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package org.bouncycastle.pqc.math.linearalgebra;
import java.math.BigInteger;
import java.security.SecureRandom;
import org.bouncycastle.util.Arrays;
/**
* This class implements an element of the finite field GF(2n ).
* It is represented in an optimal normal basis representation and holds the
* pointer mField to its corresponding field.
*
* @see GF2nField
* @see GF2nElement
*/
public class GF2nONBElement
extends GF2nElement
{
// /////////////////////////////////////////////////////////////////////
// member variables
// /////////////////////////////////////////////////////////////////////
private static final long[] mBitmask = new long[]{0x0000000000000001L,
0x0000000000000002L, 0x0000000000000004L, 0x0000000000000008L,
0x0000000000000010L, 0x0000000000000020L, 0x0000000000000040L,
0x0000000000000080L, 0x0000000000000100L, 0x0000000000000200L,
0x0000000000000400L, 0x0000000000000800L, 0x0000000000001000L,
0x0000000000002000L, 0x0000000000004000L, 0x0000000000008000L,
0x0000000000010000L, 0x0000000000020000L, 0x0000000000040000L,
0x0000000000080000L, 0x0000000000100000L, 0x0000000000200000L,
0x0000000000400000L, 0x0000000000800000L, 0x0000000001000000L,
0x0000000002000000L, 0x0000000004000000L, 0x0000000008000000L,
0x0000000010000000L, 0x0000000020000000L, 0x0000000040000000L,
0x0000000080000000L, 0x0000000100000000L, 0x0000000200000000L,
0x0000000400000000L, 0x0000000800000000L, 0x0000001000000000L,
0x0000002000000000L, 0x0000004000000000L, 0x0000008000000000L,
0x0000010000000000L, 0x0000020000000000L, 0x0000040000000000L,
0x0000080000000000L, 0x0000100000000000L, 0x0000200000000000L,
0x0000400000000000L, 0x0000800000000000L, 0x0001000000000000L,
0x0002000000000000L, 0x0004000000000000L, 0x0008000000000000L,
0x0010000000000000L, 0x0020000000000000L, 0x0040000000000000L,
0x0080000000000000L, 0x0100000000000000L, 0x0200000000000000L,
0x0400000000000000L, 0x0800000000000000L, 0x1000000000000000L,
0x2000000000000000L, 0x4000000000000000L, 0x8000000000000000L};
private static final long[] mMaxmask = new long[]{0x0000000000000001L,
0x0000000000000003L, 0x0000000000000007L, 0x000000000000000FL,
0x000000000000001FL, 0x000000000000003FL, 0x000000000000007FL,
0x00000000000000FFL, 0x00000000000001FFL, 0x00000000000003FFL,
0x00000000000007FFL, 0x0000000000000FFFL, 0x0000000000001FFFL,
0x0000000000003FFFL, 0x0000000000007FFFL, 0x000000000000FFFFL,
0x000000000001FFFFL, 0x000000000003FFFFL, 0x000000000007FFFFL,
0x00000000000FFFFFL, 0x00000000001FFFFFL, 0x00000000003FFFFFL,
0x00000000007FFFFFL, 0x0000000000FFFFFFL, 0x0000000001FFFFFFL,
0x0000000003FFFFFFL, 0x0000000007FFFFFFL, 0x000000000FFFFFFFL,
0x000000001FFFFFFFL, 0x000000003FFFFFFFL, 0x000000007FFFFFFFL,
0x00000000FFFFFFFFL, 0x00000001FFFFFFFFL, 0x00000003FFFFFFFFL,
0x00000007FFFFFFFFL, 0x0000000FFFFFFFFFL, 0x0000001FFFFFFFFFL,
0x0000003FFFFFFFFFL, 0x0000007FFFFFFFFFL, 0x000000FFFFFFFFFFL,
0x000001FFFFFFFFFFL, 0x000003FFFFFFFFFFL, 0x000007FFFFFFFFFFL,
0x00000FFFFFFFFFFFL, 0x00001FFFFFFFFFFFL, 0x00003FFFFFFFFFFFL,
0x00007FFFFFFFFFFFL, 0x0000FFFFFFFFFFFFL, 0x0001FFFFFFFFFFFFL,
0x0003FFFFFFFFFFFFL, 0x0007FFFFFFFFFFFFL, 0x000FFFFFFFFFFFFFL,
0x001FFFFFFFFFFFFFL, 0x003FFFFFFFFFFFFFL, 0x007FFFFFFFFFFFFFL,
0x00FFFFFFFFFFFFFFL, 0x01FFFFFFFFFFFFFFL, 0x03FFFFFFFFFFFFFFL,
0x07FFFFFFFFFFFFFFL, 0x0FFFFFFFFFFFFFFFL, 0x1FFFFFFFFFFFFFFFL,
0x3FFFFFFFFFFFFFFFL, 0x7FFFFFFFFFFFFFFFL, 0xFFFFFFFFFFFFFFFFL};
// mIBy64[j * 16 + i] = (j * 16 + i)/64
// i =
// 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
//
private static final int[] mIBY64 = new int[]{
// j =
