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package org.bouncycastle.pqc.math.linearalgebra;
import java.math.BigInteger;
import java.util.Random;
import org.bouncycastle.util.Arrays;
/**
* This class stores very long strings of bits and does some basic arithmetics.
* It is used by GF2nField, GF2nPolynomialField and
* GFnPolynomialElement.
*
* @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 length 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 length 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 length and value
* selected by value:
*
* - ZERO
* - ONE
* - RANDOM
* - X
* - ALL
*
*
* @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 length 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[] os
* according to 1363 and using the given length.
*
* @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 bi
* according to 1363 and using the given length.
*
* @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 b.
*
* @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 b (this ==
* b)
*/
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 + Arrays.hashCode(value);
}
/**
* Tests if all bits equal zero.
*
* @return true if this GF2Polynomial equals 'zero' (this == 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' (this == 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 b to this GF2Polynomial and assigns the result to this
* GF2Polynomial. b 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, this and b, and returns the
* result. this and b can be of different size.
*
* @param b a GF2Polynomial
* @return a new GF2Polynomial (this + b)
*/
public GF2Polynomial add(GF2Polynomial b)
{
return xor(b);
}
/**
* Subtracts b from this GF2Polynomial and assigns the result to
* this GF2Polynomial. b can be of different size.
*
* @param b a GF2Polynomial
*/
public void subtractFromThis(GF2Polynomial b)
{
expandN(b.len);
xorThisBy(b);
}
/**
* Subtracts two GF2Polynomials, this and b, and returns the
* result in a new GF2Polynomial. this and b can be of
* different size.
*
* @param b a GF2Polynomial
* @return a new GF2Polynomial (this - b)
*/
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 this + 1
*/
public GF2Polynomial increase()
{
GF2Polynomial result = new GF2Polynomial(this);
result.increaseThis();
return result;
}
/**
* Multiplies this GF2Polynomial with b 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 (this * b)
*/
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 b 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 (this * b)
*/
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 k bytes of this
* GF2Polynomial.
*
* @param k
* @return a new GF2Polynomial containing the upper k 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 k bytes of this
* GF2Polynomial.
*
* @param k
* @return a new GF2Polynomial containing the lower k 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 this divided by g in a new
* GF2Polynomial.
*
* @param g GF2Polynomial != 0
* @return a new GF2Polynomial (this % g)
*/
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 this divided by g in a
* new GF2Polynomial.
*
* @param g GF2Polynomial != 0
* @return a new GF2Polynomial |_ this / g _|
*/
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 this by g 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
*/
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 this and g in a
* new GF2Polynomial.
*
* @param g GF2Polynomial != 0
* @return a new GF2Polynomial gcd(this,g)
* @throws ArithmeticException if this and g both are equal to zero
*/
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 this is irreducible, according to IEEE P1363, A.5.5,
* p103.
* 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 this 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^m + x^tc +
* 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^m + x^pc[2] +
* x^pc[1] + x^pc[0] + 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. 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 b as boolean (1->true, 0->false)
*/
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 this and b in a new
* GF2Polynomial. this and b can be of different size.
*
* @param b GF2Polynomial
* @return a new GF2Polynomial (this ^ b)
*/
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 b and
* stores the result in this GF2Polynomial. b 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.
*
* @param i int
* @throws RuntimeException if (i < 0) || (i > (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.
*
* @param i int
* @return the bit at position i if 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.
*
* @param i int
* @throws RuntimeException if (i < 0) || (i > (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.
*
* @param i int
* @throws RuntimeException if (i < 0) || (i > (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.
*
* @param i the position of the bit to be tested
* @return true if the bit at position i is set (a(i) ==
* 1). False if (i < 0) || (i > (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 << 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 k in a new
* GF2Polynomial.
*
* @param k int
* @return a new GF2Polynomial (this << k)
*/
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
* this = add(b.shl(k));
*
* @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 b 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 << 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;
}
}
}