private static ZpMatrix getWelchBerlekampMatrix(IList <Zp> XVlaues, IList <Zp> YVlaues, int n, int e, int prime)
{
var NVanderMonde = ZpMatrix.GetVandermondeMatrix(n - e, XVlaues, prime).Transpose;
var EVanderMonde = ZpMatrix.GetVandermondeMatrix(e, XVlaues, prime).Transpose;
int[] scalarVector = new int[YVlaues.Count];
int i = 0;
foreach (Zp zp in YVlaues)
{
scalarVector[i++] = -zp.Value;
}
EVanderMonde = EVanderMonde.MulMatrixByScalarsVector(scalarVector);
return(ZpMatrix.GetConcatenationMatrix(NVanderMonde, EVanderMonde));
}
/// <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)
{
#if NO_COMPUTATION
// send some dummy shares
var shares = new Zp[numPlayers];
for (int i = 0; i < numPlayers; i++)
{
shares[i] = new Zp(secret.Prime);
}
return(shares);
#else
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 != null);
Debug.Assert(sharesArr.Length == numPlayers);
return(sharesArr);
#endif
}
/// <summary>
/// Each party in the new quorum needs to call this with the shares received from the old quorum to calculate its share
/// </summary>
public static Zp CombineReshares(IList <Zp> reshares, int newQuorumSize, int prime)
{
int oldQuorumSize = reshares.Count;
if (oldQuorumSize != newQuorumSize)
{
throw new System.ArgumentException("Do not support case where quorums are of different sizes");
}
// Compute the first row of the inverse Vandermonde matrix
var vandermonde = ZpMatrix.GetVandermondeMatrix(oldQuorumSize, newQuorumSize, prime);
var vandermondeInv = vandermonde.Inverse.GetMatrixColumn(0);
var S = new Zp(prime);
for (var i = 0; i < newQuorumSize; i++)
{
S += vandermondeInv[i] * reshares[i];
}
return(S);
}