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // 0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // 1
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // 2
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, // 3
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, // 4
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, // 5
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, // 6
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, // 7
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, // 8
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, // 9
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, // 10
2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, // 11
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, // 12
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, // 13
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, // 14
3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, // 15
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, // 16
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, // 17
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, // 18
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, // 19
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, // 20
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, // 21
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, // 22
5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5 // 23
};
private static final int MAXLONG = 64;
/**
* holds the lenght of the polynomial with 64 bit sized fields.
*/
private int mLength;
/**
* holds the value of mDeg % MAXLONG.
*/
private int mBit;
/**
* holds this element in ONB representation.
*/
private long[] mPol;
// /////////////////////////////////////////////////////////////////////
// constructors
// /////////////////////////////////////////////////////////////////////
/**
* Construct a random element over the field gf2n, using the
* specified source of randomness.
*
* @param gf2n the field
* @param rand the source of randomness
*/
public GF2nONBElement(GF2nONBField gf2n, SecureRandom rand)
{
mField = gf2n;
mDegree = mField.getDegree();
mLength = gf2n.getONBLength();
mBit = gf2n.getONBBit();
mPol = new long[mLength];
if (mLength > 1)
{
for (int j = 0; j < mLength - 1; j++)
{
mPol[j] = rand.nextLong();
}
long last = rand.nextLong();
mPol[mLength - 1] = last >>> (MAXLONG - mBit);
}
else
{
mPol[0] = rand.nextLong();
mPol[0] = mPol[0] >>> (MAXLONG - mBit);
}
}
/**
* Construct a new GF2nONBElement from its encoding.
*
* @param gf2n the field
* @param e the encoded element
*/
public GF2nONBElement(GF2nONBField gf2n, byte[] e)
{
mField = gf2n;
mDegree = mField.getDegree();
mLength = gf2n.getONBLength();
mBit = gf2n.getONBBit();
mPol = new long[mLength];
assign(e);
}
/**
* Construct the element of the field gf2n with the specified
* value val.
*
* @param gf2n the field
* @param val the value represented by a BigInteger
*/
public GF2nONBElement(GF2nONBField gf2n, BigInteger val)
{
mField = gf2n;
mDegree = mField.getDegree();
mLength = gf2n.getONBLength();
mBit = gf2n.getONBBit();
mPol = new long[mLength];
assign(val);
}
/**
* Construct the element of the field gf2n with the specified
* value val.
*
* @param gf2n the field
* @param val the value in ONB representation
*/
private GF2nONBElement(GF2nONBField gf2n, long[] val)
{
mField = gf2n;
mDegree = mField.getDegree();
mLength = gf2n.getONBLength();
mBit = gf2n.getONBBit();
mPol = val;
}
// /////////////////////////////////////////////////////////////////////
// pseudo-constructors
// /////////////////////////////////////////////////////////////////////
/**
* Copy constructor.
