/// <summary>
/// Returns a Vandermonde matrix in the field (each element is modulu prime).
/// </summary>
public static ZpMatrix GetShamirRecombineMatrix(int matrixSize, int prime)
{
var A = new ZpMatrix(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] = Zp.Modulo(A.data[i][j - 1] * A.data[i][1], prime);
}
}
return(A);
}
public static ZpMatrix GetVandermondeMatrix(int rowNum, int colNum, long prime)
{
var A = new ZpMatrix(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] = Zp.Modulo(A.data[i - 1][j] * A.data[1][j], prime);
}
}
return(A);
}
public ZpMatrix Times(ZpMatrix B)
{
var A = this;
if (A.ColCount != B.RowCount)
{
throw new ArgumentException("Illegal matrix dimensions.");
}
if (A.Prime != B.Prime)
{
throw new ArgumentException("Matrix from different fields.");
}
// create initialized matrix (zero value to all elements)
var C = new ZpMatrix(A.RowCount, B.ColCount, A.Prime);
for (int i = 0; i < C.RowCount; i++)
{
for (int j = 0; j < C.ColCount; j++)
{
for (int k = 0; k < A.ColCount; k++)
{
C.data[i][j] = Modulo(C.data[i][j] + A.data[i][k] * B.data[k][j]);
}
}
}
return(C);
}
public ZpMatrix Plus(ZpMatrix B)
{
var A = this;
if ((B.RowCount != A.RowCount) || (B.ColCount != A.ColCount))
{
throw new ArgumentException("Illegal matrix dimensions.");
}
if (A.Prime != B.Prime)
{
throw new ArgumentException("Trying to add Matrix from different fields.");
}
var C = new ZpMatrix(RowCount, ColCount, A.Prime);
for (int i = 0; i < RowCount; i++)
{
for (int j = 0; j < ColCount; j++)
{
C.data[i][j] = Modulo(A.data[i][j] + B.data[i][j]);
}
}
return(C);
}
/// <summary>
/// Evaluates the shares of secret with polynomial of degree 'polynomDeg' and 'numPlayers' players.
/// </summary>
private static IList <Zp> Share(Zp secret, int numPlayers, int polynomDeg, bool usePrimitiveShare, out IList <Zp> coeffs)
{
Debug.Assert(numPlayers > polynomDeg, "Polynomial degree cannot be greater than or equal to the number of players!");
// Create a random polynomial - f(x)
// Note: Polynomial of degree d has d+1 coefficients
var randomMatrix = ZpMatrix.GetRandomMatrix(1, polynomDeg + 1, secret.Prime);
// The free variable in the Random Polynomial (i.e. f(x)) is the secret
randomMatrix.SetMatrixCell(0, 0, secret);
// Polynomial coefficients
coeffs = randomMatrix.GetMatrixRow(0);
// Create vanderMonde matrix
ZpMatrix vanderMonde;
if (usePrimitiveShare)
{
vanderMonde = ZpMatrix.GetPrimitiveVandermondeMatrix(polynomDeg + 1, numPlayers, secret.Prime);
}
else
{
vanderMonde = ZpMatrix.GetVandermondeMatrix(polynomDeg + 1, numPlayers, secret.Prime);
}
// Compute f(i) for the i-th player
var sharesArr = randomMatrix.Times(vanderMonde).ZpVector;
Debug.Assert(sharesArr.Length == numPlayers);
return(sharesArr);
}
/* Create and return N-by-N matrix that its first "trucToSize" elements in
* its diagonal is "1" and the rest of the matrix is "0"*/
public static ZpMatrix GetTruncationMatrix(int matrixSize, int truncToSize, int prime)
{
var I = new ZpMatrix(matrixSize, matrixSize, prime);
for (int i = 0; i < truncToSize; i++)
{
I.data[i][i] = 1;
}
return(I);
}
/// <summary>
/// Create and return the N-by-N identity matrix.
/// </summary>
public static ZpMatrix GetIdentityMatrix(int matrixSize, int prime)
{
var I = new ZpMatrix(matrixSize, matrixSize, prime);
for (int i = 0; i < matrixSize; i++)
{
I.data[i][i] = 1;
}
return(I);
}
/// <summary>
/// Creates and return a random rowNum-by-colNum matrix with values between '0' and 'prime-1'.
/// </summary>
public static ZpMatrix GetRandomMatrix(int rowNum, int colNum, long prime)
{
var A = new ZpMatrix(rowNum, colNum, prime);
for (int i = 0; i < rowNum; i++)
{
for (int j = 0; j < colNum; j++)
{
A.data[i][j] = Zp.Modulo((long)(StaticRandom.NextDouble() * (prime)), prime);
}
}
return(A);
}
/* r - Array of row indices, j0 - Initial column index, j1 - Final column index
* return A(r(:),j0:j1) */
private ZpMatrix GetSubMatrix(int[] r, int j0, int j1)
{
var X = new ZpMatrix(r.Length, j1 - j0 + 1, Prime);
var B = X.data;
for (int i = 0; i < r.Length; i++)
{
for (int j = j0; j <= j1; j++)
{
B[i][j - j0] = data[r[i]][j];
}
}
return(X);
}
public bool Eq(ZpMatrix B)
{
var A = this;
if ((B.RowCount != A.RowCount) || (B.ColCount != A.ColCount) || (A.Prime != B.Prime))
{
return(false);
}
for (int i = 0; i < RowCount; i++)
{
for (int j = 0; j < ColCount; j++)
{
if (A.data[i][j] != B.data[i][j])
{
return(false);
}
}
}
return(true);
}
public static ZpMatrix GetPrimitiveVandermondeMatrix(int rowNum, int colNum, long prime)
{
int primitive = NumTheoryUtils.GetFieldMinimumPrimitive(prime);
if (primitive == 0)
{
throw new ArgumentException("Cannot create a primitive Vandermonde matrix from a non-prime number. ");
}
var A = new ZpMatrix(rowNum, colNum, prime);
for (int j = 0; j < colNum; j++)
{
A.data[0][j] = 1;
}
if (rowNum == 1)
{
return(A);
}
/* This variable represents primitive^j for the j-th player*/
long primitive_j = 1;
for (int j = 0; j < colNum; j++)
{
A.data[1][j] = primitive_j;
primitive_j = Zp.Modulo(primitive_j * primitive, prime);
}
for (int j = 0; j < colNum; j++)
{
for (int i = 2; i < rowNum; i++)
{
A.data[i][j] = Zp.Modulo(A.data[i - 1][j] * A.data[1][j], prime);
}
}
return(A);
}
public static ZpMatrix GetVandermondeMatrix(int rowNum, IList <Zp> values, int prime)
{
int colNum = values.Count;
var A = new ZpMatrix(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] = Zp.Modulo(A.data[i - 1][j] * values[j].Value, prime);
}
}
return(A);
}
private ZpMatrix(ZpMatrix A)
: this(A.data, A.Prime)
{
}