org.bouncycastle.pqc.crypto.rainbow.util.ComputeInField Maven / Gradle / Ivy
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package org.bouncycastle.pqc.crypto.rainbow.util;
/**
* This class offers different operations on matrices in field GF2^8.
*
* Implemented are functions:
* - finding inverse of a matrix
* - solving linear equation systems using the Gauss-Elimination method
* - basic operations like matrix multiplication, addition and so on.
*/
public class ComputeInField
{
private short[][] A; // used by solveEquation and inverse
short[] x;
/**
* Constructor with no parameters
*/
public ComputeInField()
{
}
/**
* This function finds a solution of the equation Bx = b.
* Exception is thrown if the linear equation system has no solution
*
* @param B this matrix is the left part of the
* equation (B in the equation above)
* @param b the right part of the equation
* (b in the equation above)
* @return x the solution of the equation if it is solvable
* null otherwise
* @throws RuntimeException if LES is not solvable
*/
public short[] solveEquation(short[][] B, short[] b)
{
if (B.length != b.length)
{
return null; // not solvable in this form
}
try
{
/** initialize **/
// this matrix stores B and b from the equation B*x = b
// b is stored as the last column.
// B contains one column more than rows.
// In this column we store a free coefficient that should be later subtracted from b
A = new short[B.length][B.length + 1];
// stores the solution of the LES
x = new short[B.length];
/** copy B into the global matrix A **/
for (int i = 0; i < B.length; i++)
{ // rows
for (int j = 0; j < B[0].length; j++)
{ // cols
A[i][j] = B[i][j];
}
}
/** copy the vector b into the global A **/
//the free coefficient, stored in the last column of A( A[i][b.length]
// is to be subtracted from b
for (int i = 0; i < b.length; i++)
{
A[i][b.length] = GF2Field.addElem(b[i], A[i][b.length]);
}
/** call the methods for gauss elimination and backward substitution **/
computeZerosUnder(false); // obtain zeros under the diagonal
substitute();
return x;
}
catch (RuntimeException rte)
{
return null; // the LES is not solvable!
}
}
/**
* This function computes the inverse of a given matrix using the Gauss-
* Elimination method.
*
* An exception is thrown if the matrix has no inverse
*
* @param coef the matrix which inverse matrix is needed
* @return inverse matrix of the input matrix.
* If the matrix is singular, null is returned.
* @throws RuntimeException if the given matrix is not invertible
*/
public short[][] inverse(short[][] coef)
{
try
{
/** Initialization: **/
short factor;
short[][] inverse;
A = new short[coef.length][2 * coef.length];
if (coef.length != coef[0].length)
{
throw new RuntimeException(
"The matrix is not invertible. Please choose another one!");
}
/** prepare: Copy coef and the identity matrix into the global A. **/
for (int i = 0; i < coef.length; i++)
{
for (int j = 0; j < coef.length; j++)
{
//copy the input matrix coef into A
A[i][j] = coef[i][j];
}
// copy the identity matrix into A.
for (int j = coef.length; j < 2 * coef.length; j++)
{
A[i][j] = 0;
}
A[i][i + A.length] = 1;
}
/** Elimination operations to get the identity matrix from the left side of A. **/
// modify A to get 0s under the diagonal.
computeZerosUnder(true);
// modify A to get only 1s on the diagonal: A[i][j] =A[i][j]/A[i][i].
for (int i = 0; i < A.length; i++)
{
factor = GF2Field.invElem(A[i][i]);
for (int j = i; j < 2 * A.length; j++)
{
A[i][j] = GF2Field.multElem(A[i][j], factor);
}
}
//modify A to get only 0s above the diagonal.
computeZerosAbove();
// copy the result (the second half of A) in the matrix inverse.
inverse = new short[A.length][A.length];
for (int i = 0; i < A.length; i++)
{
for (int j = A.length; j < 2 * A.length; j++)
{
inverse[i][j - A.length] = A[i][j];
}
}
return inverse;
}
catch (RuntimeException rte)
{
// The matrix is not invertible! A new one should be generated!
return null;
}
}
/**
* Elimination under the diagonal.
* This function changes a matrix so that it contains only zeros under the
* diagonal(Ai,i) using only Gauss-Elimination operations.
*
* It is used in solveEquaton as well as in the function for
* finding an inverse of a matrix: {@link}inverse. Both of them use the
* Gauss-Elimination Method.
*
* The result is stored in the global matrix A
*
*
* @param usedForInverse This parameter shows if the function is used by the
* solveEquation-function or by the inverse-function and according
* to this creates matrices of different sizes.
