package org.bouncycastle.pqc.math.linearalgebra;
import java.security.SecureRandom;
/**
* This class describes some operations with matrices over finite field GF(2)
* and is used in ecc and MQ-PKC (also has some specific methods and
* implementation)
*/
public class GF2Matrix
extends Matrix
{
/**
* For the matrix representation the array of type int[][] is used, thus one
* element of the array keeps 32 elements of the matrix (from one row and 32
* columns)
*/
private int[][] matrix;
/**
* the length of each array representing a row of this matrix, computed as
* <tt>(numColumns + 31) / 32</tt>
*/
private int length;
/**
* Create the matrix from encoded form.
*
* @param enc the encoded matrix
*/
public GF2Matrix(byte[] enc)
{
if (enc.length < 9)
{
throw new ArithmeticException(
"given array is not an encoded matrix over GF(2)");
}
numRows = LittleEndianConversions.OS2IP(enc, 0);
numColumns = LittleEndianConversions.OS2IP(enc, 4);
int n = ((numColumns + 7) >>> 3) * numRows;
if ((numRows <= 0) || (n != (enc.length - 8)))
{
throw new ArithmeticException(
"given array is not an encoded matrix over GF(2)");
}
length = (numColumns + 31) >>> 5;
matrix = new int[numRows][length];
// number of "full" integer
int q = numColumns >> 5;
// number of bits in non-full integer
int r = numColumns & 0x1f;
int count = 8;
for (int i = 0; i < numRows; i++)
{
for (int j = 0; j < q; j++, count += 4)
{
matrix[i][j] = LittleEndianConversions.OS2IP(enc, count);
}
for (int j = 0; j < r; j += 8)
{
matrix[i][q] ^= (enc[count++] & 0xff) << j;
}
}
}
/**
* Create the matrix with the contents of the given array. The matrix is not
* copied. Unused coefficients are masked out.
*
* @param numColumns the number of columns
* @param matrix the element array
*/
public GF2Matrix(int numColumns, int[][] matrix)
{
if (matrix[0].length != (numColumns + 31) >> 5)
{
throw new ArithmeticException(
"Int array does not match given number of columns.");
}
this.numColumns = numColumns;
numRows = matrix.length;
length = matrix[0].length;
int rest = numColumns & 0x1f;
int bitMask;
if (rest == 0)
{
bitMask = 0xffffffff;
}
else
{
bitMask = (1 << rest) - 1;
}
for (int i = 0; i < numRows; i++)
{
matrix[i][length - 1] &= bitMask;
}
this.matrix = matrix;
}
/**
* Create an nxn matrix of the given type.
*
* @param n the number of rows (and columns)
* @param typeOfMatrix the martix type (see {@link Matrix} for predefined
* constants)
*/
public GF2Matrix(int n, char typeOfMatrix)
{
this(n, typeOfMatrix, new java.security.SecureRandom());
}
/**
* Create an nxn matrix of the given type.
*
* @param n the matrix size
* @param typeOfMatrix the matrix type
* @param sr the source of randomness
*/
public GF2Matrix(int n, char typeOfMatrix, SecureRandom sr)
{
if (n <= 0)
{
throw new ArithmeticException("Size of matrix is non-positive.");
}
switch (typeOfMatrix)
{
case Matrix.MATRIX_TYPE_ZERO:
assignZeroMatrix(n, n);
break;
case Matrix.MATRIX_TYPE_UNIT:
assignUnitMatrix(n);
break;
case Matrix.MATRIX_TYPE_RANDOM_LT:
assignRandomLowerTriangularMatrix(n, sr);
break;
case Matrix.MATRIX_TYPE_RANDOM_UT:
assignRandomUpperTriangularMatrix(n, sr);
break;
case Matrix.MATRIX_TYPE_RANDOM_REGULAR:
assignRandomRegularMatrix(n, sr);
break;
default:
throw new ArithmeticException("Unknown matrix type.");
}
}
/**
* Copy constructor.