*
* @param gf2n the field
*/
public GF2nONBElement(GF2nONBElement gf2n)
{
mField = gf2n.mField;
mDegree = mField.getDegree();
mLength = ((GF2nONBField)mField).getONBLength();
mBit = ((GF2nONBField)mField).getONBBit();
mPol = new long[mLength];
assign(gf2n.getElement());
}
/**
* Create a new GF2nONBElement by cloning this GF2nPolynomialElement.
*
* @return a copy of this element
*/
public Object clone()
{
return new GF2nONBElement(this);
}
/**
* Create the zero element.
*
* @param gf2n the finite field
* @return the zero element in the given finite field
*/
public static GF2nONBElement ZERO(GF2nONBField gf2n)
{
long[] polynomial = new long[gf2n.getONBLength()];
return new GF2nONBElement(gf2n, polynomial);
}
/**
* Create the one element.
*
* @param gf2n the finite field
* @return the one element in the given finite field
*/
public static GF2nONBElement ONE(GF2nONBField gf2n)
{
int mLength = gf2n.getONBLength();
long[] polynomial = new long[mLength];
// fill mDegree coefficients with one's
for (int i = 0; i < mLength - 1; i++)
{
polynomial[i] = 0xffffffffffffffffL;
}
polynomial[mLength - 1] = mMaxmask[gf2n.getONBBit() - 1];
return new GF2nONBElement(gf2n, polynomial);
}
// /////////////////////////////////////////////////////////////////////
// assignments
// /////////////////////////////////////////////////////////////////////
/**
* assigns to this element the zero element
*/
void assignZero()
{
mPol = new long[mLength];
}
/**
* assigns to this element the one element
*/
void assignOne()
{
// fill mDegree coefficients with one's
for (int i = 0; i < mLength - 1; i++)
{
mPol[i] = 0xffffffffffffffffL;
}
mPol[mLength - 1] = mMaxmask[mBit - 1];
}
/**
* assigns to this element the value val.
*
* @param val the value represented by a BigInteger
*/
private void assign(BigInteger val)
{
assign(val.toByteArray());
}
/**
* assigns to this element the value val.
*
* @param val the value in ONB representation
*/
private void assign(long[] val)
{
System.arraycopy(val, 0, mPol, 0, mLength);
}
/**
* assigns to this element the value val. First: inverting the
* order of val into reversed[]. That means: reversed[0] = val[length - 1],
* ..., reversed[reversed.length - 1] = val[0]. Second: mPol[0] = sum{i = 0,
* ... 7} (val[i]<<(i*8)) .... mPol[1] = sum{i = 8, ... 15} (val[i]<<(i*8))
*
* @param val the value in ONB representation
*/
private void assign(byte[] val)
{
int j;
mPol = new long[mLength];
for (j = 0; j < val.length; j++)
{
mPol[j >>> 3] |= (val[val.length - 1 - j] & 0x00000000000000ffL) << ((j & 0x07) << 3);
}
}
// /////////////////////////////////////////////////////////////////
// comparison
// /////////////////////////////////////////////////////////////////
/**
* Checks whether this element is zero.
*
* @return true if this is the zero element
*/
public boolean isZero()
{
boolean result = true;
for (int i = 0; i < mLength && result; i++)
{
result = result && ((mPol[i] & 0xFFFFFFFFFFFFFFFFL) == 0);
}
return result;
}
/**
* Checks whether this element is one.
*
* @return true if this is the one element
*/
public boolean isOne()
{
boolean result = true;
for (int i = 0; i < mLength - 1 && result; i++)
{
result = result
&& ((mPol[i] & 0xFFFFFFFFFFFFFFFFL) == 0xFFFFFFFFFFFFFFFFL);
}
if (result)
{
result = result
&& ((mPol[mLength - 1] & mMaxmask[mBit - 1]) == mMaxmask[mBit - 1]);
}
return result;
}
/**
* Compare this element with another object.
