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diff --git a/bcprov/src/main/java/org/bouncycastle/pqc/math/linearalgebra/GF2Polynomial.java b/bcprov/src/main/java/org/bouncycastle/pqc/math/linearalgebra/GF2Polynomial.java
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+package org.bouncycastle.pqc.math.linearalgebra;
+
+
+import java.math.BigInteger;
+import java.util.Random;
+
+
+/**
+ * This class stores very long strings of bits and does some basic arithmetics.
+ * It is used by <tt>GF2nField</tt>, <tt>GF2nPolynomialField</tt> and
+ * <tt>GFnPolynomialElement</tt>.
+ *
+ * @see GF2nPolynomialElement
+ * @see GF2nField
+ */
+public class GF2Polynomial
+{
+
+ // number of bits stored in this GF2Polynomial
+ private int len;
+
+ // number of int used in value
+ private int blocks;
+
+ // storage
+ private int[] value;
+
+ // Random source
+ private static Random rand = new Random();
+
+ // Lookup-Table for vectorMult: parity[a]= #1(a) mod 2 == 1
+ private static final boolean[] parity = {false, true, true, false, true,
+ false, false, true, true, false, false, true, false, true, true,
+ false, true, false, false, true, false, true, true, false, false,
+ true, true, false, true, false, false, true, true, false, false,
+ true, false, true, true, false, false, true, true, false, true,
+ false, false, true, false, true, true, false, true, false, false,
+ true, true, false, false, true, false, true, true, false, true,
+ false, false, true, false, true, true, false, false, true, true,
+ false, true, false, false, true, false, true, true, false, true,
+ false, false, true, true, false, false, true, false, true, true,
+ false, false, true, true, false, true, false, false, true, true,
+ false, false, true, false, true, true, false, true, false, false,
+ true, false, true, true, false, false, true, true, false, true,
+ false, false, true, true, false, false, true, false, true, true,
+ false, false, true, true, false, true, false, false, true, false,
+ true, true, false, true, false, false, true, true, false, false,
+ true, false, true, true, false, false, true, true, false, true,
+ false, false, true, true, false, false, true, false, true, true,
+ false, true, false, false, true, false, true, true, false, false,
+ true, true, false, true, false, false, true, false, true, true,
+ false, true, false, false, true, true, false, false, true, false,
+ true, true, false, true, false, false, true, false, true, true,
+ false, false, true, true, false, true, false, false, true, true,
+ false, false, true, false, true, true, false, false, true, true,
+ false, true, false, false, true, false, true, true, false, true,
+ false, false, true, true, false, false, true, false, true, true,
+ false};
+
+ // Lookup-Table for Squaring: squaringTable[a]=a^2
+ private static final short[] squaringTable = {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};
+
+ // pre-computed Bitmask for fast masking, bitMask[a]=0x1 << a
+ private static final int[] bitMask = {0x00000001, 0x00000002, 0x00000004,
+ 0x00000008, 0x00000010, 0x00000020, 0x00000040, 0x00000080,
+ 0x00000100, 0x00000200, 0x00000400, 0x00000800, 0x00001000,
+ 0x00002000, 0x00004000, 0x00008000, 0x00010000, 0x00020000,
+ 0x00040000, 0x00080000, 0x00100000, 0x00200000, 0x00400000,
+ 0x00800000, 0x01000000, 0x02000000, 0x04000000, 0x08000000,
+ 0x10000000, 0x20000000, 0x40000000, 0x80000000, 0x00000000};
+
+ // pre-computed Bitmask for fast masking, rightMask[a]=0xffffffff >>> (32-a)
+ private static final int[] reverseRightMask = {0x00000000, 0x00000001,
+ 0x00000003, 0x00000007, 0x0000000f, 0x0000001f, 0x0000003f,
+ 0x0000007f, 0x000000ff, 0x000001ff, 0x000003ff, 0x000007ff,
+ 0x00000fff, 0x00001fff, 0x00003fff, 0x00007fff, 0x0000ffff,
+ 0x0001ffff, 0x0003ffff, 0x0007ffff, 0x000fffff, 0x001fffff,
+ 0x003fffff, 0x007fffff, 0x00ffffff, 0x01ffffff, 0x03ffffff,
+ 0x07ffffff, 0x0fffffff, 0x1fffffff, 0x3fffffff, 0x7fffffff,
+ 0xffffffff};
+
+ /**
+ * Creates a new GF2Polynomial of the given <i>length</i> and value zero.
+ *
+ * @param length the desired number of bits to store
+ */
+ public GF2Polynomial(int length)
+ {
+ int l = length;
+ if (l < 1)
+ {
+ l = 1;
+ }
+ blocks = ((l - 1) >> 5) + 1;
+ value = new int[blocks];
+ len = l;
+ }
+
+ /**
+ * Creates a new GF2Polynomial of the given <i>length</i> and random value.
+ *
+ * @param length the desired number of bits to store
+ * @param rand SecureRandom to use for randomization
+ */
+ public GF2Polynomial(int length, Random rand)
+ {
+ int l = length;
+ if (l < 1)
+ {
+ l = 1;
+ }
+ blocks = ((l - 1) >> 5) + 1;
+ value = new int[blocks];
+ len = l;
+ randomize(rand);
+ }
+
+ /**
+ * Creates a new GF2Polynomial of the given <i>length</i> and value
+ * selected by <i>value</i>:
+ * <UL>
+ * <LI>ZERO</LI>
+ * <LI>ONE</LI>
+ * <LI>RANDOM</LI>
+ * <LI>X</LI>
+ * <LI>ALL</LI>
+ * </UL>
+ *
+ * @param length the desired number of bits to store
+ * @param value the value described by a String
+ */
+ public GF2Polynomial(int length, String value)
+ {
+ int l = length;
+ if (l < 1)
+ {
+ l = 1;
+ }
+ blocks = ((l - 1) >> 5) + 1;
+ this.value = new int[blocks];
+ len = l;
+ if (value.equalsIgnoreCase("ZERO"))
+ {
+ assignZero();
+ }
+ else if (value.equalsIgnoreCase("ONE"))
+ {
+ assignOne();
+ }
+ else if (value.equalsIgnoreCase("RANDOM"))
+ {
+ randomize();
+ }
+ else if (value.equalsIgnoreCase("X"))
+ {
+ assignX();
+ }
+ else if (value.equalsIgnoreCase("ALL"))
+ {
+ assignAll();
+ }
+ else
+ {
+ throw new IllegalArgumentException(
+ "Error: GF2Polynomial was called using " + value
+ + " as value!");
+ }
+
+ }
+
+ /**
+ * Creates a new GF2Polynomial of the given <i>length</i> using the given
+ * int[]. LSB is contained in bs[0].
+ *
+ * @param length the desired number of bits to store
+ * @param bs contains the desired value, LSB in bs[0]
+ */
+ public GF2Polynomial(int length, int[] bs)
+ {
+ int leng = length;
+ if (leng < 1)
+ {
+ leng = 1;
+ }
+ blocks = ((leng - 1) >> 5) + 1;
+ value = new int[blocks];
+ len = leng;
+ int l = Math.min(blocks, bs.length);
+ System.arraycopy(bs, 0, value, 0, l);
+ zeroUnusedBits();
+ }
+
+ /**
+ * Creates a new GF2Polynomial by converting the given byte[] <i>os</i>
+ * according to 1363 and using the given <i>length</i>.