*
* @param a another {@link GF2Matrix}
*/
public GF2Matrix(GF2Matrix a)
{
numColumns = a.getNumColumns();
numRows = a.getNumRows();
length = a.length;
matrix = new int[a.matrix.length][];
for (int i = 0; i < matrix.length; i++)
{
matrix[i] = IntUtils.clone(a.matrix[i]);
}
}
/**
* create the mxn zero matrix
*/
private GF2Matrix(int m, int n)
{
if ((n <= 0) || (m <= 0))
{
throw new ArithmeticException("size of matrix is non-positive");
}
assignZeroMatrix(m, n);
}
/**
* Create the mxn zero matrix.
*
* @param m number of rows
* @param n number of columns
*/
private void assignZeroMatrix(int m, int n)
{
numRows = m;
numColumns = n;
length = (n + 31) >>> 5;
matrix = new int[numRows][length];
for (int i = 0; i < numRows; i++)
{
for (int j = 0; j < length; j++)
{
matrix[i][j] = 0;
}
}
}
/**
* Create the mxn unit matrix.
*
* @param n number of rows (and columns)
*/
private void assignUnitMatrix(int n)
{
numRows = n;
numColumns = n;
length = (n + 31) >>> 5;
matrix = new int[numRows][length];
for (int i = 0; i < numRows; i++)
{
for (int j = 0; j < length; j++)
{
matrix[i][j] = 0;
}
}
for (int i = 0; i < numRows; i++)
{
int rest = i & 0x1f;
matrix[i][i >>> 5] = 1 << rest;
}
}
/**
* Create a nxn random lower triangular matrix.
*
* @param n number of rows (and columns)
* @param sr source of randomness
*/
private void assignRandomLowerTriangularMatrix(int n, SecureRandom sr)
{
numRows = n;
numColumns = n;
length = (n + 31) >>> 5;
matrix = new int[numRows][length];
for (int i = 0; i < numRows; i++)
{
int q = i >>> 5;
int r = i & 0x1f;
int s = 31 - r;
r = 1 << r;
for (int j = 0; j < q; j++)
{
matrix[i][j] = sr.nextInt();
}
matrix[i][q] = (sr.nextInt() >>> s) | r;
for (int j = q + 1; j < length; j++)
{
matrix[i][j] = 0;
}
}
}
/**
* Create a nxn random upper triangular matrix.
*
* @param n number of rows (and columns)
* @param sr source of randomness
*/
private void assignRandomUpperTriangularMatrix(int n, SecureRandom sr)
{
numRows = n;
numColumns = n;
length = (n + 31) >>> 5;
matrix = new int[numRows][length];
int rest = n & 0x1f;
int help;
if (rest == 0)
{
help = 0xffffffff;
}
else
{
help = (1 << rest) - 1;
}
for (int i = 0; i < numRows; i++)
{
int q = i >>> 5;
int r = i & 0x1f;
int s = r;
r = 1 << r;
for (int j = 0; j < q; j++)
{
matrix[i][j] = 0;
}
matrix[i][q] = (sr.nextInt() << s) | r;
for (int j = q + 1; j < length; j++)
{
matrix[i][j] = sr.nextInt();
}
matrix[i][length - 1] &= help;
}
}
/**
* Create an nxn random regular matrix.
*
* @param n number of rows (and columns)
* @param sr source of randomness
*/
private void assignRandomRegularMatrix(int n, SecureRandom sr)
{
numRows = n;
numColumns = n;
length = (n + 31) >>> 5;
matrix = new int[numRows][length];
GF2Matrix lm = new GF2Matrix(n, Matrix.MATRIX_TYPE_RANDOM_LT, sr);
GF2Matrix um = new GF2Matrix(n, Matrix.MATRIX_TYPE_RANDOM_UT, sr);
GF2Matrix rm = (GF2Matrix)lm.rightMultiply(um);
Permutation perm = new Permutation(n, sr);
int[] p = perm.getVector();
for (int i = 0; i < n; i++)
{
System.arraycopy(rm.matrix[i], 0, matrix[p[i]], 0, length);
}
}
/**
* Create a nxn random regular matrix and its inverse.
