//Returns enumerator of shares by calculating (x, y) pair points for a given amount of shares
public IEnumerable <Share> GetShares(int totalShares)
{
for (int i = 1; i <= totalShares; ++i)
{
FFPolynom x = new FFPolynom(_irreduciblePolynom, new BigInteger(i));
FFPolynom y = FFPolynom.HornerEvaluateAt(_allCoefficients, i);
yield return(new Share(new FFPoint(x, y)));
}
}
//Returns whether two finite fields polynoms are equal
public override bool Equals(object obj)
{
FFPolynom fpp = obj as FFPolynom;
if (fpp == null)
{
return(base.Equals(obj));
}
bool res = (PrimePolynom == fpp.PrimePolynom) && (PolyValue.Equals(fpp.PolyValue));
return(res);
}
//Adjusts the finite field points by removing the high term monomial
private static FFPoint AdjustPoint(int total, FFPoint point)
{
FFPolynom corrector = new FFPolynom(point.Y.PrimePolynom, BigInteger.One);
FFPolynom corrFactor = point.X;
for (int i = 1; i <= total; i++)
{
corrector = corrector * corrFactor;
}
FFPolynom newY = point.Y + corrector;
FFPoint newPoint = new FFPoint(point.X, newY);
return(newPoint);
}
//Checks for matching with Regex and proccess the , and returns FiniteFieldPoint if success; otherwise null.
internal static bool TryParse(Match matchedShare, out FFPoint res)
{
if (!matchedShare.Success)
{
res = null;
return(false);
}
try
{
//Parse the share string: x - number by order, y - the string after '.' sign
//Gets the string matched by the particular expression. Change to lowcase and apply casing invariant
string xStr = matchedShare.Groups["x"].Value.ToLowerInvariant();
string yStr = matchedShare.Groups["y"].Value.ToLowerInvariant();
//Remove initial 0s to compare with ordinal = 4
while (xStr.StartsWith("0", StringComparison.Ordinal))
{
xStr = xStr.Substring(1);
}
// 1hexChar = 4 bits, so degree in bits = degree * 4
int polynomialDegree = yStr.Length * 4;
IrreduciblePolynom irp = new IrreduciblePolynom(polynomialDegree);
FFPolynom x = new FFPolynom(irp, BigInteger.Parse(xStr));
// Create an array of bites (big endian) with the length in bytes as initial phrase, initialize to 0
byte[] yArr = new byte[yStr.Length / 2];
for (int i = 0; i < yStr.Length; i += 2)
{
//Convert a hex-string to byte representation (1hex = 4 bits).. that's why i/2
yArr[i / 2] = Byte.Parse(yStr.Substring(i, 2), NumberStyles.HexNumber);
}
//Convert yArr to BigInteger and create a finite field polynom
FFPolynom y = new FFPolynom(irp, yArr.FromBigEndUnsignedBytesToBigInt());
res = new FFPoint(x, y);
return(true);
}
catch (Exception e)
{
res = null;
return(false);
}
}
//Combine shares to recover the secret by applying Lagrange Interpolation for all FFPoints
private RecoveredSecret RecoverImpl(IEnumerable <Share> shares)
{
Share[] allShares = shares.ToArray();
//Create a collection of finite field points out from generated shares
IEnumerable <FFPoint> collection = allShares.Select(s => s.Point);
//Recover the secret phrase using the points -> f(0)
FFPolynom secretCoeff = LagrangeInterpolation.LagrInterpolate(collection);
byte[] secret = secretCoeff.PolyValue.ToUnsignedBigEnd();
RecoveredSecret newRecSecret = new RecoveredSecret(secret);
return(newRecSecret);
}
//Shares the secret respectfully to number of shares and threshold
protected virtual SharedSecret ShareImpl(byte[] secret, int threshold, int numberOfShares)
{
//Define irred polynom for a secret
IrreduciblePolynom irreduciblePolynom = IrreduciblePolynom.GiveFromBytes(secret.Length);