+ *
+ * @param length the intended length of this polynomial
+ * @param os the octet string to assign to this polynomial
+ * @see "P1363 5.5.2 p22f, OS2BSP"
+ */
+ public GF2Polynomial(int length, byte[] os)
+ {
+ int l = length;
+ if (l < 1)
+ {
+ l = 1;
+ }
+ blocks = ((l - 1) >> 5) + 1;
+ value = new int[blocks];
+ len = l;
+ int i, m;
+ int k = Math.min(((os.length - 1) >> 2) + 1, blocks);
+ for (i = 0; i < k - 1; i++)
+ {
+ m = os.length - (i << 2) - 1;
+ value[i] = (os[m]) & 0x000000ff;
+ value[i] |= (os[m - 1] << 8) & 0x0000ff00;
+ value[i] |= (os[m - 2] << 16) & 0x00ff0000;
+ value[i] |= (os[m - 3] << 24) & 0xff000000;
+ }
+ i = k - 1;
+ m = os.length - (i << 2) - 1;
+ value[i] = os[m] & 0x000000ff;
+ if (m > 0)
+ {
+ value[i] |= (os[m - 1] << 8) & 0x0000ff00;
+ }
+ if (m > 1)
+ {
+ value[i] |= (os[m - 2] << 16) & 0x00ff0000;
+ }
+ if (m > 2)
+ {
+ value[i] |= (os[m - 3] << 24) & 0xff000000;
+ }
+ zeroUnusedBits();
+ reduceN();
+ }
+
+ /**
+ * Creates a new GF2Polynomial by converting the given FlexiBigInt <i>bi</i>
+ * according to 1363 and using the given <i>length</i>.
+ *
+ * @param length the intended length of this polynomial
+ * @param bi the FlexiBigInt to assign to this polynomial
+ * @see "P1363 5.5.1 p22, I2BSP"
+ */
+ public GF2Polynomial(int length, BigInteger bi)
+ {
+ int l = length;
+ if (l < 1)
+ {
+ l = 1;
+ }
+ blocks = ((l - 1) >> 5) + 1;
+ value = new int[blocks];
+ len = l;
+ int i;
+ byte[] val = bi.toByteArray();
+ if (val[0] == 0)
+ {
+ byte[] dummy = new byte[val.length - 1];
+ System.arraycopy(val, 1, dummy, 0, dummy.length);
+ val = dummy;
+ }
+ int ov = val.length & 0x03;
+ int k = ((val.length - 1) >> 2) + 1;
+ for (i = 0; i < ov; i++)
+ {
+ value[k - 1] |= (val[i] & 0x000000ff) << ((ov - 1 - i) << 3);
+ }
+ int m = 0;
+ for (i = 0; i <= (val.length - 4) >> 2; i++)
+ {
+ m = val.length - 1 - (i << 2);
+ value[i] = (val[m]) & 0x000000ff;
+ value[i] |= ((val[m - 1]) << 8) & 0x0000ff00;
+ value[i] |= ((val[m - 2]) << 16) & 0x00ff0000;
+ value[i] |= ((val[m - 3]) << 24) & 0xff000000;
+ }
+ if ((len & 0x1f) != 0)
+ {
+ value[blocks - 1] &= reverseRightMask[len & 0x1f];
+ }
+ reduceN();
+ }
+
+ /**
+ * Creates a new GF2Polynomial by cloneing the given GF2Polynomial <i>b</i>.
+ *
+ * @param b the GF2Polynomial to clone
+ */
+ public GF2Polynomial(GF2Polynomial b)
+ {
+ len = b.len;
+ blocks = b.blocks;
+ value = IntUtils.clone(b.value);
+ }
+
+ /**
+ * @return a copy of this GF2Polynomial
+ */
+ public Object clone()
+ {
+ return new GF2Polynomial(this);
+ }
+
+ /**
+ * Returns the length of this GF2Polynomial. The length can be greater than
+ * the degree. To get the degree call reduceN() before calling getLength().
+ *
+ * @return the length of this GF2Polynomial
+ */
+ public int getLength()
+ {
+ return len;
+ }
+
+ /**
+ * Returns the value of this GF2Polynomial in an int[].
+ *
+ * @return the value of this GF2Polynomial in a new int[], LSB in int[0]
+ */
+ public int[] toIntegerArray()
+ {
+ int[] result;
+ result = new int[blocks];
+ System.arraycopy(value, 0, result, 0, blocks);
+ return result;
+ }
+
+ /**
+ * Returns a string representing this GF2Polynomials value using hexadecimal
+ * or binary radix in MSB-first order.
+ *
+ * @param radix the radix to use (2 or 16, otherwise 2 is used)
+ * @return a String representing this GF2Polynomials value.
+ */
+ public String toString(int radix)
+ {
+ final char[] HEX_CHARS = {'0', '1', '2', '3', '4', '5', '6', '7', '8',
+ '9', 'a', 'b', 'c', 'd', 'e', 'f'};
+ final String[] BIN_CHARS = {"0000", "0001", "0010", "0011", "0100",
+ "0101", "0110", "0111", "1000", "1001", "1010", "1011", "1100",
+ "1101", "1110", "1111"};
+ String res;
+ int i;
+ res = new String();
+ if (radix == 16)
+ {
+ for (i = blocks - 1; i >= 0; i--)
+ {
+ res += HEX_CHARS[(value[i] >>> 28) & 0x0f];
+ res += HEX_CHARS[(value[i] >>> 24) & 0x0f];
+ res += HEX_CHARS[(value[i] >>> 20) & 0x0f];
+ res += HEX_CHARS[(value[i] >>> 16) & 0x0f];
+ res += HEX_CHARS[(value[i] >>> 12) & 0x0f];
+ res += HEX_CHARS[(value[i] >>> 8) & 0x0f];
+ res += HEX_CHARS[(value[i] >>> 4) & 0x0f];
+ res += HEX_CHARS[(value[i]) & 0x0f];
+ res += " ";
+ }
+ }
+ else
+ {
+ for (i = blocks - 1; i >= 0; i--)
+ {
+ res += BIN_CHARS[(value[i] >>> 28) & 0x0f];
+ res += BIN_CHARS[(value[i] >>> 24) & 0x0f];
+ res += BIN_CHARS[(value[i] >>> 20) & 0x0f];
+ res += BIN_CHARS[(value[i] >>> 16) & 0x0f];
+ res += BIN_CHARS[(value[i] >>> 12) & 0x0f];
+ res += BIN_CHARS[(value[i] >>> 8) & 0x0f];
+ res += BIN_CHARS[(value[i] >>> 4) & 0x0f];
+ res += BIN_CHARS[(value[i]) & 0x0f];
+ res += " ";
+ }
+ }
+ return res;
+ }
+
+ /**
+ * Converts this polynomial to a byte[] (octet string) according to 1363.
+ *
+ * @return a byte[] representing the value of this polynomial
+ * @see "P1363 5.5.2 p22f, BS2OSP"
+ */
+ public byte[] toByteArray()
+ {
+ int k = ((len - 1) >> 3) + 1;
+ int ov = k & 0x03;
+ int m;
+ byte[] res = new byte[k];
+ int i;
+ for (i = 0; i < (k >> 2); i++)
+ {
+ m = k - (i << 2) - 1;
+ res[m] = (byte)((value[i] & 0x000000ff));
+ res[m - 1] = (byte)((value[i] & 0x0000ff00) >>> 8);
+ res[m - 2] = (byte)((value[i] & 0x00ff0000) >>> 16);
+ res[m - 3] = (byte)((value[i] & 0xff000000) >>> 24);
+ }
+ for (i = 0; i < ov; i++)
+ {
+ m = (ov - i - 1) << 3;
+ res[i] = (byte)((value[blocks - 1] & (0x000000ff << m)) >>> m);
+ }
+ return res;
+ }
+
+ /**
+ * Converts this polynomial to an integer according to 1363.
+ *
+ * @return a FlexiBigInt representing the value of this polynomial
+ * @see "P1363 5.5.1 p22, BS2IP"
+ */
+ public BigInteger toFlexiBigInt()
+ {
+ if (len == 0 || isZero())
+ {
+ return new BigInteger(0, new byte[0]);
+ }
+ return new BigInteger(1, toByteArray());
+ }
+
+ /**
+ * Sets the LSB to 1 and all other to 0, assigning 'one' to this
+ * GF2Polynomial.
+ */
+ public void assignOne()
+ {
+ int i;
+ for (i = 1; i < blocks; i++)
+ {
+ value[i] = 0x00;
+ }
+ value[0] = 0x01;
+ }
+
+ /**
+ * Sets Bit 1 to 1 and all other to 0, assigning 'x' to this GF2Polynomial.
+ */
+ public void assignX()
+ {
+ int i;
+ for (i = 1; i < blocks; i++)
+ {
+ value[i] = 0x00;
+ }
+ value[0] = 0x02;
+ }
+
+ /**
+ * Sets all Bits to 1.
