/// <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;
}
/// <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);
}
public static Zp Reconstruct(IList<Zp> sharedSecrets, int polyDeg, int prime)
{
if (sharedSecrets.Count < polyDeg)
throw new System.ArgumentException("Polynomial degree cannot be bigger or equal to the number of shares");
// find Lagrange basis polynomials free coefficients
var L = new Zp[polyDeg + 1];
for (int i = 0; i < polyDeg + 1; i++)
L[i] = new Zp(prime, 1);
int ix = 0;
for (var i = new Zp(prime, 1); i < polyDeg + 2; i++, ix++)
{
for (var j = new Zp(prime, 1); j < polyDeg + 2; j++)
{
if (j != i)
{
var additiveInverse = j.AdditiveInverse;
L[ix] = L[ix] * (additiveInverse / (i + additiveInverse)); // note: division done in finite-field
}
}
}
// find the secret by multiplying each share to the corresponding Lagrange's free coefficient
var secret = new Zp(prime, 0);
for (int i = 0; i < polyDeg + 1; i++)
secret = secret + (L[i] * sharedSecrets[i]);
return secret;
}
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 Zp ConstMul(Zp operand)
{
var temp = new Zp(this);
temp.num = Modulo(num * operand.Value);
return(temp);
}
/// <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 void SetMatrixCell(int rowNumber, int colNumber, Zp value)
{
if ((RowCount <= rowNumber) || (ColCount <= colNumber))
{
throw new ArgumentException("Illegal matrix cell.");
}
data[rowNumber][colNumber] = value.Value;
}
public Zp ConstDvide(Zp operand)
{
if (operand.num == 0)
{
throw new System.ArgumentException("Cannot divide by zero!");
}
return(this * operand.MultipInverse);
}
public static Zp EvalutePolynomialAtPoint(IList <Zp> polynomial, Zp point)
{
long evaluation = 0;
for (int i = 0; i < polynomial.Count; i++)
{
evaluation += polynomial[i].Value * NumTheoryUtils.ModPow(point.Value, i, point.Prime);
}
return(new Zp(point.Prime, evaluation));
}
public override bool Equals(object obj)
{
if (!(obj is Zp))
{
return(false);
}
Zp compare = (Zp)obj;
return(Value == compare.Value && Prime == compare.Prime);
}
/// <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);
}
public Zp Calculate(Zp operand, Operation operation)
{
switch (operation)
{
case Operation.Add:
return(Add(operand));
case Operation.Mul:
return(Mul(operand));
case Operation.Sub:
return(Sub(operand));
case Operation.Div:
return(Div(operand));
default:
throw new Exception("Unknown operation: " + operation);
}
}
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 Zp Reconstruct(IList <Zp> sharedSecrets, int polyDeg, int prime)
{
if (sharedSecrets.Count < polyDeg)
{
throw new System.ArgumentException("Polynomial degree cannot be bigger or equal to the number of shares");
}
// find Lagrange basis polynomials free coefficients
var L = new Zp[polyDeg + 1];
for (int i = 0; i < polyDeg + 1; i++)
{
L[i] = new Zp(prime, 1);
}
int ix = 0;
for (var i = new Zp(prime, 1); i < polyDeg + 2; i++, ix++)
{
for (var j = new Zp(prime, 1); j < polyDeg + 2; j++)
{
if (j != i)
{
var additiveInverse = j.AdditiveInverse;
L[ix] = L[ix] * (additiveInverse / (i + additiveInverse)); // note: division done in finite-field
}
}
}
// find the secret by multiplying each share to the corresponding Lagrange's free coefficient
var secret = new Zp(prime, 0);
for (int i = 0; i < polyDeg + 1; i++)
{
secret = secret + (L[i] * sharedSecrets[i]);
}
return(secret);
}
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);
}
public Zp(Zp toCopy)
{
this.Prime = toCopy.Prime;
this.num = Modulo(toCopy.num, this.Prime);
}
public Zp Sub(Zp operand)
{
num = Modulo(num - operand.Value);
return this;
}
public Zp Mul(Zp operand)
{
num = Modulo(num * operand.Value);
return this;
}
public Zp Div(Zp operand)
{
if (operand.num == 0)
throw new ArgumentException("Cannot divide by zero!");
return this * operand.MultipInverse;
}
/// <summary>
/// Calculates the shares of a secret with polynomial of degree t and numPlayers players.
/// The method also returns the array of coefficients of the polynomial.
/// </summary>
public static IList<Zp> Share(Zp secret, int numPlayers, int polyDeg, out IList<Zp> coeffs)
{
return Share(secret, numPlayers, polyDeg, false, out coeffs);
}
public Zp Add(Zp operand)
{
num = Modulo(num + operand.Value);
return(this);
}
public Zp Mul(Zp operand)
{
num = Modulo(num * operand.Value);
return(this);
}
public BridgeJoinMessage(long pseudonym, Zp idShare)
{
Pseudonym = pseudonym;
IdShare = idShare;
}
/* calculate i mod prime */
private long Modulo(long i)
{
return(Zp.Modulo(i, Prime));
}
public Zp Add(Zp operand)
{
num = Modulo(num + operand.Value);
return this;
}
public Zp Calculate(Zp operand, Operation operation)
{
switch (operation)
{
case Operation.Add:
return Add(operand);
case Operation.Mul:
return Mul(operand);
case Operation.Sub:
return Sub(operand);
case Operation.Div:
return Div(operand);
default:
throw new Exception("Unknown operation: " + operation);
}
}
public Zp ConstSub(Zp operand)
{
var temp = new Zp(this);
temp.num = Modulo(num - operand.Value);
return temp;
}
public Zp(Zp toCopy)
{
this.Prime = toCopy.Prime;
this.num = Modulo(toCopy.num, this.Prime);
}
public Zp Sub(Zp operand)
{
num = Modulo(num - operand.Value);
return(this);
}
public static Zp EvalutePolynomialAtPoint(IList<Zp> polynomial, Zp point)
{
long evaluation = 0;
for (int i = 0; i < polynomial.Count; i++)
{
evaluation += polynomial[i].Value * NumTheoryUtils.ModPow(point.Value, i, point.Prime);
}
return new Zp(point.Prime, evaluation);
}
/// <summary>
/// Calculates the shares of a secret with polynomial of degree t and numPlayers players.
/// The method also returns the array of coefficients of the polynomial.
/// </summary>
public static IList <Zp> Share(Zp secret, int numPlayers, int polyDeg, out IList <Zp> coeffs)
{
return(Share(secret, numPlayers, polyDeg, false, out coeffs));
}