((ulong)x >> 26) & 0x1FFF) << 2
+ | Interleave3_13to65((int)((ulong)x >> 39) & 0x1FFF) << 3
+ | Interleave3_13to65((int)((ulong)x >> 52) & 0x1FFF) << 4;
+
+ // long z = 0;
+ // int zPos = 0, wPos = 0, xPos = 0;
+ // for (;;)
+ // {
+ // z |= ((x >>> xPos) & 1L) << zPos;
+ // if (++zPos == 64)
+ // {
+ // return z;
+ // }
+ // if ((xPos += 13) >= 64)
+ // {
+ // xPos = ++wPos;
+ // }
+ // }
+ }
+
+ private static long Interleave3_13to65(int x)
+ {
+ int r00 = INTERLEAVE5_TABLE[x & 0x7F];
+ int r35 = INTERLEAVE5_TABLE[(uint)x >> 7];
+ return (r35 & 0xFFFFFFFFL) << 35 | (r00 & 0xFFFFFFFFL);
+ }
+
+ private static void Interleave7(long[] x, int xOff, long[] z, int zOff, int count)
+ {
+ for (int i = 0; i < count; ++i)
+ {
+ z[zOff + i] = Interleave7(x[xOff + i]);
+ }
+ }
+
+ private static long Interleave7(long x)
+ {
+ long z = x & (1L << 63);
+ return z
+ | INTERLEAVE7_TABLE[(int)x & 0x1FF]
+ | INTERLEAVE7_TABLE[(int)((ulong)x >> 9) & 0x1FF] << 1
+ | INTERLEAVE7_TABLE[(int)((ulong)x >> 18) & 0x1FF] << 2
+ | INTERLEAVE7_TABLE[(int)((ulong)x >> 27) & 0x1FF] << 3
+ | INTERLEAVE7_TABLE[(int)((ulong)x >> 36) & 0x1FF] << 4
+ | INTERLEAVE7_TABLE[(int)((ulong)x >> 45) & 0x1FF] << 5
+ | INTERLEAVE7_TABLE[(int)((ulong)x >> 54) & 0x1FF] << 6;
+
+ // int zPos = 0, wPos = 0, xPos = 0;
+ // for (;;)
+ // {
+ // z |= ((x >>> xPos) & 1L) << zPos;
+ // if (++zPos == 63)
+ // {
+ // return z;
+ // }
+ // if ((xPos += 9) >= 63)
+ // {
+ // xPos = ++wPos;
+ // }
+ // }
+ }
+
+ private static void Interleave2_n(long[] x, int xOff, long[] z, int zOff, int count, int rounds)
+ {
+ for (int i = 0; i < count; ++i)
+ {
+ z[zOff + i] = Interleave2_n(x[xOff + i], rounds);
+ }
+ }
+
+ private static long Interleave2_n(long x, int rounds)
+ {
+ while (rounds > 1)
+ {
+ rounds -= 2;
+ x = Interleave4_16to64((int)x & 0xFFFF)
+ | Interleave4_16to64((int)((ulong)x >> 16) & 0xFFFF) << 1
+ | Interleave4_16to64((int)((ulong)x >> 32) & 0xFFFF) << 2
+ | Interleave4_16to64((int)((ulong)x >> 48) & 0xFFFF) << 3;
+ }
+ if (rounds > 0)
+ {
+ x = Interleave2_32to64((int)x) | Interleave2_32to64((int)((ulong)x >> 32)) << 1;
+ }
+ return x;
+ }
+
+ private static long Interleave4_16to64(int x)
+ {
+ int r00 = INTERLEAVE4_TABLE[x & 0xFF];
+ int r32 = INTERLEAVE4_TABLE[(uint)x >> 8];
+ return (r32 & 0xFFFFFFFFL) << 32 | (r00 & 0xFFFFFFFFL);
+ }
+
+ private static long Interleave2_32to64(int x)
+ {
+ int r00 = INTERLEAVE2_TABLE[x & 0xFF] | INTERLEAVE2_TABLE[((uint)x >> 8) & 0xFF] << 16;
+ int r32 = INTERLEAVE2_TABLE[((uint)x >> 16) & 0xFF] | INTERLEAVE2_TABLE[(uint)x >> 24] << 16;
+ return (r32 & 0xFFFFFFFFL) << 32 | (r00 & 0xFFFFFFFFL);
+ }
+
+ // private static LongArray ExpItohTsujii2(LongArray B, int n, int m, int[] ks)
+ // {
+ // LongArray t1 = B, t3 = new LongArray(new long[]{ 1L });
+ // int scale = 1;
+ //
+ // int numTerms = n;
+ // while (numTerms > 1)
+ // {
+ // if ((numTerms & 1) != 0)
+ // {
+ // t3 = t3.ModMultiply(t1, m, ks);
+ // t1 = t1.modSquareN(scale, m, ks);
+ // }
+ //
+ // LongArray t2 = t1.modSquareN(scale, m, ks);