+ */
+ public void assignAll()
+ {
+ int i;
+ for (i = 0; i < blocks; i++)
+ {
+ value[i] = 0xffffffff;
+ }
+ zeroUnusedBits();
+ }
+
+ /**
+ * Resets all bits to zero.
+ */
+ public void assignZero()
+ {
+ int i;
+ for (i = 0; i < blocks; i++)
+ {
+ value[i] = 0x00;
+ }
+ }
+
+ /**
+ * Fills all len bits of this GF2Polynomial with random values.
+ */
+ public void randomize()
+ {
+ int i;
+ for (i = 0; i < blocks; i++)
+ {
+ value[i] = rand.nextInt();
+ }
+ zeroUnusedBits();
+ }
+
+ /**
+ * Fills all len bits of this GF2Polynomial with random values using the
+ * specified source of randomness.
+ *
+ * @param rand the source of randomness
+ */
+ public void randomize(Random rand)
+ {
+ int i;
+ for (i = 0; i < blocks; i++)
+ {
+ value[i] = rand.nextInt();
+ }
+ zeroUnusedBits();
+ }
+
+ /**
+ * Returns true if two GF2Polynomials have the same size and value and thus
+ * are equal.
+ *
+ * @param other the other GF2Polynomial
+ * @return true if this GF2Polynomial equals <i>b</i> (<i>this</i> ==
+ * <i>b</i>)
+ */
+ public boolean equals(Object other)
+ {
+ if (other == null || !(other instanceof GF2Polynomial))
+ {
+ return false;
+ }
+
+ GF2Polynomial otherPol = (GF2Polynomial)other;
+
+ if (len != otherPol.len)
+ {
+ return false;
+ }
+ for (int i = 0; i < blocks; i++)
+ {
+ if (value[i] != otherPol.value[i])
+ {
+ return false;
+ }
+ }
+ return true;
+ }
+
+ /**
+ * @return the hash code of this polynomial
+ */
+ public int hashCode()
+ {
+ return len + value.hashCode();
+ }
+
+ /**
+ * Tests if all bits equal zero.
+ *
+ * @return true if this GF2Polynomial equals 'zero' (<i>this</i> == 0)
+ */
+ public boolean isZero()
+ {
+ int i;
+ if (len == 0)
+ {
+ return true;
+ }
+ for (i = 0; i < blocks; i++)
+ {
+ if (value[i] != 0)
+ {
+ return false;
+ }
+ }
+ return true;
+ }
+
+ /**
+ * Tests if all bits are reset to 0 and LSB is set to 1.
+ *
+ * @return true if this GF2Polynomial equals 'one' (<i>this</i> == 1)
+ */
+ public boolean isOne()
+ {
+ int i;
+ for (i = 1; i < blocks; i++)
+ {
+ if (value[i] != 0)
+ {
+ return false;
+ }
+ }
+ if (value[0] != 0x01)
+ {
+ return false;
+ }
+ return true;
+ }
+
+ /**
+ * Adds <i>b</i> to this GF2Polynomial and assigns the result to this
+ * GF2Polynomial. <i>b</i> can be of different size.
+ *
+ * @param b GF2Polynomial to add to this GF2Polynomial
+ */
+ public void addToThis(GF2Polynomial b)
+ {
+ expandN(b.len);
+ xorThisBy(b);
+ }
+
+ /**
+ * Adds two GF2Polynomials, <i>this</i> and <i>b</i>, and returns the
+ * result. <i>this</i> and <i>b</i> can be of different size.
+ *
+ * @param b a GF2Polynomial
+ * @return a new GF2Polynomial (<i>this</i> + <i>b</i>)
+ */
+ public GF2Polynomial add(GF2Polynomial b)
+ {
+ return xor(b);
+ }
+
+ /**
+ * Subtracts <i>b</i> from this GF2Polynomial and assigns the result to
+ * this GF2Polynomial. <i>b</i> can be of different size.
+ *
+ * @param b a GF2Polynomial
+ */
+ public void subtractFromThis(GF2Polynomial b)
+ {
+ expandN(b.len);
+ xorThisBy(b);
+ }
+
+ /**
+ * Subtracts two GF2Polynomials, <i>this</i> and <i>b</i>, and returns the
+ * result in a new GF2Polynomial. <i>this</i> and <i>b</i> can be of
+ * different size.
+ *
+ * @param b a GF2Polynomial
+ * @return a new GF2Polynomial (<i>this</i> - <i>b</i>)
+ */
+ public GF2Polynomial subtract(GF2Polynomial b)
+ {
+ return xor(b);
+ }
+
+ /**
+ * Toggles the LSB of this GF2Polynomial, increasing its value by 'one'.
+ */
+ public void increaseThis()
+ {
+ xorBit(0);
+ }
+
+ /**
+ * Toggles the LSB of this GF2Polynomial, increasing the value by 'one' and
+ * returns the result in a new GF2Polynomial.
+ *
+ * @return <tt>this + 1</tt>
+ */
+ public GF2Polynomial increase()
+ {
+ GF2Polynomial result = new GF2Polynomial(this);
+ result.increaseThis();
+ return result;
+ }
+
+ /**
+ * Multiplies this GF2Polynomial with <i>b</i> and returns the result in a
+ * new GF2Polynomial. This method does not reduce the result in GF(2^N).
+ * This method uses classic multiplication (schoolbook).
+ *
+ * @param b a GF2Polynomial
+ * @return a new GF2Polynomial (<i>this</i> * <i>b</i>)
+ */
+ public GF2Polynomial multiplyClassic(GF2Polynomial b)
+ {
+ GF2Polynomial result = new GF2Polynomial(Math.max(len, b.len) << 1);
+ GF2Polynomial[] m = new GF2Polynomial[32];
+ int i, j;
+ m[0] = new GF2Polynomial(this);
+ for (i = 1; i <= 31; i++)
+ {
+ m[i] = m[i - 1].shiftLeft();
+ }
+ for (i = 0; i < b.blocks; i++)
+ {
+ for (j = 0; j <= 31; j++)
+ {
+ if ((b.value[i] & bitMask[j]) != 0)
+ {
+ result.xorThisBy(m[j]);
+ }
+ }
+ for (j = 0; j <= 31; j++)
+ {
+ m[j].shiftBlocksLeft();
+ }
+ }
+ return result;
+ }
+
+ /**
+ * Multiplies this GF2Polynomial with <i>b</i> and returns the result in a
+ * new GF2Polynomial. This method does not reduce the result in GF(2^N).
+ * This method uses Karatzuba multiplication.
+ *
+ * @param b a GF2Polynomial
+ * @return a new GF2Polynomial (<i>this</i> * <i>b</i>)
+ */
+ public GF2Polynomial multiply(GF2Polynomial b)
+ {
+ int n = Math.max(len, b.len);
+ expandN(n);
+ b.expandN(n);
+ return karaMult(b);
+ }
+
+ /**
+ * Does the recursion for Karatzuba multiplication.
+ */
+ private GF2Polynomial karaMult(GF2Polynomial b)
+ {
+ GF2Polynomial result = new GF2Polynomial(len << 1);
+ if (len <= 32)
+ {
+ result.value = mult32(value[0], b.value[0]);
+ return result;
+ }
+ if (len <= 64)
+ {
+ result.value = mult64(value, b.value);
+ return result;
+ }
+ if (len <= 128)
+ {
+ result.value = mult128(value, b.value);
+ return result;
+ }
+ if (len <= 256)
+ {
+ result.value = mult256(value, b.value);
+ return result;
+ }
+ if (len <= 512)
+ {
+ result.value = mult512(value, b.value);
+ return result;
+ }
+
+ int n = IntegerFunctions.floorLog(len - 1);
+ n = bitMask[n];
+
+ GF2Polynomial a0 = lower(((n - 1) >> 5) + 1);
+ GF2Polynomial a1 = upper(((n - 1) >> 5) + 1);
+ GF2Polynomial b0 = b.lower(((n - 1) >> 5) + 1);
+ GF2Polynomial b1 = b.upper(((n - 1) >> 5) + 1);
+
+ GF2Polynomial c = a1.karaMult(b1); // c = a1*b1
+ GF2Polynomial e = a0.karaMult(b0); // e = a0*b0
+ a0.addToThis(a1); // a0 = a0 + a1
+ b0.addToThis(b1); // b0 = b0 + b1
+ GF2Polynomial d = a0.karaMult(b0); // d = (a0+a1)*(b0+b1)
+
+ result.shiftLeftAddThis(c, n << 1);
+ result.shiftLeftAddThis(c, n);
+ result.shiftLeftAddThis(d, n);
+ result.shiftLeftAddThis(e, n);
+ result.addToThis(e);
+ return result;
+ }
+
+ /**
+ * 16-Integer Version of Karatzuba multiplication.