*
* @param n number of rows (and columns)
* @param sr source of randomness
* @return the created random regular matrix and its inverse
*/
public static GF2Matrix[] createRandomRegularMatrixAndItsInverse(int n,
SecureRandom sr)
{
GF2Matrix[] result = new GF2Matrix[2];
// ------------------------------------
// First part: create regular matrix
// ------------------------------------
// ------
int length = (n + 31) >> 5;
GF2Matrix lm = new GF2Matrix(n, Matrix.MATRIX_TYPE_RANDOM_LT, sr);
GF2Matrix um = new GF2Matrix(n, Matrix.MATRIX_TYPE_RANDOM_UT, sr);
GF2Matrix rm = (GF2Matrix)lm.rightMultiply(um);
Permutation p = new Permutation(n, sr);
int[] pVec = p.getVector();
int[][] matrix = new int[n][length];
for (int i = 0; i < n; i++)
{
System.arraycopy(rm.matrix[pVec[i]], 0, matrix[i], 0, length);
}
result[0] = new GF2Matrix(n, matrix);
// ------------------------------------
// Second part: create inverse matrix
// ------------------------------------
// inverse to lm
GF2Matrix invLm = new GF2Matrix(n, Matrix.MATRIX_TYPE_UNIT);
for (int i = 0; i < n; i++)
{
int rest = i & 0x1f;
int q = i >>> 5;
int r = 1 << rest;
for (int j = i + 1; j < n; j++)
{
int b = (lm.matrix[j][q]) & r;
if (b != 0)
{
for (int k = 0; k <= q; k++)
{
invLm.matrix[j][k] ^= invLm.matrix[i][k];
}
}
}
}
// inverse to um
GF2Matrix invUm = new GF2Matrix(n, Matrix.MATRIX_TYPE_UNIT);
for (int i = n - 1; i >= 0; i--)
{
int rest = i & 0x1f;
int q = i >>> 5;
int r = 1 << rest;
for (int j = i - 1; j >= 0; j--)
{
int b = (um.matrix[j][q]) & r;
if (b != 0)
{
for (int k = q; k < length; k++)
{
invUm.matrix[j][k] ^= invUm.matrix[i][k];
}
}
}
}
// inverse matrix
result[1] = (GF2Matrix)invUm.rightMultiply(invLm.rightMultiply(p));
return result;
}
/**
* @return the array keeping the matrix elements
*/
public int[][] getIntArray()
{
return matrix;
}
/**
* @return the length of each array representing a row of this matrix
*/
public int getLength()
{
return length;
}
/**
* Return the row of this matrix with the given index.
*
* @param index the index
* @return the row of this matrix with the given index
*/
public int[] getRow(int index)
{
return matrix[index];
}
/**
* Returns encoded matrix, i.e., this matrix in byte array form
*
* @return the encoded matrix
*/
public byte[] getEncoded()
{
int n = (numColumns + 7) >>> 3;
n *= numRows;
n += 8;
byte[] enc = new byte[n];
LittleEndianConversions.I2OSP(numRows, enc, 0);
LittleEndianConversions.I2OSP(numColumns, enc, 4);
// number of "full" integer
int q = numColumns >>> 5;
// number of bits in non-full integer
int r = numColumns & 0x1f;
int count = 8;
for (int i = 0; i < numRows; i++)
{
for (int j = 0; j < q; j++, count += 4)
{
LittleEndianConversions.I2OSP(matrix[i][j], enc, count);
}
for (int j = 0; j < r; j += 8)
{
enc[count++] = (byte)((matrix[i][q] >>> j) & 0xff);
}
}
return enc;
}
/**
* Returns the percentage of the number of "ones" in this matrix.