+ // t1 = t1.ModMultiply(t2, m, ks);
+ // numTerms >>>= 1; scale <<= 1;
+ // }
+ //
+ // return t3.ModMultiply(t1, m, ks);
+ // }
+ //
+ // private static LongArray ExpItohTsujii23(LongArray B, int n, int m, int[] ks)
+ // {
+ // LongArray t1 = B, t3 = new LongArray(new long[]{ 1L });
+ // int scale = 1;
+ //
+ // int numTerms = n;
+ // while (numTerms > 1)
+ // {
+ // bool m03 = numTerms % 3 == 0;
+ // bool m14 = !m03 && (numTerms & 1) != 0;
+ //
+ // if (m14)
+ // {
+ // t3 = t3.ModMultiply(t1, m, ks);
+ // t1 = t1.modSquareN(scale, m, ks);
+ // }
+ //
+ // LongArray t2 = t1.modSquareN(scale, m, ks);
+ // t1 = t1.ModMultiply(t2, m, ks);
+ //
+ // if (m03)
+ // {
+ // t2 = t2.modSquareN(scale, m, ks);
+ // t1 = t1.ModMultiply(t2, m, ks);
+ // numTerms /= 3; scale *= 3;
+ // }
+ // else
+ // {
+ // numTerms >>>= 1; scale <<= 1;
+ // }
+ // }
+ //
+ // return t3.ModMultiply(t1, m, ks);
+ // }
+ //
+ // private static LongArray ExpItohTsujii235(LongArray B, int n, int m, int[] ks)
+ // {
+ // LongArray t1 = B, t4 = new LongArray(new long[]{ 1L });
+ // int scale = 1;
+ //
+ // int numTerms = n;
+ // while (numTerms > 1)
+ // {
+ // if (numTerms % 5 == 0)
+ // {
+ //// t1 = ExpItohTsujii23(t1, 5, m, ks);
+ //
+ // LongArray t3 = t1;
+ // t1 = t1.modSquareN(scale, m, ks);
+ //
+ // LongArray t2 = t1.modSquareN(scale, m, ks);
+ // t1 = t1.ModMultiply(t2, m, ks);
+ // t2 = t1.modSquareN(scale << 1, m, ks);
+ // t1 = t1.ModMultiply(t2, m, ks);
+ //
+ // t1 = t1.ModMultiply(t3, m, ks);
+ //
+ // numTerms /= 5; scale *= 5;
+ // continue;
+ // }
+ //
+ // bool m03 = numTerms % 3 == 0;
+ // bool m14 = !m03 && (numTerms & 1) != 0;
+ //
+ // if (m14)
+ // {
+ // t4 = t4.ModMultiply(t1, m, ks);
+ // t1 = t1.modSquareN(scale, m, ks);
+ // }
+ //
+ // LongArray t2 = t1.modSquareN(scale, m, ks);
+ // t1 = t1.ModMultiply(t2, m, ks);
+ //
+ // if (m03)
+ // {
+ // t2 = t2.modSquareN(scale, m, ks);
+ // t1 = t1.ModMultiply(t2, m, ks);
+ // numTerms /= 3; scale *= 3;
+ // }
+ // else
+ // {
+ // numTerms >>>= 1; scale <<= 1;
+ // }
+ // }
+ //
+ // return t4.ModMultiply(t1, m, ks);
+ // }
+
+ public LongArray ModInverse(int m, int[] ks)
+ {
+ /*
+ * Fermat's Little Theorem
+ */
+ // LongArray A = this;
+ // LongArray B = A.modSquare(m, ks);
+ // LongArray R0 = B, R1 = B;
+ // for (int i = 2; i < m; ++i)
+ // {
+ // R1 = R1.modSquare(m, ks);
+ // R0 = R0.ModMultiply(R1, m, ks);
+ // }
+ //
+ // return R0;
+
+ /*
+ * Itoh-Tsujii
+ */
+ // LongArray B = modSquare(m, ks);
+ // switch (m)
+ // {
+ // case 409:
+ // return ExpItohTsujii23(B, m - 1, m, ks);
+ // case 571:
+ // return ExpItohTsujii235(B, m - 1, m, ks);
+ // case 163:
+ // case 233:
+ // case 283:
+ // default:
+ // return ExpItohTsujii2(B, m - 1, m, ks);
+ // }
+
+ /*
+ * Inversion in F2m using the extended Euclidean algorithm
+ *
+ * Input: A nonzero polynomial a(z) of degree at most m-1
+ * Output: a(z)^(-1) mod f(z)
+ */
+ int uzDegree = Degree();
+ if (uzDegree == 1)
+ {
+ return this;
+ }
+
+ // u(z) := a(z)
+ LongArray uz = (LongArray)Copy();