+ */
+ private static int[] mult512(int[] a, int[] b)
+ {
+ int[] result = new int[32];
+ int[] a0 = new int[8];
+ System.arraycopy(a, 0, a0, 0, Math.min(8, a.length));
+ int[] a1 = new int[8];
+ if (a.length > 8)
+ {
+ System.arraycopy(a, 8, a1, 0, Math.min(8, a.length - 8));
+ }
+ int[] b0 = new int[8];
+ System.arraycopy(b, 0, b0, 0, Math.min(8, b.length));
+ int[] b1 = new int[8];
+ if (b.length > 8)
+ {
+ System.arraycopy(b, 8, b1, 0, Math.min(8, b.length - 8));
+ }
+ int[] c = mult256(a1, b1);
+ result[31] ^= c[15];
+ result[30] ^= c[14];
+ result[29] ^= c[13];
+ result[28] ^= c[12];
+ result[27] ^= c[11];
+ result[26] ^= c[10];
+ result[25] ^= c[9];
+ result[24] ^= c[8];
+ result[23] ^= c[7] ^ c[15];
+ result[22] ^= c[6] ^ c[14];
+ result[21] ^= c[5] ^ c[13];
+ result[20] ^= c[4] ^ c[12];
+ result[19] ^= c[3] ^ c[11];
+ result[18] ^= c[2] ^ c[10];
+ result[17] ^= c[1] ^ c[9];
+ result[16] ^= c[0] ^ c[8];
+ result[15] ^= c[7];
+ result[14] ^= c[6];
+ result[13] ^= c[5];
+ result[12] ^= c[4];
+ result[11] ^= c[3];
+ result[10] ^= c[2];
+ result[9] ^= c[1];
+ result[8] ^= c[0];
+ a1[0] ^= a0[0];
+ a1[1] ^= a0[1];
+ a1[2] ^= a0[2];
+ a1[3] ^= a0[3];
+ a1[4] ^= a0[4];
+ a1[5] ^= a0[5];
+ a1[6] ^= a0[6];
+ a1[7] ^= a0[7];
+ b1[0] ^= b0[0];
+ b1[1] ^= b0[1];
+ b1[2] ^= b0[2];
+ b1[3] ^= b0[3];
+ b1[4] ^= b0[4];
+ b1[5] ^= b0[5];
+ b1[6] ^= b0[6];
+ b1[7] ^= b0[7];
+ int[] d = mult256(a1, b1);
+ result[23] ^= d[15];
+ result[22] ^= d[14];
+ result[21] ^= d[13];
+ result[20] ^= d[12];
+ result[19] ^= d[11];
+ result[18] ^= d[10];
+ result[17] ^= d[9];
+ result[16] ^= d[8];
+ result[15] ^= d[7];
+ result[14] ^= d[6];
+ result[13] ^= d[5];
+ result[12] ^= d[4];
+ result[11] ^= d[3];
+ result[10] ^= d[2];
+ result[9] ^= d[1];
+ result[8] ^= d[0];
+ int[] e = mult256(a0, b0);
+ result[23] ^= e[15];
+ result[22] ^= e[14];
+ result[21] ^= e[13];
+ result[20] ^= e[12];
+ result[19] ^= e[11];
+ result[18] ^= e[10];
+ result[17] ^= e[9];
+ result[16] ^= e[8];
+ result[15] ^= e[7] ^ e[15];
+ result[14] ^= e[6] ^ e[14];
+ result[13] ^= e[5] ^ e[13];
+ result[12] ^= e[4] ^ e[12];
+ result[11] ^= e[3] ^ e[11];
+ result[10] ^= e[2] ^ e[10];
+ result[9] ^= e[1] ^ e[9];
+ result[8] ^= e[0] ^ e[8];
+ result[7] ^= e[7];
+ result[6] ^= e[6];
+ result[5] ^= e[5];
+ result[4] ^= e[4];
+ result[3] ^= e[3];
+ result[2] ^= e[2];
+ result[1] ^= e[1];
+ result[0] ^= e[0];
+ return result;
+ }
+
+ /**
+ * 8-Integer Version of Karatzuba multiplication.
+ */
+ private static int[] mult256(int[] a, int[] b)
+ {
+ int[] result = new int[16];
+ int[] a0 = new int[4];
+ System.arraycopy(a, 0, a0, 0, Math.min(4, a.length));
+ int[] a1 = new int[4];
+ if (a.length > 4)
+ {
+ System.arraycopy(a, 4, a1, 0, Math.min(4, a.length - 4));
+ }
+ int[] b0 = new int[4];
+ System.arraycopy(b, 0, b0, 0, Math.min(4, b.length));
+ int[] b1 = new int[4];
+ if (b.length > 4)
+ {
+ System.arraycopy(b, 4, b1, 0, Math.min(4, b.length - 4));
+ }
+ if (a1[3] == 0 && a1[2] == 0 && b1[3] == 0 && b1[2] == 0)
+ {
+ if (a1[1] == 0 && b1[1] == 0)
+ {
+ if (a1[0] != 0 || b1[0] != 0)
+ { // [3]=[2]=[1]=0, [0]!=0
+ int[] c = mult32(a1[0], b1[0]);
+ result[9] ^= c[1];
+ result[8] ^= c[0];
+ result[5] ^= c[1];
+ result[4] ^= c[0];
+ }
+ }
+ else
+ { // [3]=[2]=0 [1]!=0, [0]!=0
+ int[] c = mult64(a1, b1);
+ result[11] ^= c[3];
+ result[10] ^= c[2];
+ result[9] ^= c[1];
+ result[8] ^= c[0];
+ result[7] ^= c[3];
+ result[6] ^= c[2];
+ result[5] ^= c[1];
+ result[4] ^= c[0];
+ }
+ }
+ else
+ { // [3]!=0 [2]!=0 [1]!=0, [0]!=0
+ int[] c = mult128(a1, b1);
+ result[15] ^= c[7];
+ result[14] ^= c[6];
+ result[13] ^= c[5];
+ result[12] ^= c[4];
+ result[11] ^= c[3] ^ c[7];
+ result[10] ^= c[2] ^ c[6];
+ result[9] ^= c[1] ^ c[5];
+ result[8] ^= c[0] ^ c[4];
+ result[7] ^= c[3];
+ result[6] ^= c[2];
+ result[5] ^= c[1];
+ result[4] ^= c[0];
+ }
+ a1[0] ^= a0[0];
+ a1[1] ^= a0[1];
+ a1[2] ^= a0[2];
+ a1[3] ^= a0[3];
+ b1[0] ^= b0[0];
+ b1[1] ^= b0[1];
+ b1[2] ^= b0[2];
+ b1[3] ^= b0[3];
+ int[] d = mult128(a1, b1);
+ result[11] ^= d[7];
+ result[10] ^= d[6];
+ result[9] ^= d[5];
+ result[8] ^= d[4];
+ result[7] ^= d[3];
+ result[6] ^= d[2];
+ result[5] ^= d[1];
+ result[4] ^= d[0];
+ int[] e = mult128(a0, b0);
+ result[11] ^= e[7];
+ result[10] ^= e[6];
+ result[9] ^= e[5];
+ result[8] ^= e[4];
+ result[7] ^= e[3] ^ e[7];
+ result[6] ^= e[2] ^ e[6];
+ result[5] ^= e[1] ^ e[5];
+ result[4] ^= e[0] ^ e[4];
+ result[3] ^= e[3];
+ result[2] ^= e[2];
+ result[1] ^= e[1];
+ result[0] ^= e[0];
+ return result;
+ }
+
+ /**
+ * 4-Integer Version of Karatzuba multiplication.