*
* @return the Hamming weight of this matrix (as a ratio).
*/
public double getHammingWeight()
{
double counter = 0.0;
double elementCounter = 0.0;
int rest = numColumns & 0x1f;
int d;
if (rest == 0)
{
d = length;
}
else
{
d = length - 1;
}
for (int i = 0; i < numRows; i++)
{
for (int j = 0; j < d; j++)
{
int a = matrix[i][j];
for (int k = 0; k < 32; k++)
{
int b = (a >>> k) & 1;
counter = counter + b;
elementCounter = elementCounter + 1;
}
}
int a = matrix[i][length - 1];
for (int k = 0; k < rest; k++)
{
int b = (a >>> k) & 1;
counter = counter + b;
elementCounter = elementCounter + 1;
}
}
return counter / elementCounter;
}
/**
* Check if this is the zero matrix (i.e., all entries are zero).
*
* @return <tt>true</tt> if this is the zero matrix
*/
public boolean isZero()
{
for (int i = 0; i < numRows; i++)
{
for (int j = 0; j < length; j++)
{
if (matrix[i][j] != 0)
{
return false;
}
}
}
return true;
}
/**
* Get the quadratic submatrix of this matrix consisting of the leftmost
* <tt>numRows</tt> columns.
*
* @return the <tt>(numRows x numRows)</tt> submatrix
*/
public GF2Matrix getLeftSubMatrix()
{
if (numColumns <= numRows)
{
throw new ArithmeticException("empty submatrix");
}
int length = (numRows + 31) >> 5;
int[][] result = new int[numRows][length];
int bitMask = (1 << (numRows & 0x1f)) - 1;
if (bitMask == 0)
{
bitMask = -1;
}
for (int i = numRows - 1; i >= 0; i--)
{
System.arraycopy(matrix[i], 0, result[i], 0, length);
result[i][length - 1] &= bitMask;
}
return new GF2Matrix(numRows, result);
}
/**
* Compute the full form matrix <tt>(this | Id)</tt> from this matrix in
* left compact form, where <tt>Id</tt> is the <tt>k x k</tt> identity
* matrix and <tt>k</tt> is the number of rows of this matrix.
*
* @return <tt>(this | Id)</tt>
*/
public GF2Matrix extendLeftCompactForm()
{
int newNumColumns = numColumns + numRows;
GF2Matrix result = new GF2Matrix(numRows, newNumColumns);
int ind = numRows - 1 + numColumns;
for (int i = numRows - 1; i >= 0; i--, ind--)
{
// copy this matrix to first columns
System.arraycopy(matrix[i], 0, result.matrix[i], 0, length);
// store the identity in last columns
result.matrix[i][ind >> 5] |= 1 << (ind & 0x1f);
}
return result;
}
/**
* Get the submatrix of this matrix consisting of the rightmost
* <tt>numColumns-numRows</tt> columns.
*
* @return the <tt>(numRows x (numColumns-numRows))</tt> submatrix
*/
public GF2Matrix getRightSubMatrix()
{
if (numColumns <= numRows)
{
throw new ArithmeticException("empty submatrix");
}
int q = numRows >> 5;
int r = numRows & 0x1f;
GF2Matrix result = new GF2Matrix(numRows, numColumns - numRows);
for (int i = numRows - 1; i >= 0; i--)
{
// if words have to be shifted
if (r != 0)
{
int ind = q;
// process all but last word
for (int j = 0; j < result.length - 1; j++)
{
// shift to correct position
result.matrix[i][j] = (matrix[i][ind++] >>> r)
| (matrix[i][ind] << (32 - r));
}
// process last word
result.matrix[i][result.length - 1] = matrix[i][ind++] >>> r;
if (ind < length)
{
result.matrix[i][result.length - 1] |= matrix[i][ind] << (32 - r);
}
}
else
{
// no shifting necessary
System.arraycopy(matrix[i], q, result.matrix[i], 0,
result.length);
}
}
return result;
}
/**
* Compute the full form matrix <tt>(Id | this)</tt> from this matrix in
* right compact form, where <tt>Id</tt> is the <tt>k x k</tt> identity
* matrix and <tt>k</tt> is the number of rows of this matrix.