+
+ int t = (int)((uint)(m + 63) >> 6);
+
+ // v(z) := f(z)
+ LongArray vz = new LongArray(t);
+ ReduceBit(vz.m_ints, 0, m, m, ks);
+
+ // g1(z) := 1, g2(z) := 0
+ LongArray g1z = new LongArray(t);
+ g1z.m_ints[0] = 1L;
+ LongArray g2z = new LongArray(t);
+
+ int[] uvDeg = new int[]{ uzDegree, m + 1 };
+ LongArray[] uv = new LongArray[]{ uz, vz };
+
+ int[] ggDeg = new int[]{ 1, 0 };
+ LongArray[] gg = new LongArray[]{ g1z, g2z };
+
+ int b = 1;
+ int duv1 = uvDeg[b];
+ int dgg1 = ggDeg[b];
+ int j = duv1 - uvDeg[1 - b];
+
+ for (;;)
+ {
+ if (j < 0)
+ {
+ j = -j;
+ uvDeg[b] = duv1;
+ ggDeg[b] = dgg1;
+ b = 1 - b;
+ duv1 = uvDeg[b];
+ dgg1 = ggDeg[b];
+ }
+
+ uv[b].AddShiftedByBitsSafe(uv[1 - b], uvDeg[1 - b], j);
+
+ int duv2 = uv[b].DegreeFrom(duv1);
+ if (duv2 == 0)
+ {
+ return gg[1 - b];
+ }
+
+ {
+ int dgg2 = ggDeg[1 - b];
+ gg[b].AddShiftedByBitsSafe(gg[1 - b], dgg2, j);
+ dgg2 += j;
+
+ if (dgg2 > dgg1)
+ {
+ dgg1 = dgg2;
+ }
+ else if (dgg2 == dgg1)
+ {
+ dgg1 = gg[b].DegreeFrom(dgg1);
+ }
+ }
+
+ j += (duv2 - duv1);
+ duv1 = duv2;
+ }
+ }
+
+ public override bool Equals(object obj)
+ {
+ return Equals(obj as LongArray);
+ }
+
+ public virtual bool Equals(LongArray other)
+ {
+ if (this == other)
+ return true;
+ if (null == other)
+ return false;
+ int usedLen = GetUsedLength();
+ if (other.GetUsedLength() != usedLen)
+ {
+ return false;
+ }
+ for (int i = 0; i < usedLen; i++)
+ {
+ if (m_ints[i] != other.m_ints[i])
+ {
+ return false;
+ }
+ }
+ return true;
+ }
+
+ public override int GetHashCode()
+ {
+ int usedLen = GetUsedLength();
+ int hash = 1;
+ for (int i = 0; i < usedLen; i++)
+ {
+ long mi = m_ints[i];
+ hash *= 31;
+ hash ^= (int)mi;
+ hash *= 31;
+ hash ^= (int)((ulong)mi >> 32);
+ }
+ return hash;
+ }
+
+ public LongArray Copy()
+ {
+ return new LongArray(Arrays.Clone(m_ints));
+ }
+
+ public override string ToString()
+ {
+ int i = GetUsedLength();
+ if (i == 0)
+ {
+ return "0";
+ }
+
+ StringBuilder sb = new StringBuilder(Convert.ToString(m_ints[--i], 2));
+ while (--i >= 0)
+ {
+ string s = Convert.ToString(m_ints[i], 2);
+
+ // Add leading zeroes, except for highest significant word
+ int len = s.Length;
+ if (len < 64)
+ {
+ sb.Append(ZEROES.Substring(len));
+ }
+
+ sb.Append(s);
+ }
+ return sb.ToString();
+ }
+ }
+}
diff --git a/crypto/src/util/Arrays.cs b/crypto/src/util/Arrays.cs
index 59c91bdd1..8f8cebedc 100644
--- a/crypto/src/util/Arrays.cs
+++ b/crypto/src/util/Arrays.cs
@@ -216,7 +216,7 @@ namespace Org.BouncyCastle.Utilities
public static byte[] Clone(
byte[] data)
{
- return data == null ? null : (byte[]) data.Clone();
+ return data == null ? null : (byte[])data.Clone();
}
public static byte[] Clone(
@@ -238,7 +238,12 @@ namespace Org.BouncyCastle.Utilities
public static int[] Clone(
int[] data)
{
- return data == null ? null : (int[]) data.Clone();
+ return data == null ? null : (int[])data.Clone();
+ }
+
+ public static long[] Clone(long[] data)
+ {
+ return data == null ? null : (long[])data.Clone();
}
[CLSCompliantAttribute(false)]
|