+ */
+ private static int[] mult128(int[] a, int[] b)
+ {
+ int[] result = new int[8];
+ int[] a0 = new int[2];
+ System.arraycopy(a, 0, a0, 0, Math.min(2, a.length));
+ int[] a1 = new int[2];
+ if (a.length > 2)
+ {
+ System.arraycopy(a, 2, a1, 0, Math.min(2, a.length - 2));
+ }
+ int[] b0 = new int[2];
+ System.arraycopy(b, 0, b0, 0, Math.min(2, b.length));
+ int[] b1 = new int[2];
+ if (b.length > 2)
+ {
+ System.arraycopy(b, 2, b1, 0, Math.min(2, b.length - 2));
+ }
+ if (a1[1] == 0 && b1[1] == 0)
+ {
+ if (a1[0] != 0 || b1[0] != 0)
+ {
+ int[] c = mult32(a1[0], b1[0]);
+ result[5] ^= c[1];
+ result[4] ^= c[0];
+ result[3] ^= c[1];
+ result[2] ^= c[0];
+ }
+ }
+ else
+ {
+ int[] c = mult64(a1, b1);
+ result[7] ^= c[3];
+ result[6] ^= c[2];
+ result[5] ^= c[1] ^ c[3];
+ result[4] ^= c[0] ^ c[2];
+ result[3] ^= c[1];
+ result[2] ^= c[0];
+ }
+ a1[0] ^= a0[0];
+ a1[1] ^= a0[1];
+ b1[0] ^= b0[0];
+ b1[1] ^= b0[1];
+ if (a1[1] == 0 && b1[1] == 0)
+ {
+ int[] d = mult32(a1[0], b1[0]);
+ result[3] ^= d[1];
+ result[2] ^= d[0];
+ }
+ else
+ {
+ int[] d = mult64(a1, b1);
+ result[5] ^= d[3];
+ result[4] ^= d[2];
+ result[3] ^= d[1];
+ result[2] ^= d[0];
+ }
+ if (a0[1] == 0 && b0[1] == 0)
+ {
+ int[] e = mult32(a0[0], b0[0]);
+ result[3] ^= e[1];
+ result[2] ^= e[0];
+ result[1] ^= e[1];
+ result[0] ^= e[0];
+ }
+ else
+ {
+ int[] e = mult64(a0, b0);
+ result[5] ^= e[3];
+ result[4] ^= e[2];
+ result[3] ^= e[1] ^ e[3];
+ result[2] ^= e[0] ^ e[2];
+ result[1] ^= e[1];
+ result[0] ^= e[0];
+ }
+ return result;
+ }
+
+ /**
+ * 2-Integer Version of Karatzuba multiplication.
+ */
+ private static int[] mult64(int[] a, int[] b)
+ {
+ int[] result = new int[4];
+ int a0 = a[0];
+ int a1 = 0;
+ if (a.length > 1)
+ {
+ a1 = a[1];
+ }
+ int b0 = b[0];
+ int b1 = 0;
+ if (b.length > 1)
+ {
+ b1 = b[1];
+ }
+ if (a1 != 0 || b1 != 0)
+ {
+ int[] c = mult32(a1, b1);
+ result[3] ^= c[1];
+ result[2] ^= c[0] ^ c[1];
+ result[1] ^= c[0];
+ }
+ int[] d = mult32(a0 ^ a1, b0 ^ b1);
+ result[2] ^= d[1];
+ result[1] ^= d[0];
+ int[] e = mult32(a0, b0);
+ result[2] ^= e[1];
+ result[1] ^= e[0] ^ e[1];
+ result[0] ^= e[0];
+ return result;
+ }
+
+ /**
+ * 4-Byte Version of Karatzuba multiplication. Here the actual work is done.
+ */
+ private static int[] mult32(int a, int b)
+ {
+ int[] result = new int[2];
+ if (a == 0 || b == 0)
+ {
+ return result;
+ }
+ long b2 = b;
+ b2 &= 0x00000000ffffffffL;
+ int i;
+ long h = 0;
+ for (i = 1; i <= 32; i++)
+ {
+ if ((a & bitMask[i - 1]) != 0)
+ {
+ h ^= b2;
+ }
+ b2 <<= 1;
+ }
+ result[1] = (int)(h >>> 32);
+ result[0] = (int)(h & 0x00000000ffffffffL);
+ return result;
+ }
+
+ /**
+ * Returns a new GF2Polynomial containing the upper <i>k</i> bytes of this
+ * GF2Polynomial.
+ *
+ * @param k
+ * @return a new GF2Polynomial containing the upper <i>k</i> bytes of this
+ * GF2Polynomial
+ * @see GF2Polynomial#karaMult
+ */
+ private GF2Polynomial upper(int k)
+ {
+ int j = Math.min(k, blocks - k);
+ GF2Polynomial result = new GF2Polynomial(j << 5);
+ if (blocks >= k)
+ {
+ System.arraycopy(value, k, result.value, 0, j);
+ }
+ return result;
+ }
+
+ /**
+ * Returns a new GF2Polynomial containing the lower <i>k</i> bytes of this
+ * GF2Polynomial.
+ *
+ * @param k
+ * @return a new GF2Polynomial containing the lower <i>k</i> bytes of this
+ * GF2Polynomial
+ * @see GF2Polynomial#karaMult
+ */
+ private GF2Polynomial lower(int k)
+ {
+ GF2Polynomial result = new GF2Polynomial(k << 5);
+ System.arraycopy(value, 0, result.value, 0, Math.min(k, blocks));
+ return result;
+ }
+
+ /**
+ * Returns the remainder of <i>this</i> divided by <i>g</i> in a new
+ * GF2Polynomial.
+ *
+ * @param g GF2Polynomial != 0
+ * @return a new GF2Polynomial (<i>this</i> % <i>g</i>)
+ * @throws PolynomialIsZeroException if <i>g</i> equals zero
+ */
+ public GF2Polynomial remainder(GF2Polynomial g)
+ throws RuntimeException
+ {
+ /* a div b = q / r */
+ GF2Polynomial a = new GF2Polynomial(this);
+ GF2Polynomial b = new GF2Polynomial(g);
+ GF2Polynomial j;
+ int i;
+ if (b.isZero())
+ {
+ throw new RuntimeException();
+ }
+ a.reduceN();
+ b.reduceN();
+ if (a.len < b.len)
+ {
+ return a;
+ }
+ i = a.len - b.len;
+ while (i >= 0)
+ {
+ j = b.shiftLeft(i);
+ a.subtractFromThis(j);
+ a.reduceN();
+ i = a.len - b.len;
+ }
+ return a;
+ }
+
+ /**
+ * Returns the absolute quotient of <i>this</i> divided by <i>g</i> in a
+ * new GF2Polynomial.
+ *
+ * @param g GF2Polynomial != 0
+ * @return a new GF2Polynomial |_ <i>this</i> / <i>g</i> _|
+ * @throws PolynomialIsZeroException if <i>g</i> equals zero
+ */
+ public GF2Polynomial quotient(GF2Polynomial g)
+ throws RuntimeException
+ {
+ /* a div b = q / r */
+ GF2Polynomial q = new GF2Polynomial(len);
+ GF2Polynomial a = new GF2Polynomial(this);
+ GF2Polynomial b = new GF2Polynomial(g);
+ GF2Polynomial j;
+ int i;
+ if (b.isZero())
+ {
+ throw new RuntimeException();
+ }
+ a.reduceN();
+ b.reduceN();
+ if (a.len < b.len)
+ {
+ return new GF2Polynomial(0);
+ }
+ i = a.len - b.len;
+ q.expandN(i + 1);
+
+ while (i >= 0)
+ {
+ j = b.shiftLeft(i);
+ a.subtractFromThis(j);
+ a.reduceN();
+ q.xorBit(i);
+ i = a.len - b.len;
+ }
+
+ return q;
+ }
+
+ /**
+ * Divides <i>this</i> by <i>g</i> and returns the quotient and remainder
+ * in a new GF2Polynomial[2], quotient in [0], remainder in [1].