*
* @return <tt>(Id | this)</tt>
*/
public GF2Matrix extendRightCompactForm()
{
GF2Matrix result = new GF2Matrix(numRows, numRows + numColumns);
int q = numRows >> 5;
int r = numRows & 0x1f;
for (int i = numRows - 1; i >= 0; i--)
{
// store the identity in first columns
result.matrix[i][i >> 5] |= 1 << (i & 0x1f);
// copy this matrix to last columns
// if words have to be shifted
if (r != 0)
{
int ind = q;
// process all but last word
for (int j = 0; j < length - 1; j++)
{
// obtain matrix word
int mw = matrix[i][j];
// shift to correct position
result.matrix[i][ind++] |= mw << r;
result.matrix[i][ind] |= mw >>> (32 - r);
}
// process last word
int mw = matrix[i][length - 1];
result.matrix[i][ind++] |= mw << r;
if (ind < result.length)
{
result.matrix[i][ind] |= mw >>> (32 - r);
}
}
else
{
// no shifting necessary
System.arraycopy(matrix[i], 0, result.matrix[i], q, length);
}
}
return result;
}
/**
* Compute the transpose of this matrix.
*
* @return <tt>(this)<sup>T</sup></tt>
*/
public Matrix computeTranspose()
{
int[][] result = new int[numColumns][(numRows + 31) >>> 5];
for (int i = 0; i < numRows; i++)
{
for (int j = 0; j < numColumns; j++)
{
int qs = j >>> 5;
int rs = j & 0x1f;
int b = (matrix[i][qs] >>> rs) & 1;
int qt = i >>> 5;
int rt = i & 0x1f;
if (b == 1)
{
result[j][qt] |= 1 << rt;
}
}
}
return new GF2Matrix(numRows, result);
}
/**
* Compute the inverse of this matrix.
*
* @return the inverse of this matrix (newly created).
* @throws ArithmeticException if this matrix is not invertible.
*/
public Matrix computeInverse()
{
if (numRows != numColumns)
{
throw new ArithmeticException("Matrix is not invertible.");
}
// clone this matrix
int[][] tmpMatrix = new int[numRows][length];
for (int i = numRows - 1; i >= 0; i--)
{
tmpMatrix[i] = IntUtils.clone(matrix[i]);
}
// initialize inverse matrix as unit matrix
int[][] invMatrix = new int[numRows][length];
for (int i = numRows - 1; i >= 0; i--)
{
int q = i >> 5;
int r = i & 0x1f;
invMatrix[i][q] = 1 << r;
}
// simultaneously compute Gaussian reduction of tmpMatrix and unit
// matrix
for (int i = 0; i < numRows; i++)
{
// i = q * 32 + (i mod 32)
int q = i >> 5;
int bitMask = 1 << (i & 0x1f);
// if diagonal element is zero
if ((tmpMatrix[i][q] & bitMask) == 0)
{
boolean foundNonZero = false;
// find a non-zero element in the same column
for (int j = i + 1; j < numRows; j++)
{
if ((tmpMatrix[j][q] & bitMask) != 0)
{
// found it, swap rows ...
foundNonZero = true;
swapRows(tmpMatrix, i, j);
swapRows(invMatrix, i, j);
// ... and quit searching
j = numRows;
continue;
}
}
// if no non-zero element was found ...
if (!foundNonZero)
{
// ... the matrix is not invertible
throw new ArithmeticException("Matrix is not invertible.");
}
}
// normalize all but i-th row
for (int j = numRows - 1; j >= 0; j--)
{
if ((j != i) && ((tmpMatrix[j][q] & bitMask) != 0))
{
addToRow(tmpMatrix[i], tmpMatrix[j], q);
addToRow(invMatrix[i], invMatrix[j], 0);
}
}
}
return new GF2Matrix(numColumns, invMatrix);
}
/**
* Compute the product of a permutation matrix (which is generated from an
* n-permutation) and this matrix.