*
* @param other the other object
* @return true if the two objects are equal, false
* otherwise
*/
public boolean equals(Object other)
{
if (other == null || !(other instanceof GF2nONBElement))
{
return false;
}
GF2nONBElement otherElem = (GF2nONBElement)other;
for (int i = 0; i < mLength; i++)
{
if (mPol[i] != otherElem.mPol[i])
{
return false;
}
}
return true;
}
/**
* @return the hash code of this element
*/
public int hashCode()
{
return Arrays.hashCode(mPol);
}
// /////////////////////////////////////////////////////////////////////
// access
// /////////////////////////////////////////////////////////////////////
/**
* Returns whether the highest bit of the bit representation is set
*
* @return true, if the highest bit of mPol is set, false, otherwise
*/
public boolean testRightmostBit()
{
// due to the reverse bit order (compared to 1363) this method returns
// the value of the leftmost bit
return (mPol[mLength - 1] & mBitmask[mBit - 1]) != 0L;
}
/**
* Checks whether the indexed bit of the bit representation is set. Warning:
* GF2nONBElement currently stores its bits in reverse order (compared to
* 1363) !!!
*
* @param index the index of the bit to test
* @return true if the indexed bit of mPol is set, false
* otherwise.
*/
boolean testBit(int index)
{
if (index < 0 || index > mDegree)
{
return false;
}
long test = mPol[index >>> 6] & mBitmask[index & 0x3f];
return test != 0x0L;
}
/**
* @return this element in its ONB representation
*/
private long[] getElement()
{
long[] result = new long[mPol.length];
System.arraycopy(mPol, 0, result, 0, mPol.length);
return result;
}
/**
* Returns the ONB representation of this element. The Bit-Order is
* exchanged (according to 1363)!
*
* @return this element in its representation and reverse bit-order
*/
private long[] getElementReverseOrder()
{
long[] result = new long[mPol.length];
for (int i = 0; i < mDegree; i++)
{
if (testBit(mDegree - i - 1))
{
result[i >>> 6] |= mBitmask[i & 0x3f];
}
}
return result;
}
/**
* Reverses the bit-order in this element(according to 1363). This is a
* hack!
*/
void reverseOrder()
{
mPol = getElementReverseOrder();
}
// /////////////////////////////////////////////////////////////////////
// arithmetic
// /////////////////////////////////////////////////////////////////////
/**
* Compute the sum of this element and addend.
*
* @param addend the addend
* @return this + other (newly created)
*/
public GFElement add(GFElement addend)
throws RuntimeException
{
GF2nONBElement result = new GF2nONBElement(this);
result.addToThis(addend);
return result;
}
/**
* Compute this + addend (overwrite this).
*
* @param addend the addend
*/
public void addToThis(GFElement addend)
throws RuntimeException
{
if (!(addend instanceof GF2nONBElement))
{
throw new RuntimeException();
}
if (!mField.equals(((GF2nONBElement)addend).mField))
{
throw new RuntimeException();
}
for (int i = 0; i < mLength; i++)
{
mPol[i] ^= ((GF2nONBElement)addend).mPol[i];
}
}
/**
* returns this element + 1.
*
* @return this + 1
*/
public GF2nElement increase()
{
GF2nONBElement result = new GF2nONBElement(this);
result.increaseThis();
return result;
}
/**
* increases this element.
*/
public void increaseThis()
{
addToThis(ONE((GF2nONBField)mField));
}
/**
* Compute the product of this element and factor.
*
* @param factor the factor
* @return this * factor (newly created)
*/
public GFElement multiply(GFElement factor)
throws RuntimeException
{
GF2nONBElement result = new GF2nONBElement(this);
result.multiplyThisBy(factor);
return result;
}
/**
* Compute this * factor (overwrite this).