+ *
+ * @param g GF2Polynomial != 0
+ * @return a new GF2Polynomial[2] containing quotient and remainder
+ * @throws PolynomialIsZeroException if <i>g</i> equals zero
+ */
+ public GF2Polynomial[] divide(GF2Polynomial g)
+ throws RuntimeException
+ {
+ /* a div b = q / r */
+ GF2Polynomial[] result = new GF2Polynomial[2];
+ GF2Polynomial q = new GF2Polynomial(len);
+ GF2Polynomial a = new GF2Polynomial(this);
+ GF2Polynomial b = new GF2Polynomial(g);
+ GF2Polynomial j;
+ int i;
+ if (b.isZero())
+ {
+ throw new RuntimeException();
+ }
+ a.reduceN();
+ b.reduceN();
+ if (a.len < b.len)
+ {
+ result[0] = new GF2Polynomial(0);
+ result[1] = a;
+ return result;
+ }
+ i = a.len - b.len;
+ q.expandN(i + 1);
+
+ while (i >= 0)
+ {
+ j = b.shiftLeft(i);
+ a.subtractFromThis(j);
+ a.reduceN();
+ q.xorBit(i);
+ i = a.len - b.len;
+ }
+
+ result[0] = q;
+ result[1] = a;
+ return result;
+ }
+
+ /**
+ * Returns the greatest common divisor of <i>this</i> and <i>g</i> in a
+ * new GF2Polynomial.
+ *
+ * @param g GF2Polynomial != 0
+ * @return a new GF2Polynomial gcd(<i>this</i>,<i>g</i>)
+ * @throws ArithmeticException if <i>this</i> and <i>g</i> both are equal to zero
+ * @throws PolynomialIsZeroException to be API-compliant (should never be thrown).
+ */
+ public GF2Polynomial gcd(GF2Polynomial g)
+ throws RuntimeException
+ {
+ if (isZero() && g.isZero())
+ {
+ throw new ArithmeticException("Both operands of gcd equal zero.");
+ }
+ if (isZero())
+ {
+ return new GF2Polynomial(g);
+ }
+ if (g.isZero())
+ {
+ return new GF2Polynomial(this);
+ }
+ GF2Polynomial a = new GF2Polynomial(this);
+ GF2Polynomial b = new GF2Polynomial(g);
+ GF2Polynomial c;
+
+ while (!b.isZero())
+ {
+ c = a.remainder(b);
+ a = b;
+ b = c;
+ }
+
+ return a;
+ }
+
+ /**
+ * Checks if <i>this</i> is irreducible, according to IEEE P1363, A.5.5,
+ * p103.<br>
+ * Note: The algorithm from IEEE P1363, A5.5 can be used to check a
+ * polynomial with coefficients in GF(2^r) for irreducibility. As this class
+ * only represents polynomials with coefficients in GF(2), the algorithm is
+ * adapted to the case r=1.
+ *
+ * @return true if <i>this</i> is irreducible
+ * @see "P1363, A.5.5, p103"
+ */
+ public boolean isIrreducible()
+ {
+ if (isZero())
+ {
+ return false;
+ }
+ GF2Polynomial f = new GF2Polynomial(this);
+ int d, i;
+ GF2Polynomial u, g;
+ GF2Polynomial dummy;
+ f.reduceN();
+ d = f.len - 1;
+ u = new GF2Polynomial(f.len, "X");
+
+ for (i = 1; i <= (d >> 1); i++)
+ {
+ u.squareThisPreCalc();
+ u = u.remainder(f);
+ dummy = u.add(new GF2Polynomial(32, "X"));
+ if (!dummy.isZero())
+ {
+ g = f.gcd(dummy);
+ if (!g.isOne())
+ {
+ return false;
+ }
+ }
+ else
+ {
+ return false;
+ }
+ }
+
+ return true;
+ }
+
+ /**
+ * Reduces this GF2Polynomial using the trinomial x^<i>m</i> + x^<i>tc</i> +
+ * 1.
+ *
+ * @param m the degree of the used field
+ * @param tc degree of the middle x in the trinomial
+ */
+ void reduceTrinomial(int m, int tc)
+ {
+ int i;
+ int p0, p1;
+ int q0, q1;
+ long t;
+ p0 = m >>> 5; // block which contains 2^m
+ q0 = 32 - (m & 0x1f); // (32-index) of 2^m within block p0
+ p1 = (m - tc) >>> 5; // block which contains 2^tc
+ q1 = 32 - ((m - tc) & 0x1f); // (32-index) of 2^tc within block q1
+ int max = ((m << 1) - 2) >>> 5; // block which contains 2^(2m-2)
+ int min = p0; // block which contains 2^m
+ for (i = max; i > min; i--)
+ { // for i = maxBlock to minBlock
+ // reduce coefficients contained in t
+ // t = block[i]
+ t = value[i] & 0x00000000ffffffffL;
+ // block[i-p0-1] ^= t << q0
+ value[i - p0 - 1] ^= (int)(t << q0);
+ // block[i-p0] ^= t >>> (32-q0)
+ value[i - p0] ^= t >>> (32 - q0);
+ // block[i-p1-1] ^= << q1
+ value[i - p1 - 1] ^= (int)(t << q1);
+ // block[i-p1] ^= t >>> (32-q1)
+ value[i - p1] ^= t >>> (32 - q1);
+ value[i] = 0x00;
+ }
+ // reduce last coefficients in block containing 2^m
+ t = value[min] & 0x00000000ffffffffL & (0xffffffffL << (m & 0x1f)); // t
+ // contains the last coefficients > m
+ value[0] ^= t >>> (32 - q0);
+ if (min - p1 - 1 >= 0)
+ {
+ value[min - p1 - 1] ^= (int)(t << q1);
+ }
+ value[min - p1] ^= t >>> (32 - q1);
+
+ value[min] &= reverseRightMask[m & 0x1f];
+ blocks = ((m - 1) >>> 5) + 1;
+ len = m;
+ }
+
+ /**
+ * Reduces this GF2Polynomial using the pentanomial x^<i>m</i> + x^<i>pc[2]</i> +
+ * x^<i>pc[1]</i> + x^<i>pc[0]</i> + 1.
+ *
+ * @param m the degree of the used field
+ * @param pc degrees of the middle x's in the pentanomial
+ */
+ void reducePentanomial(int m, int[] pc)
+ {
+ int i;
+ int p0, p1, p2, p3;
+ int q0, q1, q2, q3;
+ long t;
+ p0 = m >>> 5;
+ q0 = 32 - (m & 0x1f);
+ p1 = (m - pc[0]) >>> 5;
+ q1 = 32 - ((m - pc[0]) & 0x1f);
+ p2 = (m - pc[1]) >>> 5;
+ q2 = 32 - ((m - pc[1]) & 0x1f);
+ p3 = (m - pc[2]) >>> 5;
+ q3 = 32 - ((m - pc[2]) & 0x1f);
+ int max = ((m << 1) - 2) >>> 5;
+ int min = p0;
+ for (i = max; i > min; i--)
+ {
+ t = value[i] & 0x00000000ffffffffL;
+ value[i - p0 - 1] ^= (int)(t << q0);
+ value[i - p0] ^= t >>> (32 - q0);
+ value[i - p1 - 1] ^= (int)(t << q1);
+ value[i - p1] ^= t >>> (32 - q1);
+ value[i - p2 - 1] ^= (int)(t << q2);
+ value[i - p2] ^= t >>> (32 - q2);
+ value[i - p3 - 1] ^= (int)(t << q3);
+ value[i - p3] ^= t >>> (32 - q3);
+ value[i] = 0;
+ }
+ t = value[min] & 0x00000000ffffffffL & (0xffffffffL << (m & 0x1f));
+ value[0] ^= t >>> (32 - q0);
+ if (min - p1 - 1 >= 0)
+ {
+ value[min - p1 - 1] ^= (int)(t << q1);
+ }
+ value[min - p1] ^= t >>> (32 - q1);
+ if (min - p2 - 1 >= 0)
+ {
+ value[min - p2 - 1] ^= (int)(t << q2);
+ }
+ value[min - p2] ^= t >>> (32 - q2);
+ if (min - p3 - 1 >= 0)
+ {
+ value[min - p3 - 1] ^= (int)(t << q3);
+ }
+ value[min - p3] ^= t >>> (32 - q3);
+ value[min] &= reverseRightMask[m & 0x1f];
+
+ blocks = ((m - 1) >>> 5) + 1;
+ len = m;
+ }
+
+ /**
+ * Reduces len by finding the most significant bit set to one and reducing
+ * len and blocks.