*
* @param p the permutation
* @return {@link GF2Matrix} <tt>P*this</tt>
*/
public Matrix leftMultiply(Permutation p)
{
int[] pVec = p.getVector();
if (pVec.length != numRows)
{
throw new ArithmeticException("length mismatch");
}
int[][] result = new int[numRows][];
for (int i = numRows - 1; i >= 0; i--)
{
result[i] = IntUtils.clone(matrix[pVec[i]]);
}
return new GF2Matrix(numRows, result);
}
/**
* compute product a row vector and this matrix
*
* @param vec a vector over GF(2)
* @return Vector product a*matrix
*/
public Vector leftMultiply(Vector vec)
{
if (!(vec instanceof GF2Vector))
{
throw new ArithmeticException("vector is not defined over GF(2)");
}
if (vec.length != numRows)
{
throw new ArithmeticException("length mismatch");
}
int[] v = ((GF2Vector)vec).getVecArray();
int[] res = new int[length];
int q = numRows >> 5;
int r = 1 << (numRows & 0x1f);
// compute scalar products with full words of vector
int row = 0;
for (int i = 0; i < q; i++)
{
int bitMask = 1;
do
{
int b = v[i] & bitMask;
if (b != 0)
{
for (int j = 0; j < length; j++)
{
res[j] ^= matrix[row][j];
}
}
row++;
bitMask <<= 1;
}
while (bitMask != 0);
}
// compute scalar products with last word of vector
int bitMask = 1;
while (bitMask != r)
{
int b = v[q] & bitMask;
if (b != 0)
{
for (int j = 0; j < length; j++)
{
res[j] ^= matrix[row][j];
}
}
row++;
bitMask <<= 1;
}
return new GF2Vector(res, numColumns);
}
/**
* Compute the product of the matrix <tt>(this | Id)</tt> and a column
* vector, where <tt>Id</tt> is a <tt>(numRows x numRows)</tt> unit
* matrix.
*
* @param vec the vector over GF(2)
* @return <tt>(this | Id)*vector</tt>
*/
public Vector leftMultiplyLeftCompactForm(Vector vec)
{
if (!(vec instanceof GF2Vector))
{
throw new ArithmeticException("vector is not defined over GF(2)");
}
if (vec.length != numRows)
{
throw new ArithmeticException("length mismatch");
}
int[] v = ((GF2Vector)vec).getVecArray();
int[] res = new int[(numRows + numColumns + 31) >>> 5];
// process full words of vector
int words = numRows >>> 5;
int row = 0;
for (int i = 0; i < words; i++)
{
int bitMask = 1;
do
{
int b = v[i] & bitMask;
if (b != 0)
{
// compute scalar product part
for (int j = 0; j < length; j++)
{
res[j] ^= matrix[row][j];
}
// set last bit
int q = (numColumns + row) >>> 5;
int r = (numColumns + row) & 0x1f;
res[q] |= 1 << r;
}
row++;
bitMask <<= 1;
}
while (bitMask != 0);
}
// process last word of vector
int rem = 1 << (numRows & 0x1f);
int bitMask = 1;
while (bitMask != rem)
{
int b = v[words] & bitMask;
if (b != 0)
{
// compute scalar product part
for (int j = 0; j < length; j++)
{
res[j] ^= matrix[row][j];
}
// set last bit
int q = (numColumns + row) >>> 5;
int r = (numColumns + row) & 0x1f;
res[q] |= 1 << r;
}
row++;
bitMask <<= 1;
}
return new GF2Vector(res, numRows + numColumns);
}
/**
* Compute the product of this matrix and a matrix A over GF(2).