* @throws RuntimeException in case a multiplicative inverse of 0 is needed
*/
private void computeZerosUnder(boolean usedForInverse)
throws RuntimeException
{
//the number of columns in the global A where the tmp results are stored
int length;
short tmp = 0;
//the function is used in inverse() - A should have 2 times more columns than rows
if (usedForInverse)
{
length = 2 * A.length;
}
//the function is used in solveEquation - A has 1 column more than rows
else
{
length = A.length + 1;
}
//elimination operations to modify A so that that it contains only 0s under the diagonal
for (int k = 0; k < A.length - 1; k++)
{ // the fixed row
for (int i = k + 1; i < A.length; i++)
{ // rows
short factor1 = A[i][k];
short factor2 = GF2Field.invElem(A[k][k]);
//The element which multiplicative inverse is needed, is 0
//in this case is the input matrix not invertible
if (factor2 == 0)
{
throw new IllegalStateException("Matrix not invertible! We have to choose another one!");
}
for (int j = k; j < length; j++)
{// columns
// tmp=A[k,j] / A[k,k]
tmp = GF2Field.multElem(A[k][j], factor2);
// tmp = A[i,k] * A[k,j] / A[k,k]
tmp = GF2Field.multElem(factor1, tmp);
// A[i,j]=A[i,j]-A[i,k]/A[k,k]*A[k,j];
A[i][j] = GF2Field.addElem(A[i][j], tmp);
}
}
}
}
/**
* Elimination above the diagonal.
* This function changes a matrix so that it contains only zeros above the
* diagonal(Ai,i) using only Gauss-Elimination operations.
*
* It is used in the inverse-function
* The result is stored in the global matrix A
*
*
* @throws RuntimeException in case a multiplicative inverse of 0 is needed
*/
private void computeZerosAbove()
throws RuntimeException
{
short tmp = 0;
for (int k = A.length - 1; k > 0; k--)
{ // the fixed row
for (int i = k - 1; i >= 0; i--)
{ // rows
short factor1 = A[i][k];
short factor2 = GF2Field.invElem(A[k][k]);
if (factor2 == 0)
{
throw new RuntimeException("The matrix is not invertible");
}
for (int j = k; j < 2 * A.length; j++)
{ // columns
// tmp = A[k,j] / A[k,k]
tmp = GF2Field.multElem(A[k][j], factor2);
// tmp = A[i,k] * A[k,j] / A[k,k]
tmp = GF2Field.multElem(factor1, tmp);
// A[i,j] = A[i,j] - A[i,k] / A[k,k] * A[k,j];
A[i][j] = GF2Field.addElem(A[i][j], tmp);
}
}
}
}
/**
* This function uses backward substitution to find x
* of the linear equation system (LES) B*x = b,
* where A a triangle-matrix is (contains only zeros under the diagonal)
* and b is a vector
*
* If the multiplicative inverse of 0 is needed, an exception is thrown.
* In this case is the LES not solvable
*
*
* @throws RuntimeException in case a multiplicative inverse of 0 is needed
*/
private void substitute()
throws IllegalStateException
{
// for the temporary results of the operations in field
short tmp, temp;
temp = GF2Field.invElem(A[A.length - 1][A.length - 1]);
if (temp == 0)
{
throw new IllegalStateException("The equation system is not solvable");
}
/** backward substitution **/
x[A.length - 1] = GF2Field.multElem(A[A.length - 1][A.length], temp);
for (int i = A.length - 2; i >= 0; i--)
{
tmp = A[i][A.length];
for (int j = A.length - 1; j > i; j--)
{
temp = GF2Field.multElem(A[i][j], x[j]);
tmp = GF2Field.addElem(tmp, temp);
}
temp = GF2Field.invElem(A[i][i]);
if (temp == 0)
{
throw new IllegalStateException("Not solvable equation system");
}
x[i] = GF2Field.multElem(tmp, temp);
}
}
/**
* This function multiplies two given matrices.
* If the given matrices cannot be multiplied due
* to different sizes, an exception is thrown.
*
* @param M1 -the 1st matrix
* @param M2 -the 2nd matrix
* @return A = M1*M2
* @throws RuntimeException in case the given matrices cannot be multiplied
* due to different dimensions.