*
* @param factor the factor
*/
public void multiplyThisBy(GFElement factor)
throws RuntimeException
{
if (!(factor instanceof GF2nONBElement))
{
throw new RuntimeException("The elements have different"
+ " representation: not yet" + " implemented");
}
if (!mField.equals(((GF2nONBElement)factor).mField))
{
throw new RuntimeException();
}
if (equals(factor))
{
squareThis();
}
else
{
long[] a = mPol;
long[] b = ((GF2nONBElement)factor).mPol;
long[] c = new long[mLength];
int[][] m = ((GF2nONBField)mField).mMult;
int degf, degb, s, fielda, fieldb, bita, bitb;
degf = mLength - 1;
degb = mBit - 1;
s = 0;
long TWOTOMAXLONGM1 = mBitmask[MAXLONG - 1];
long TWOTODEGB = mBitmask[degb];
boolean old, now;
// the product c of a and b (a*b = c) is calculated in mDegree
// cicles
// in every cicle one coefficient of c is calculated and stored
// k indicates the coefficient
//
for (int k = 0; k < mDegree; k++)
{
s = 0;
for (int i = 0; i < mDegree; i++)
{
// fielda = i / MAXLONG
//
fielda = mIBY64[i];
// bita = i % MAXLONG
//
bita = i & (MAXLONG - 1);
// fieldb = m[i][0] / MAXLONG
//
fieldb = mIBY64[m[i][0]];
// bitb = m[i][0] % MAXLONG
//
bitb = m[i][0] & (MAXLONG - 1);
if ((a[fielda] & mBitmask[bita]) != 0)
{
if ((b[fieldb] & mBitmask[bitb]) != 0)
{
s ^= 1;
}
if (m[i][1] != -1)
{
// fieldb = m[i][1] / MAXLONG
//
fieldb = mIBY64[m[i][1]];
// bitb = m[i][1] % MAXLONG
//
bitb = m[i][1] & (MAXLONG - 1);
if ((b[fieldb] & mBitmask[bitb]) != 0)
{
s ^= 1;
}
}
}
}
fielda = mIBY64[k];
bita = k & (MAXLONG - 1);
if (s != 0)
{
c[fielda] ^= mBitmask[bita];
}
// Circular shift of x and y one bit to the right,
// respectively.
if (mLength > 1)
{
// Shift x.
//
old = (a[degf] & 1) == 1;
for (int i = degf - 1; i >= 0; i--)
{
now = (a[i] & 1) != 0;
a[i] = a[i] >>> 1;
if (old)
{
a[i] ^= TWOTOMAXLONGM1;
}
old = now;
}
a[degf] = a[degf] >>> 1;
if (old)
{
a[degf] ^= TWOTODEGB;
}
// Shift y.
//
old = (b[degf] & 1) == 1;
for (int i = degf - 1; i >= 0; i--)
{
now = (b[i] & 1) != 0;
b[i] = b[i] >>> 1;
if (old)
{
b[i] ^= TWOTOMAXLONGM1;
}
old = now;
}
b[degf] = b[degf] >>> 1;
if (old)
{
b[degf] ^= TWOTODEGB;
}
}
else
{
old = (a[0] & 1) == 1;
a[0] = a[0] >>> 1;
if (old)
{
a[0] ^= TWOTODEGB;
}
old = (b[0] & 1) == 1;
b[0] = b[0] >>> 1;
if (old)
{
b[0] ^= TWOTODEGB;
}
}
}
assign(c);
}
}
/**
* returns this element to the power of 2.
*
* @return this2
*/
public GF2nElement square()
{
GF2nONBElement result = new GF2nONBElement(this);
result.squareThis();
return result;
}
/**
* squares this element.
*/
public void squareThis()
{
long[] pol = getElement();
int f = mLength - 1;
int b = mBit - 1;
// Shift the coefficients one bit to the left.
//
long TWOTOMAXLONGM1 = mBitmask[MAXLONG - 1];
boolean old, now;
old = (pol[f] & mBitmask[b]) != 0;
for (int i = 0; i < f; i++)
{
now = (pol[i] & TWOTOMAXLONGM1) != 0;
pol[i] = pol[i] << 1;
if (old)
{
pol[i] ^= 1;
}
old = now;
}
now = (pol[f] & mBitmask[b]) != 0;
pol[f] = pol[f] << 1;
if (old)
{
pol[f] ^= 1;
}
// Set the bit with index mDegree to zero.
//
if (now)
{
pol[f] ^= mBitmask[b + 1];
}
assign(pol);
}
/**
* Compute the multiplicative inverse of this element.
