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diff --git a/core/src/main/java/org/bouncycastle/pqc/math/linearalgebra/GF2Polynomial.java b/core/src/main/java/org/bouncycastle/pqc/math/linearalgebra/GF2Polynomial.java
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@@ -1,2039 +0,0 @@
-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 BitDoesNotExistException 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();
- }
- if (i > (len - 1))
- {
- return;
- }
- 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 || 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 BitDoesNotExistException if (<i>i</i> &lt; 0) || (<i>i</i> &gt; (len - 1))
- */
- public void resetBit(int i)
- throws RuntimeException
- {
- if (i < 0 || i > (len - 1))
- {
- 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 BitDoesNotExistException 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();
- }
- if (i > (len - 1))
- {
- return;
- }
- 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 || 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 2024-05-23 09:36:49 +0300