*/
public short[][] multiplyMatrix(short[][] M1, short[][] M2)
throws RuntimeException
{
if (M1[0].length != M2.length)
{
throw new RuntimeException("Multiplication is not possible!");
}
short tmp = 0;
A = new short[M1.length][M2[0].length];
for (int i = 0; i < M1.length; i++)
{
for (int j = 0; j < M2.length; j++)
{
for (int k = 0; k < M2[0].length; k++)
{
tmp = GF2Field.multElem(M1[i][j], M2[j][k]);
A[i][k] = GF2Field.addElem(A[i][k], tmp);
}
}
}
return A;
}
/**
* This function multiplies a given matrix with a one-dimensional array.
*
* An exception is thrown, if the number of columns in the matrix and
* the number of rows in the one-dim. array differ.
*
* @param M1 the matrix to be multiplied
* @param m the one-dimensional array to be multiplied
* @return M1*m
* @throws RuntimeException in case of dimension inconsistency
*/
public short[] multiplyMatrix(short[][] M1, short[] m)
throws RuntimeException
{
if (M1[0].length != m.length)
{
throw new RuntimeException("Multiplication is not possible!");
}
short tmp = 0;
short[] B = new short[M1.length];
for (int i = 0; i < M1.length; i++)
{
for (int j = 0; j < m.length; j++)
{
tmp = GF2Field.multElem(M1[i][j], m[j]);
B[i] = GF2Field.addElem(B[i], tmp);
}
}
return B;
}
/**
* Addition of two vectors
*
* @param vector1 first summand, always of dim n
* @param vector2 second summand, always of dim n
* @return addition of vector1 and vector2
* @throws RuntimeException in case the addition is impossible
* due to inconsistency in the dimensions
*/
public short[] addVect(short[] vector1, short[] vector2)
{
if (vector1.length != vector2.length)
{
throw new RuntimeException("Multiplication is not possible!");
}
short rslt[] = new short[vector1.length];
for (int n = 0; n < rslt.length; n++)
{
rslt[n] = GF2Field.addElem(vector1[n], vector2[n]);
}
return rslt;
}
/**
* Multiplication of column vector with row vector
*
* @param vector1 column vector, always n x 1
* @param vector2 row vector, always 1 x n
* @return resulting n x n matrix of multiplication
* @throws RuntimeException in case the multiplication is impossible due to
* inconsistency in the dimensions
*/
public short[][] multVects(short[] vector1, short[] vector2)
{
if (vector1.length != vector2.length)
{
throw new RuntimeException("Multiplication is not possible!");
}
short rslt[][] = new short[vector1.length][vector2.length];
for (int i = 0; i < vector1.length; i++)
{
for (int j = 0; j < vector2.length; j++)
{
rslt[i][j] = GF2Field.multElem(vector1[i], vector2[j]);
}
}
return rslt;
}
/**
* Multiplies vector with scalar
*
* @param scalar galois element to multiply vector with
* @param vector vector to be multiplied
* @return vector multiplied with scalar
*/
public short[] multVect(short scalar, short[] vector)
{
short rslt[] = new short[vector.length];
for (int n = 0; n < rslt.length; n++)
{
rslt[n] = GF2Field.multElem(scalar, vector[n]);
}
return rslt;
}
/**
* Multiplies matrix with scalar
*
* @param scalar galois element to multiply matrix with
* @param matrix 2-dim n x n matrix to be multiplied
* @return matrix multiplied with scalar
*/
public short[][] multMatrix(short scalar, short[][] matrix)
{
short[][] rslt = new short[matrix.length][matrix[0].length];
for (int i = 0; i < matrix.length; i++)
{
for (int j = 0; j < matrix[0].length; j++)
{
rslt[i][j] = GF2Field.multElem(scalar, matrix[i][j]);
}
}
return rslt;
}
/**
* Adds the n x n matrices matrix1 and matrix2
*
* @param matrix1 first summand
* @param matrix2 second summand
* @return addition of matrix1 and matrix2; both having the dimensions n x n
* @throws RuntimeException in case the addition is not possible because of
* different dimensions of the matrices
*/
public short[][] addSquareMatrix(short[][] matrix1, short[][] matrix2)
{
if (matrix1.length != matrix2.length || matrix1[0].length != matrix2[0].length)
{
throw new RuntimeException("Addition is not possible!");
}
short[][] rslt = new short[matrix1.length][matrix1.length];//
for (int i = 0; i < matrix1.length; i++)
{
for (int j = 0; j < matrix2.length; j++)
{
rslt[i][j] = GF2Field.addElem(matrix1[i][j], matrix2[i][j]);
}
}
return rslt;
}
}