*
* @return this-1 (newly created)
* @throws ArithmeticException if this is the zero element.
*/
public GFElement invert()
throws ArithmeticException
{
GF2nONBElement result = new GF2nONBElement(this);
result.invertThis();
return result;
}
/**
* Multiplicatively invert of this element (overwrite this).
*
* @throws ArithmeticException if this is the zero element.
*/
public void invertThis()
throws ArithmeticException
{
if (isZero())
{
throw new ArithmeticException();
}
int r = 31; // mDegree kann nur 31 Bits lang sein!!!
// Bitlaenge von mDegree:
for (boolean found = false; !found && r >= 0; r--)
{
if (((mDegree - 1) & mBitmask[r]) != 0)
{
found = true;
}
}
r++;
GF2nElement m = ZERO((GF2nONBField)mField);
GF2nElement n = new GF2nONBElement(this);
int k = 1;
for (int i = r - 1; i >= 0; i--)
{
m = (GF2nElement)n.clone();
for (int j = 1; j <= k; j++)
{
m.squareThis();
}
n.multiplyThisBy(m);
k <<= 1;
if (((mDegree - 1) & mBitmask[i]) != 0)
{
n.squareThis();
n.multiplyThisBy(this);
k++;
}
}
n.squareThis();
}
/**
* returns the root ofthis element.
*
* @return this1/2
*/
public GF2nElement squareRoot()
{
GF2nONBElement result = new GF2nONBElement(this);
result.squareRootThis();
return result;
}
/**
* square roots this element.
*/
public void squareRootThis()
{
long[] pol = getElement();
int f = mLength - 1;
int b = mBit - 1;
// Shift the coefficients one bit to the right.
//
long TWOTOMAXLONGM1 = mBitmask[MAXLONG - 1];
boolean old, now;
old = (pol[0] & 1) != 0;
for (int i = f; i >= 0; i--)
{
now = (pol[i] & 1) != 0;
pol[i] = pol[i] >>> 1;
if (old)
{
if (i == f)
{
pol[i] ^= mBitmask[b];
}
else
{
pol[i] ^= TWOTOMAXLONGM1;
}
}
old = now;
}
assign(pol);
}
/**
* Returns the trace of this element.
*
* @return the trace of this element
*/
public int trace()
{
// trace = sum of coefficients
//
int result = 0;
int max = mLength - 1;
for (int i = 0; i < max; i++)
{
for (int j = 0; j < MAXLONG; j++)
{
if ((mPol[i] & mBitmask[j]) != 0)
{
result ^= 1;
}
}
}
int b = mBit;
for (int j = 0; j < b; j++)
{
if ((mPol[max] & mBitmask[j]) != 0)
{
result ^= 1;
}
}
return result;
}
/**
* Solves a quadratic equation.
* Let z2 + z = this. Then this method returns z.
*
* @return z with z2 + z = this
*/
public GF2nElement solveQuadraticEquation()
throws RuntimeException
{
if (trace() == 1)
{
throw new RuntimeException();
}
long TWOTOMAXLONGM1 = mBitmask[MAXLONG - 1];
long ZERO = 0L;
long ONE = 1L;
long[] p = new long[mLength];
long z = 0L;
int j = 1;
for (int i = 0; i < mLength - 1; i++)
{
for (j = 1; j < MAXLONG; j++)
{
//
if (!((((mBitmask[j] & mPol[i]) != ZERO) && ((z & mBitmask[j - 1]) != ZERO)) || (((mPol[i] & mBitmask[j]) == ZERO) && ((z & mBitmask[j - 1]) == ZERO))))
{
z ^= mBitmask[j];
}
}
p[i] = z;
if (((TWOTOMAXLONGM1 & z) != ZERO && (ONE & mPol[i + 1]) == ONE)
|| ((TWOTOMAXLONGM1 & z) == ZERO && (ONE & mPol[i + 1]) == ZERO))
{
z = ZERO;
}
else
{
z = ONE;
}
}
int b = mDegree & (MAXLONG - 1);
long LASTLONG = mPol[mLength - 1];
for (j = 1; j < b; j++)
{
if (!((((mBitmask[j] & LASTLONG) != ZERO) && ((mBitmask[j - 1] & z) != ZERO)) || (((mBitmask[j] & LASTLONG) == ZERO) && ((mBitmask[j - 1] & z) == ZERO))))
{
z ^= mBitmask[j];
}
}
p[mLength - 1] = z;
return new GF2nONBElement((GF2nONBField)mField, p);
}
// /////////////////////////////////////////////////////////////////
// conversion
// /////////////////////////////////////////////////////////////////
/**
* Returns a String representation of this element.
