public void McElieseGenericFormTest(int n, int k, int d, int t, int fieldPower, MatrixInt message, MatrixInt errorVector, MatrixInt scrambler, int[] permutation, int[] mask)
{
var galoisField = new GaloisField(2, fieldPower);
var generator = new ParityCheckMatrixGeneratorEllyptic(2);
var linearCode = new LinearCode(n, k, d, t, galoisField);
while (true)
{
linearCode.ParityCheckMatrix = generator.Generate(linearCode);
if (Helper.Weight(linearCode.ParityCheckMatrix) < Math.Ceiling(linearCode.ParityCheckMatrix.RowCount * linearCode.ParityCheckMatrix.ColumnCount * 0.7))
{
continue;
}
try
{
linearCode.GeneratorMatrix = GeneratorMatrixCalculator.CalculateGeneratorMatrixAlt(linearCode);
}
catch (LinearCodeException ex)
{
Console.WriteLine(ex.Message);
continue;
}
if (Helper.Weight(MatrixAlgorithms.DotMultiplication(linearCode.GeneratorMatrix, linearCode.ParityCheckMatrix.Transpose(), galoisField)) == 0)
{
linearCode.GeneratorMatrix = linearCode.GeneratorMatrix;
break;
}
}
var crytptogram = McElieseGenericForm.Encrypt(linearCode, scrambler, permutation, mask, generator, message, errorVector);
var decryptedMessage = McElieseGenericForm.Decrypt(linearCode, permutation, mask, scrambler, generator, crytptogram);
Assert.True(message == decryptedMessage);
}
public static int[] LocateErrors(ILinearCode linearCode, MatrixInt syndrome, ParityCheckMatrixGeneratorEllyptic generator)
{
#region Error locator polynomial
var rowCount = linearCode.T;
var columnCount = linearCode.T + 1;
var system = new int[rowCount, columnCount];
for (int row = 0; row < rowCount; row++)
{
for (int col = 0; col < columnCount - 1; col++)
{
system[row, col] = syndrome[0, generator.Terms[(row + col), linearCode.T - 2]];
}
system[row, columnCount - 1] = syndrome[0, generator.Terms[row, linearCode.T - 1]];
}
var coefficients = MatrixAlgorithms.Solve(new MatrixInt(system), linearCode.GaloisField).Transpose();
#endregion
#region Calculate Error Positions
var errorLocators = new int[linearCode.N];
for (int position = 0; position < linearCode.N; position++)
{
var sum = 0;
for (int i = 0; i < linearCode.T; i++)
{
var wordToAdd = linearCode.GaloisField.MultiplyWords(coefficients[0, i], linearCode.GaloisField.Power(generator.Points[position].x, i));
sum = linearCode.GaloisField.AddWords(sum, wordToAdd);
}
sum = linearCode.GaloisField.AddWords(sum, generator.Points[position].y);
errorLocators[position] = sum;
}
#endregion
return(errorLocators);
}
public static MatrixInt DecodeAndCorrect(ILinearCode linearCode, MatrixInt message, ParityCheckMatrixGeneratorEllyptic generator)
{
if (message.ColumnCount != linearCode.ParityCheckMatrix.ColumnCount)
{
throw new DimensionMismatchException("Incorrect length of message. Meesage length should be equal number of columns in parity check matrix.");
}
#region Calculate syndrome
var syndrome = MatrixAlgorithms.DotMultiplication(message, linearCode.ParityCheckMatrix.Transpose(), linearCode.GaloisField);
#endregion
#region Locate errors
var errorLocators = ErrorLocatorEllyptic.LocateErrors(linearCode, syndrome, generator);
var errorCount = errorLocators.Where(v => v == 0).Count();
#endregion
Debug.WriteLine(linearCode.ParityCheckMatrix);
#region Caclulate Error vector
var system = new MatrixInt(linearCode.D, errorCount);
for (int row = 0; row < linearCode.D; row++)
{
for (int col = 0, i = 0; col < linearCode.N; col++)
{
if (errorLocators[col] == 0)
{
system[row, i] = linearCode.ParityCheckMatrix[row, col];
i++;
}
}
}
Debug.WriteLine(system);
system |= syndrome.Transpose();
Debug.WriteLine(system);
var errorVectorValues = MatrixAlgorithms.Solve(system, linearCode.GaloisField);
var errorVector = new int[errorLocators.Length];
for (int i = 0, j = 0; i < errorVector.Length; i++)
{
if (errorLocators[i] == 0)
{
errorVector[i] = errorVectorValues[j, 0];
j++;
}
else
{
errorVector[i] = 0;
}
}
#endregion
var rawOriginalMessage = new int[linearCode.K];
for (int i = 0; i < linearCode.K; i++)
{
rawOriginalMessage[i] = linearCode.GaloisField.AddWords(message.Data[0, i + linearCode.D], errorVector[i + linearCode.D]);
}
var originalMessage = new MatrixInt(rawOriginalMessage);
return(originalMessage);
}
public static MatrixInt Decrypt(ILinearCode linearCode, IList <int> permutation, IList <int> mask, MatrixInt scramblerMatrix, ParityCheckMatrixGeneratorEllyptic generator, MatrixInt encryptedMessage)
{
var message = encryptedMessage.Clone();
#region Unmask
for (int col = 0; col < message.ColumnCount; col++)
{
for (int row = 0; row < message.RowCount; row++)