*
* @param mat a matrix A over GF(2)
* @return matrix product <tt>this*matrixA</tt>
*/
public Matrix rightMultiply(Matrix mat)
{
if (!(mat instanceof GF2Matrix))
{
throw new ArithmeticException("matrix is not defined over GF(2)");
}
if (mat.numRows != numColumns)
{
throw new ArithmeticException("length mismatch");
}
GF2Matrix a = (GF2Matrix)mat;
GF2Matrix result = new GF2Matrix(numRows, mat.numColumns);
int d;
int rest = numColumns & 0x1f;
if (rest == 0)
{
d = length;
}
else
{
d = length - 1;
}
for (int i = 0; i < numRows; i++)
{
int count = 0;
for (int j = 0; j < d; j++)
{
int e = matrix[i][j];
for (int h = 0; h < 32; h++)
{
int b = e & (1 << h);
if (b != 0)
{
for (int g = 0; g < a.length; g++)
{
result.matrix[i][g] ^= a.matrix[count][g];
}
}
count++;
}
}
int e = matrix[i][length - 1];
for (int h = 0; h < rest; h++)
{
int b = e & (1 << h);
if (b != 0)
{
for (int g = 0; g < a.length; g++)
{
result.matrix[i][g] ^= a.matrix[count][g];
}
}
count++;
}
}
return result;
}
/**
* Compute the product of this matrix and a permutation matrix which is
* generated from an n-permutation.
*
* @param p the permutation
* @return {@link GF2Matrix} <tt>this*P</tt>
*/
public Matrix rightMultiply(Permutation p)
{
int[] pVec = p.getVector();
if (pVec.length != numColumns)
{
throw new ArithmeticException("length mismatch");
}
GF2Matrix result = new GF2Matrix(numRows, numColumns);
for (int i = numColumns - 1; i >= 0; i--)
{
int q = i >>> 5;
int r = i & 0x1f;
int pq = pVec[i] >>> 5;
int pr = pVec[i] & 0x1f;
for (int j = numRows - 1; j >= 0; j--)
{
result.matrix[j][q] |= ((matrix[j][pq] >>> pr) & 1) << r;
}
}
return result;
}
/**
* Compute the product of this matrix and the given column vector.
*
* @param vec the vector over GF(2)
* @return <tt>this*vector</tt>
*/
public Vector rightMultiply(Vector vec)
{
if (!(vec instanceof GF2Vector))
{
throw new ArithmeticException("vector is not defined over GF(2)");
}
if (vec.length != numColumns)
{
throw new ArithmeticException("length mismatch");
}
int[] v = ((GF2Vector)vec).getVecArray();
int[] res = new int[(numRows + 31) >>> 5];
for (int i = 0; i < numRows; i++)
{
// compute full word scalar products
int help = 0;
for (int j = 0; j < length; j++)
{
help ^= matrix[i][j] & v[j];
}
// compute single word scalar product
int bitValue = 0;
for (int j = 0; j < 32; j++)
{
bitValue ^= (help >>> j) & 1;
}
// set result bit
if (bitValue == 1)
{
res[i >>> 5] |= 1 << (i & 0x1f);
}
}
return new GF2Vector(res, numRows);
}
/**
* Compute the product of the matrix <tt>(Id | this)</tt> and a column
* vector, where <tt>Id</tt> is a <tt>(numRows x numRows)</tt> unit
* matrix.