BigInteger rawSecret = secret.FromBigEndUnsignedBytesToBigInt();
FFPolynom secretCoeff = new FFPolynom(irreduciblePolynom, rawSecret);
//Generate random polynom with corresponding irred. polynom and given threshold
IEnumerable <FFPolynom> randPolynom = GenerateRandomPolynom(irreduciblePolynom, threshold - 1);
//Construct an array of all coefficients represented as finite field polynoms
FFPolynom[] consTerm = new[] { secretCoeff };
//Concatenate previously created random coefficients converting them as an array
FFPolynom[] allCoefficients = consTerm.Concat(randPolynom).ToArray();
return(new SharedSecret(threshold, irreduciblePolynom, allCoefficients));
}
//Evaluate polynom of coefficients for certain x using Horner's method http//en.wikipedia.org/wiki/Horner_scheme
public static FFPolynom HornerEvaluateAt(FFPolynom[] coefficients, long x)
{
FFPolynom xPoly = coefficients[0].ReturnValueInField(x);
//The coefficient for the highest mono-polynom = 1
FFPolynom resValue = xPoly.DeepCopy();
//For all the coeffs, go thru them and add lowest first coeff, further multiolying by x-polyn
//Start backwards
for (int i = coefficients.Length - 1; i > 0; i--)
{
resValue = resValue + coefficients[i];
resValue = resValue * xPoly;
}
resValue = resValue + coefficients[0];
return(resValue);
}
/// <summary>
/// /Calculate f(0) in a finite field
/// </summary>
/// <param name="points"></param>
/// <returns></returns>
public static FFPolynom LagrInterpolate(IEnumerable <FFPoint> points)
{
FFPoint[] originalPoints = points.ToArray();
if (originalPoints.Length == 0)
{
throw new ArgumentOutOfRangeException();
}
int threshold = originalPoints.Length;
//"Correct" these points by removing the high term monomial
FFPoint[] adjustedPoints = originalPoints.Select(p => AdjustPoint(threshold, p)).ToArray();
//Use Lagrange interpolating polynomials ( http//en.wikipedia.org/wiki/Lagrange_polynomial )
//to solve:
// (x-x2)(x-x3)...(x-xn) (x-x1)(x-x3)...(x-xn)
//P(x) = ------------------------ y1 + -------------------------- y2 + ... +
// (x1-x2)(x1-x3)...(x1-xn) (x2-x1)(x2-x3)...(x2-xn-1)
//Simplifying things is that x is 0 since we want to find the constant term
//Polynomial that belongs to the GF[2] and represents the initially constructed polynom
FFPolynom originalPolynom = originalPoints[0].Y;
FFPolynom total = originalPolynom.ReturnValueInField(0);
for (int iPoint = 0; iPoint < threshold; iPoint++)// where iPoint is currently processing point
{
FFPolynom processingNumerator = originalPolynom.ReturnValueInField(1);
FFPolynom processingDenominator = originalPolynom.ReturnValueInField(1);
FFPoint processingPoint = adjustedPoints[iPoint];
for (int tempPoint = 0; tempPoint < threshold; tempPoint++)
{
//Skip if both are the same
if (iPoint == tempPoint)
{
continue;
}
//numerator needs multiplied by
//(0-x_i) = -x_i = x_i
//subtraction and addition are the same in GF[2]
processingNumerator *= adjustedPoints[tempPoint].X;
processingDenominator *= (processingPoint.X + adjustedPoints[tempPoint].X);
}
//Dividing is just multiplying by the inverse
FFPolynom denomInv = processingDenominator.GetInverse();
FFPolynom fraction = processingNumerator * denomInv;
//Multiply the fraction by the corresponding y_i
FFPolynom currentTermValue = fraction * processingPoint.Y;
total += currentTermValue;
}
return(total);
}
//Constructs the point using two polynoms for x and y dimension respectfully
public FFPoint(FFPolynom x, FFPolynom y)
{
X = x; Y = y;
}