{
message[row, col] = linearCode.GaloisField.MultiplyWords(message[row, col], linearCode.GaloisField.GetMultiplicativeInverse(mask[col]));
}
}
#endregion
Debug.WriteLine(message);
#region Inverse permutation
var inversePermutation = Helper.InversePermutation(permutation);
message = message.PermuteColumns(inversePermutation);
#endregion
Debug.WriteLine(message);
#region Correct Errors
var correctedMessage = DecoderEllyptic.DecodeAndCorrect(linearCode, message, generator);
#endregion
Debug.WriteLine(correctedMessage);
#region Apply the inverse scrambler matrix
var inverseScramblerMatrix = MatrixAlgorithms.MatrixInverse(scramblerMatrix, linearCode.GaloisField);
var decryptedMessage = MatrixAlgorithms.DotMultiplication(correctedMessage, inverseScramblerMatrix, linearCode.GaloisField);
#endregion
return(decryptedMessage);
}
public static MatrixInt Encrypt(ILinearCode linearCode, MatrixInt scramblerMatrix, IList <int> permutation, IList <int> mask, ParityCheckMatrixGeneratorEllyptic generator, MatrixInt message, MatrixInt errorVector)
{
var encryptionMatrix = MatrixAlgorithms.DotMultiplication(scramblerMatrix, linearCode.GeneratorMatrix, linearCode.GaloisField);
Debug.WriteLine(encryptionMatrix);
encryptionMatrix = encryptionMatrix.PermuteColumns(permutation);
Debug.WriteLine(encryptionMatrix);
for (int col = 0; col < encryptionMatrix.ColumnCount; col++)
{
for (int row = 0; row < encryptionMatrix.RowCount; row++)
{
encryptionMatrix[row, col] = linearCode.GaloisField.MultiplyWords(encryptionMatrix[row, col], mask[col]);
}
}
Debug.WriteLine(encryptionMatrix);
var encryptedMessage = MatrixAlgorithms.DotMultiplication(message, encryptionMatrix, linearCode.GaloisField);
for (int i = 0; i < encryptedMessage.ColumnCount; i++)
{
encryptedMessage[0, i] = linearCode.GaloisField.AddWords(encryptedMessage[0, i], errorVector[0, i]);
}
return(encryptedMessage);
}
public McElieseEllyptic(int n, int k, int d, int t, GaloisField galoisField, MatrixInt scramblerMatrix = null, IList <int> permutation = null, IList <int> mask = null)
{
_generator = new ParityCheckMatrixGeneratorEllyptic(2);
LinearCode = new LinearCode(n, k, d, t, galoisField);
MatrixInt parityCheckMatrix = null;
MatrixInt generatorMatrix = null;
while (true)
{
parityCheckMatrix = _generator.Generate(LinearCode);
LinearCode.ParityCheckMatrix = parityCheckMatrix;
Debug.WriteLine(parityCheckMatrix);
var minValueFillPercentage = 0.7;
if (Helper.Weight(parityCheckMatrix) < Math.Ceiling(parityCheckMatrix.RowCount * parityCheckMatrix.ColumnCount * minValueFillPercentage))
{
continue;
}
try
{
generatorMatrix = GeneratorMatrixCalculator.CalculateGeneratorMatrixAlt(LinearCode);
Debug.WriteLine(generatorMatrix);
}
catch (LinearCodeException ex)
{
Debug.WriteLine(ex.Message);
continue;
}
if (IsGeneratorMatrixValid(parityCheckMatrix, generatorMatrix, galoisField))
{
LinearCode.GeneratorMatrix = generatorMatrix;
break;
}
}
if (scramblerMatrix is null)
{
scramblerMatrix = Helper.GenerateScramblerMatrix(LinearCode.K);
while (true)
{
try
{
MatrixAlgorithms.MatrixInverse(scramblerMatrix, galoisField);
break;
}
catch (SolveMatrixException)
{
Debug.WriteLine("Reattempting to generate scrambler matrix");
}
}
}
if (permutation is null)
{
permutation = Helper.GeneratePermutaionList(LinearCode.N);
}
if (mask is null)
{
mask = Helper.GenerateMask(LinearCode.N, LinearCode.GaloisField);
}
var inverseMask = new List <int>(LinearCode.N);
for (int i = 0; i < LinearCode.N; i++)
{
inverseMask.Add(LinearCode.GaloisField.GetMultiplicativeInverse(mask[i]));
}
PrivateKey = new PrivateKey
{
GeneratorMatrix = LinearCode.GeneratorMatrix,
ScramblerMatrix = scramblerMatrix,
InverseScramblerMatrix = MatrixAlgorithms.MatrixInverse(scramblerMatrix, galoisField),
Permutation = permutation,
InversePermutation = Helper.InversePermutation(permutation),
Mask = mask,
InverseMask = inverseMask
};
var encryptionMatrix = MatrixAlgorithms.DotMultiplication(PrivateKey.ScramblerMatrix, generatorMatrix, LinearCode.GaloisField);
Debug.WriteLine(encryptionMatrix);
encryptionMatrix = encryptionMatrix.PermuteColumns(PrivateKey.Permutation);
Debug.WriteLine(encryptionMatrix);
for (int col = 0; col < encryptionMatrix.ColumnCount; col++)
{
for (int row = 0; row < encryptionMatrix.RowCount; row++)
{
encryptionMatrix[row, col] = LinearCode.GaloisField.MultiplyWords(encryptionMatrix[row, col], PrivateKey.Mask[col]);
}
}
Debug.WriteLine(encryptionMatrix);
PublicKey = new PublicKey
{
EncryptionMatrix = encryptionMatrix,
};
}