*
* @return String representation of this element with the specified radix
*/
public String toString()
{
return toString(16);
}
/**
* Returns a String representation of this element. radix
* specifies the radix of the String representation.
* NOTE: ONLY radix = 2 or radix = 16 IS IMPLEMENTED
*
* @param radix specifies the radix of the String representation
* @return String representation of this element with the specified radix
*/
public String toString(int radix)
{
String s = "";
long[] a = getElement();
int b = mBit;
if (radix == 2)
{
for (int j = b - 1; j >= 0; j--)
{
if ((a[a.length - 1] & ((long)1 << j)) == 0)
{
s += "0";
}
else
{
s += "1";
}
}
for (int i = a.length - 2; i >= 0; i--)
{
for (int j = MAXLONG - 1; j >= 0; j--)
{
if ((a[i] & mBitmask[j]) == 0)
{
s += "0";
}
else
{
s += "1";
}
}
}
}
else if (radix == 16)
{
final char[] HEX_CHARS = {'0', '1', '2', '3', '4', '5', '6', '7',
'8', '9', 'a', 'b', 'c', 'd', 'e', 'f'};
for (int i = a.length - 1; i >= 0; i--)
{
s += HEX_CHARS[(int)(a[i] >>> 60) & 0x0f];
s += HEX_CHARS[(int)(a[i] >>> 56) & 0x0f];
s += HEX_CHARS[(int)(a[i] >>> 52) & 0x0f];
s += HEX_CHARS[(int)(a[i] >>> 48) & 0x0f];
s += HEX_CHARS[(int)(a[i] >>> 44) & 0x0f];
s += HEX_CHARS[(int)(a[i] >>> 40) & 0x0f];
s += HEX_CHARS[(int)(a[i] >>> 36) & 0x0f];
s += HEX_CHARS[(int)(a[i] >>> 32) & 0x0f];
s += HEX_CHARS[(int)(a[i] >>> 28) & 0x0f];
s += HEX_CHARS[(int)(a[i] >>> 24) & 0x0f];
s += HEX_CHARS[(int)(a[i] >>> 20) & 0x0f];
s += HEX_CHARS[(int)(a[i] >>> 16) & 0x0f];
s += HEX_CHARS[(int)(a[i] >>> 12) & 0x0f];
s += HEX_CHARS[(int)(a[i] >>> 8) & 0x0f];
s += HEX_CHARS[(int)(a[i] >>> 4) & 0x0f];
s += HEX_CHARS[(int)(a[i]) & 0x0f];
s += " ";
}
}
return s;
}
/**
* Returns this element as FlexiBigInt. The conversion is P1363-conform.
*
* @return this element as BigInteger
*/
public BigInteger toFlexiBigInt()
{
/** @todo this method does not reverse the bit-order as it should!!! */
return new BigInteger(1, toByteArray());
}
/**
* Returns this element as byte array. The conversion is P1363-conform.
*
* @return this element as byte array
*/
public byte[] toByteArray()
{
/** @todo this method does not reverse the bit-order as it should!!! */
int k = ((mDegree - 1) >> 3) + 1;
byte[] result = new byte[k];
int i;
for (i = 0; i < k; i++)
{
result[k - i - 1] = (byte)((mPol[i >>> 3] & (0x00000000000000ffL << ((i & 0x07) << 3))) >>> ((i & 0x07) << 3));
}
return result;
}
}