+ */
+ public void reduceN()
+ {
+ int i, j, h;
+ i = blocks - 1;
+ while ((value[i] == 0) && (i > 0))
+ {
+ i--;
+ }
+ h = value[i];
+ j = 0;
+ while (h != 0)
+ {
+ h >>>= 1;
+ j++;
+ }
+ len = (i << 5) + j;
+ blocks = i + 1;
+ }
+
+ /**
+ * Expands len and int[] value to <i>i</i>. This is useful before adding
+ * two GF2Polynomials of different size.
+ *
+ * @param i the intended length
+ */
+ public void expandN(int i)
+ {
+ int k;
+ int[] bs;
+ if (len >= i)
+ {
+ return;
+ }
+ len = i;
+ k = ((i - 1) >>> 5) + 1;
+ if (blocks >= k)
+ {
+ return;
+ }
+ if (value.length >= k)
+ {
+ int j;
+ for (j = blocks; j < k; j++)
+ {
+ value[j] = 0;
+ }
+ blocks = k;
+ return;
+ }
+ bs = new int[k];
+ System.arraycopy(value, 0, bs, 0, blocks);
+ blocks = k;
+ value = null;
+ value = bs;
+ }
+
+ /**
+ * Squares this GF2Polynomial and expands it accordingly. This method does
+ * not reduce the result in GF(2^N). There exists a faster method for
+ * squaring in GF(2^N).
+ *
+ * @see GF2nPolynomialElement#square
+ */
+ public void squareThisBitwise()
+ {
+ int i, h, j, k;
+ if (isZero())
+ {
+ return;
+ }
+ int[] result = new int[blocks << 1];
+ for (i = blocks - 1; i >= 0; i--)
+ {
+ h = value[i];
+ j = 0x00000001;
+ for (k = 0; k < 16; k++)
+ {
+ if ((h & 0x01) != 0)
+ {
+ result[i << 1] |= j;
+ }
+ if ((h & 0x00010000) != 0)
+ {
+ result[(i << 1) + 1] |= j;
+ }
+ j <<= 2;
+ h >>>= 1;
+ }
+ }
+ value = null;
+ value = result;
+ blocks = result.length;
+ len = (len << 1) - 1;
+ }
+
+ /**
+ * Squares this GF2Polynomial by using precomputed values of squaringTable.
+ * This method does not reduce the result in GF(2^N).
+ */
+ public void squareThisPreCalc()
+ {
+ int i;
+ if (isZero())
+ {
+ return;
+ }
+ if (value.length >= (blocks << 1))
+ {
+ for (i = blocks - 1; i >= 0; i--)
+ {
+ value[(i << 1) + 1] = GF2Polynomial.squaringTable[(value[i] & 0x00ff0000) >>> 16]
+ | (GF2Polynomial.squaringTable[(value[i] & 0xff000000) >>> 24] << 16);
+ value[i << 1] = GF2Polynomial.squaringTable[value[i] & 0x000000ff]
+ | (GF2Polynomial.squaringTable[(value[i] & 0x0000ff00) >>> 8] << 16);
+ }
+ blocks <<= 1;
+ len = (len << 1) - 1;
+ }
+ else
+ {
+ int[] result = new int[blocks << 1];
+ for (i = 0; i < blocks; i++)
+ {
+ result[i << 1] = GF2Polynomial.squaringTable[value[i] & 0x000000ff]
+ | (GF2Polynomial.squaringTable[(value[i] & 0x0000ff00) >>> 8] << 16);
+ result[(i << 1) + 1] = GF2Polynomial.squaringTable[(value[i] & 0x00ff0000) >>> 16]
+ | (GF2Polynomial.squaringTable[(value[i] & 0xff000000) >>> 24] << 16);
+ }
+ value = null;
+ value = result;
+ blocks <<= 1;
+ len = (len << 1) - 1;
+ }
+ }
+
+ /**
+ * Does a vector-multiplication modulo 2 and returns the result as boolean.
+ *
+ * @param b GF2Polynomial
+ * @return this x <i>b</i> as boolean (1-&gt;true, 0-&gt;false)
+ * @throws PolynomialsHaveDifferentLengthException if <i>this</i> and <i>b</i> have a different length and
+ * thus cannot be vector-multiplied
+ */
+ public boolean vectorMult(GF2Polynomial b)
+ throws RuntimeException
+ {
+ int i;
+ int h;
+ boolean result = false;
+ if (len != b.len)
+ {
+ throw new RuntimeException();
+ }
+ for (i = 0; i < blocks; i++)
+ {
+ h = value[i] & b.value[i];
+ result ^= parity[h & 0x000000ff];
+ result ^= parity[(h >>> 8) & 0x000000ff];
+ result ^= parity[(h >>> 16) & 0x000000ff];
+ result ^= parity[(h >>> 24) & 0x000000ff];
+ }
+ return result;
+ }
+
+ /**
+ * Returns the bitwise exclusive-or of <i>this</i> and <i>b</i> in a new
+ * GF2Polynomial. <i>this</i> and <i>b</i> can be of different size.
+ *
+ * @param b GF2Polynomial
+ * @return a new GF2Polynomial (<i>this</i> ^ <i>b</i>)
+ */
+ public GF2Polynomial xor(GF2Polynomial b)
+ {
+ int i;
+ GF2Polynomial result;
+ int k = Math.min(blocks, b.blocks);
+ if (len >= b.len)
+ {
+ result = new GF2Polynomial(this);
+ for (i = 0; i < k; i++)
+ {
+ result.value[i] ^= b.value[i];
+ }
+ }
+ else
+ {
+ result = new GF2Polynomial(b);
+ for (i = 0; i < k; i++)
+ {
+ result.value[i] ^= value[i];
+ }
+ }
+ // If we xor'ed some bits too many by proceeding blockwise,
+ // restore them to zero:
+ result.zeroUnusedBits();
+ return result;
+ }
+
+ /**
+ * Computes the bitwise exclusive-or of this GF2Polynomial and <i>b</i> and
+ * stores the result in this GF2Polynomial. <i>b</i> can be of different
+ * size.
+ *
+ * @param b GF2Polynomial
+ */
+ public void xorThisBy(GF2Polynomial b)
+ {
+ int i;
+ for (i = 0; i < Math.min(blocks, b.blocks); i++)
+ {
+ value[i] ^= b.value[i];
+ }
+ // If we xor'ed some bits too many by proceeding blockwise,
+ // restore them to zero:
+ zeroUnusedBits();
+ }
+
+ /**
+ * If {@link #len} is not a multiple of the block size (32), some extra bits
+ * of the last block might have been modified during a blockwise operation.
+ * This method compensates for that by restoring these "extra" bits to zero.
+ */
+ private void zeroUnusedBits()
+ {
+ if ((len & 0x1f) != 0)
+ {
+ value[blocks - 1] &= reverseRightMask[len & 0x1f];
+ }
+ }
+
+ /**
+ * Sets the bit at position <i>i</i>.
+ *
+ * @param i int
+ * @throws RuntimeException if (<i>i</i> &lt; 0) || (<i>i</i> &gt; (len - 1))
+ */
+ public void setBit(int i)
+ throws RuntimeException
+ {
+ if (i < 0 || i > (len - 1))
+ {
+ throw new RuntimeException();
+ }
+ value[i >>> 5] |= bitMask[i & 0x1f];
+ return;
+ }
+
+ /**
+ * Returns the bit at position <i>i</i>.
+ *
+ * @param i int
+ * @return the bit at position <i>i</i> if <i>i</i> is a valid position, 0
+ * otherwise.
+ */
+ public int getBit(int i)
+ {
+ if (i < 0)
+ {
+ throw new RuntimeException();
+ }
+ if (i > (len - 1))
+ {
+ return 0;
+ }
+ return ((value[i >>> 5] & bitMask[i & 0x1f]) != 0) ? 1 : 0;
+ }
+
+ /**
+ * Resets the bit at position <i>i</i>.
