/// <summary>
/// Returns a Vandermonde matrix in the field (each element is modulu prime).
/// </summary>
public static BigZpMatrix GetShamirRecombineMatrix(int matrixSize, BigInteger prime)
{
var A = new BigZpMatrix(matrixSize, matrixSize, prime);
if (matrixSize == 1)
{
A.data[0][0] = 1;
return(A);
}
for (int i = 0; i < matrixSize; i++)
{
A.data[i][0] = 1;
}
for (int i = 0; i < matrixSize; i++)
{
A.data[i][1] = i + 1;
}
for (int i = 0; i < matrixSize; i++)
{
for (int j = 2; j < matrixSize; j++)
{
A.data[i][j] = BigZp.Modulo(A.data[i][j - 1] * A.data[i][1], prime);
}
}
return(A);
}
public static BigZpMatrix GetVandermondeMatrix(int rowNum, int colNum, BigInteger prime)
{
var A = new BigZpMatrix(rowNum, colNum, prime);
for (int j = 0; j < colNum; j++)
{
A.data[0][j] = 1;
}
if (rowNum == 1)
{
return(A);
}
for (int j = 0; j < colNum; j++)
{
A.data[1][j] = j + 1;
}
for (int j = 0; j < colNum; j++)
{
for (int i = 2; i < rowNum; i++)
{
A.data[i][j] = BigZp.Modulo(A.data[i - 1][j] * A.data[1][j], prime);
}
}
return(A);
}
public void SetMatrixCell(int rowNumber, int colNumber, BigZp value)
{
if ((RowCount <= rowNumber) || (ColCount <= colNumber))
{
throw new ArgumentException("Illegal matrix cell.");
}
data[rowNumber][colNumber] = value.Value;
}
/// <summary>
/// Creates and return a random rowNum-by-colNum matrix with values between '0' and 'prime-1'.
/// </summary>
public static BigZpMatrix GetRandomMatrix(int rowNum, int colNum, BigInteger prime)
{
var A = new BigZpMatrix(rowNum, colNum, prime);
for (int i = 0; i < rowNum; i++)
{
for (int j = 0; j < colNum; j++)
{
A.data[i][j] = BigZp.Modulo(StaticRandom.Next(prime), prime);
}
}
return(A);
}
public BigZp[] SumMatrixRows()
{
var sum = new BigInteger[ColCount];
for (int i = 0; i < RowCount; i++)
{
for (int j = 0; j < ColCount; j++)
{
sum[j] += data[i][j];
}
}
var zpSum = new BigZp[ColCount];
for (int j = 0; j < ColCount; j++)
{
zpSum[j] = new BigZp(Prime, sum[j]);
}
return(zpSum);
}
public static BigZpMatrix GetVandermondeMatrix(int rowNum, IList <BigZp> values, BigInteger prime)
{
int colNum = values.Count;
var A = new BigZpMatrix(rowNum, colNum, prime);
for (int j = 0; j < colNum; j++)
{
A.data[0][j] = 1;
}
if (rowNum == 1)
{
return(A);
}
for (int j = 0; j < colNum; j++)
{
for (int i = 1; i < rowNum; i++)
{
A.data[i][j] = BigZp.Modulo(A.data[i - 1][j] * values[j].Value, prime);
}
}
return(A);
}
/// <summary>
/// Discrete logarithm encryption.
/// </summary>
/// <param name="x">Value to be encrypted.</param>
/// <param name="p">Prime modulus. Should be large enough (> 1024 bits) to ensure security.</param>
public static BigInteger DLEncrypt(BigZp x, BigInteger p)
{
return(BigInteger.ModPow(2, x.Value, p));
}
/* calculate i mod prime */
private BigInteger Modulo(BigInteger i)
{
return(BigZp.Modulo(i, Prime));
}