*
* @param vec the vector over GF(2)
* @return <tt>(Id | this)*vector</tt>
*/
public Vector rightMultiplyRightCompactForm(Vector vec)
{
if (!(vec instanceof GF2Vector))
{
throw new ArithmeticException("vector is not defined over GF(2)");
}
if (vec.length != numColumns + numRows)
{
throw new ArithmeticException("length mismatch");
}
int[] v = ((GF2Vector)vec).getVecArray();
int[] res = new int[(numRows + 31) >>> 5];
int q = numRows >> 5;
int r = numRows & 0x1f;
// for all rows
for (int i = 0; i < numRows; i++)
{
// get vector bit
int help = (v[i >> 5] >>> (i & 0x1f)) & 1;
// compute full word scalar products
int vInd = q;
// if words have to be shifted
if (r != 0)
{
int vw = 0;
// process all but last word
for (int j = 0; j < length - 1; j++)
{
// shift to correct position
vw = (v[vInd++] >>> r) | (v[vInd] << (32 - r));
help ^= matrix[i][j] & vw;
}
// process last word
vw = v[vInd++] >>> r;
if (vInd < v.length)
{
vw |= v[vInd] << (32 - r);
}
help ^= matrix[i][length - 1] & vw;
}
else
{
// no shifting necessary
for (int j = 0; j < length; j++)
{
help ^= matrix[i][j] & v[vInd++];
}
}
// compute single word scalar product
int bitValue = 0;
for (int j = 0; j < 32; j++)
{
bitValue ^= help & 1;
help >>>= 1;
}
// set result bit
if (bitValue == 1)
{
res[i >> 5] |= 1 << (i & 0x1f);
}
}
return new GF2Vector(res, numRows);
}
/**
* Compare this matrix with another object.
*
* @param other another object
* @return the result of the comparison
*/
public boolean equals(Object other)
{
if (!(other instanceof GF2Matrix))
{
return false;
}
GF2Matrix otherMatrix = (GF2Matrix)other;
if ((numRows != otherMatrix.numRows)
|| (numColumns != otherMatrix.numColumns)
|| (length != otherMatrix.length))
{
return false;
}
for (int i = 0; i < numRows; i++)
{
if (!IntUtils.equals(matrix[i], otherMatrix.matrix[i]))
{
return false;
}
}
return true;
}
/**
* @return the hash code of this matrix
*/
public int hashCode()
{
int hash = (numRows * 31 + numColumns) * 31 + length;
for (int i = 0; i < numRows; i++)
{
hash = hash * 31 + matrix[i].hashCode();
}
return hash;
}
/**
* @return a human readable form of the matrix
*/
public String toString()
{
int rest = numColumns & 0x1f;
int d;
if (rest == 0)
{
d = length;
}
else
{
d = length - 1;
}
StringBuffer buf = new StringBuffer();
for (int i = 0; i < numRows; i++)
{
buf.append(i + ": ");
for (int j = 0; j < d; j++)
{
int a = matrix[i][j];
for (int k = 0; k < 32; k++)
{
int b = (a >>> k) & 1;
if (b == 0)
{
buf.append('0');
}
else
{
buf.append('1');
}
}
buf.append(' ');
}
int a = matrix[i][length - 1];
for (int k = 0; k < rest; k++)
{
int b = (a >>> k) & 1;
if (b == 0)
{
buf.append('0');
}
else
{
buf.append('1');
}
}
buf.append('\n');
}
return buf.toString();
}
/**
* Swap two rows of the given matrix.
*
* @param matrix the matrix
* @param first the index of the first row
* @param second the index of the second row
*/
private static void swapRows(int[][] matrix, int first, int second)
{
int[] tmp = matrix[first];
matrix[first] = matrix[second];
matrix[second] = tmp;
}
/**
* Partially add one row to another.
*
* @param fromRow the addend
* @param toRow the row to add to
* @param startIndex the array index to start from
*/
private static void addToRow(int[] fromRow, int[] toRow, int startIndex)
{
for (int i = toRow.length - 1; i >= startIndex; i--)
{
toRow[i] = fromRow[i] ^ toRow[i];
}
}
}