+ *
+ * @param i int
+ * @throws RuntimeException if (<i>i</i> &lt; 0) || (<i>i</i> &gt; (len - 1))
+ */
+ public void resetBit(int i)
+ throws RuntimeException
+ {
+ if (i < 0)
+ {
+ throw new RuntimeException();
+ }
+ if (i > (len - 1))
+ {
+ return;
+ }
+ value[i >>> 5] &= ~bitMask[i & 0x1f];
+ }
+
+ /**
+ * Xors the bit at position <i>i</i>.
+ *
+ * @param i int
+ * @throws RuntimeException if (<i>i</i> &lt; 0) || (<i>i</i> &gt; (len - 1))
+ */
+ public void xorBit(int i)
+ throws RuntimeException
+ {
+ if (i < 0 || i > (len - 1))
+ {
+ throw new RuntimeException();
+ }
+ value[i >>> 5] ^= bitMask[i & 0x1f];
+ }
+
+ /**
+ * Tests the bit at position <i>i</i>.
+ *
+ * @param i the position of the bit to be tested
+ * @return true if the bit at position <i>i</i> is set (a(<i>i</i>) ==
+ * 1). False if (<i>i</i> &lt; 0) || (<i>i</i> &gt; (len - 1))
+ */
+ public boolean testBit(int i)
+ {
+ if (i < 0)
+ {
+ throw new RuntimeException();
+ }
+ if (i > (len - 1))
+ {
+ return false;
+ }
+ return (value[i >>> 5] & bitMask[i & 0x1f]) != 0;
+ }
+
+ /**
+ * Returns this GF2Polynomial shift-left by 1 in a new GF2Polynomial.
+ *
+ * @return a new GF2Polynomial (this &lt;&lt; 1)
+ */
+ public GF2Polynomial shiftLeft()
+ {
+ GF2Polynomial result = new GF2Polynomial(len + 1, value);
+ int i;
+ for (i = result.blocks - 1; i >= 1; i--)
+ {
+ result.value[i] <<= 1;
+ result.value[i] |= result.value[i - 1] >>> 31;
+ }
+ result.value[0] <<= 1;
+ return result;
+ }
+
+ /**
+ * Shifts-left this by one and enlarges the size of value if necesary.
+ */
+ public void shiftLeftThis()
+ {
+ /** @todo This is untested. */
+ int i;
+ if ((len & 0x1f) == 0)
+ { // check if blocks increases
+ len += 1;
+ blocks += 1;
+ if (blocks > value.length)
+ { // enlarge value
+ int[] bs = new int[blocks];
+ System.arraycopy(value, 0, bs, 0, value.length);
+ value = null;
+ value = bs;
+ }
+ for (i = blocks - 1; i >= 1; i--)
+ {
+ value[i] |= value[i - 1] >>> 31;
+ value[i - 1] <<= 1;
+ }
+ }
+ else
+ {
+ len += 1;
+ for (i = blocks - 1; i >= 1; i--)
+ {
+ value[i] <<= 1;
+ value[i] |= value[i - 1] >>> 31;
+ }
+ value[0] <<= 1;
+ }
+ }
+
+ /**
+ * Returns this GF2Polynomial shift-left by <i>k</i> in a new
+ * GF2Polynomial.
+ *
+ * @param k int
+ * @return a new GF2Polynomial (this &lt;&lt; <i>k</i>)
+ */
+ public GF2Polynomial shiftLeft(int k)
+ {
+ // Variant 2, requiring a modified shiftBlocksLeft(k)
+ // In case of modification, consider a rename to doShiftBlocksLeft()
+ // with an explicit note that this method assumes that the polynomial
+ // has already been resized. Or consider doing things inline.
+ // Construct the resulting polynomial of appropriate length:
+ GF2Polynomial result = new GF2Polynomial(len + k, value);
+ // Shift left as many multiples of the block size as possible:
+ if (k >= 32)
+ {
+ result.doShiftBlocksLeft(k >>> 5);
+ }
+ // Shift left by the remaining (<32) amount:
+ final int remaining = k & 0x1f;
+ if (remaining != 0)
+ {
+ for (int i = result.blocks - 1; i >= 1; i--)
+ {
+ result.value[i] <<= remaining;
+ result.value[i] |= result.value[i - 1] >>> (32 - remaining);
+ }
+ result.value[0] <<= remaining;
+ }
+ return result;
+ }
+
+ /**
+ * Shifts left b and adds the result to Its a fast version of
+ * <tt>this = add(b.shl(k));</tt>
+ *
+ * @param b GF2Polynomial to shift and add to this
+ * @param k the amount to shift
+ * @see GF2nPolynomialElement#invertEEA
+ */
+ public void shiftLeftAddThis(GF2Polynomial b, int k)
+ {
+ if (k == 0)
+ {
+ addToThis(b);
+ return;
+ }
+ int i;
+ expandN(b.len + k);
+ int d = k >>> 5;
+ for (i = b.blocks - 1; i >= 0; i--)
+ {
+ if ((i + d + 1 < blocks) && ((k & 0x1f) != 0))
+ {
+ value[i + d + 1] ^= b.value[i] >>> (32 - (k & 0x1f));
+ }
+ value[i + d] ^= b.value[i] << (k & 0x1f);
+ }
+ }
+
+ /**
+ * Shifts-left this GF2Polynomial's value blockwise 1 block resulting in a
+ * shift-left by 32.
+ *
+ * @see GF2Polynomial#multiply
+ */
+ void shiftBlocksLeft()
+ {
+ blocks += 1;
+ len += 32;
+ if (blocks <= value.length)
+ {
+ int i;
+ for (i = blocks - 1; i >= 1; i--)
+ {
+ value[i] = value[i - 1];
+ }
+ value[0] = 0x00;
+ }
+ else
+ {
+ int[] result = new int[blocks];
+ System.arraycopy(value, 0, result, 1, blocks - 1);
+ value = null;
+ value = result;
+ }
+ }
+
+ /**
+ * Shifts left this GF2Polynomial's value blockwise <i>b</i> blocks
+ * resulting in a shift-left by b*32. This method assumes that {@link #len}
+ * and {@link #blocks} have already been updated to reflect the final state.
+ *
+ * @param b shift amount (in blocks)
+ */
+ private void doShiftBlocksLeft(int b)
+ {
+ if (blocks <= value.length)
+ {
+ int i;
+ for (i = blocks - 1; i >= b; i--)
+ {
+ value[i] = value[i - b];
+ }
+ for (i = 0; i < b; i++)
+ {
+ value[i] = 0x00;
+ }
+ }
+ else
+ {
+ int[] result = new int[blocks];
+ System.arraycopy(value, 0, result, b, blocks - b);
+ value = null;
+ value = result;
+ }
+ }
+
+ /**
+ * Returns this GF2Polynomial shift-right by 1 in a new GF2Polynomial.
+ *
+ * @return a new GF2Polynomial (this &lt;&lt; 1)
+ */
+ public GF2Polynomial shiftRight()
+ {
+ GF2Polynomial result = new GF2Polynomial(len - 1);
+ int i;
+ System.arraycopy(value, 0, result.value, 0, result.blocks);
+ for (i = 0; i <= result.blocks - 2; i++)
+ {
+ result.value[i] >>>= 1;
+ result.value[i] |= result.value[i + 1] << 31;
+ }
+ result.value[result.blocks - 1] >>>= 1;
+ if (result.blocks < blocks)
+ {
+ result.value[result.blocks - 1] |= value[result.blocks] << 31;
+ }
+ return result;
+ }
+
+ /**
+ * Shifts-right this GF2Polynomial by 1.
+ */
+ public void shiftRightThis()
+ {
+ int i;
+ len -= 1;
+ blocks = ((len - 1) >>> 5) + 1;
+ for (i = 0; i <= blocks - 2; i++)
+ {
+ value[i] >>>= 1;
+ value[i] |= value[i + 1] << 31;
+ }
+ value[blocks - 1] >>>= 1;
+ if ((len & 0x1f) == 0)
+ {
+ value[blocks - 1] |= value[blocks] << 31;
+ }
+ }
+
+}
generated by cgit v1.2.3 (git 2.25.1) at 2024-07-01 03:50:12 +0000