public string Decrypt(VectorND cipher)
{
List <char> result = new List <char>();
int blockCount = cipher.dim / dim;
for (int i = 0; i < blockCount; i++)
{
MatrixND cipherVector = new MatrixND(dim, 1);
for (int j = 0; j < dim; j++)
{
cipherVector[j, 0] = (double)cipher.values[i * dim + j];
}
MatrixND babai = privateKeyR1 * cipherVector;
for (int j = 0; j < dim; j++)
{
babai[j, 0] = Math.Round(babai[j, 0]);
}
MatrixND messageVector = publicKeyB1 * privateKeyR * babai;
for (int j = 0; j < dim; j++)
{
int messageInt = (int)Math.Round(messageVector[j, 0]);
if (messageInt == 0)
{
break;
}
result.Add(Convert.ToChar(messageInt));
}
}
return(new string(result.ToArray()));
}
public VectorND Encrypt(string message)
{
char[] chars = message.ToCharArray();
int rem;
int blockCount = Math.DivRem(chars.Length, dim, out rem);
if (rem > 0)
{
blockCount++;
}
VectorND cipher = new VectorND(dim * blockCount);
for (int i = 0; i < blockCount; i++)
{
MatrixND messagePart = new MatrixND(dim, 1);
for (int j = 0; j < dim && chars.Length > i * dim + j; j++)
{
messagePart[j, 0] = chars[i * dim + j];
}
MatrixND cipherPart = publicKeyB * messagePart + errorVectorIntern;
for (int j = 0; j < dim; j++)
{
cipher.values[i * dim + j] = (int)cipherPart[j, 0];
}
}
return(cipher);
}
public GGHModel(int dim, int l, VectorND errorVector)
{
this.dim = dim;
this.l = l;
k = (int)Math.Round(l * Math.Sqrt(dim));
do
{
GeneratePrivateKey();
GeneratePublicKey();
} while (privateKeyR.Det() == 0 || publicKeyB.Det() == 0);
privateKeyR1 = privateKeyR.Invert();
publicKeyB1 = publicKeyB.Invert();
GenerateLattice();
if (errorVector == null || errorVector.dim != dim)
{
GenerateErrorVector();
}
else
{
this.errorVector = errorVector;
errorVectorIntern = new MatrixND(dim, 1);
for (int i = 0; i < dim; i++)
{
errorVectorIntern[i, 0] = (double)errorVector.values[i];
}
}
}
public MerkleHellmanModel(VectorND privateKey, BigInteger r, BigInteger mod)
{
dim = privateKey.dim;
this.privateKey = privateKey;
this.r = r;
this.mod = mod;
rI = ModInverse(r, mod);
ComputePublicKey();
}
public VectorND Add(VectorND v2)
{
VectorND result = new VectorND(values.Length);
for (int i = 0; i < dim; i++)
{
result.values[i] = values[i] + v2.values[i];
}
return(result);
}
public void SetErrorVectorManually(VectorND newErrorVector)
{
errorVector = newErrorVector;
dim = newErrorVector.dim;
errorVectorIntern = new MatrixND(dim, 1);
for (int i = 0; i < dim; i++)
{
errorVectorIntern[i, 0] = (int)errorVector.values[i];
}
}
public VectorND Multiply(BigInteger scalar)
{
VectorND result = new VectorND(values.Length);
for (int i = 0; i < dim; i++)
{
result.values[i] = values[i] * scalar;
}
return(result);
}
public BigInteger Multiply(VectorND v2)
{
BigInteger result = 0;
for (int i = 0; i < dim; i++)
{
result += values[i] * v2.values[i];
}
return(result);
}
public VectorND GetMinimalReducedVector()
{
VectorND minimalVector = ReducedVectors[0];
foreach (VectorND reducedVector in ReducedVectors.Where(reducedVector => reducedVector.Length < minimalVector.Length))
{
minimalVector = reducedVector;
}
return(minimalVector);
}
public string Decrypt(VectorND vector)
{
BigInteger[] decryptVector = new BigInteger[vector.dim];
for (int i = 0; i < vector.dim; i++)
{
BigInteger bigInt = (vector.values[i] * rI) % mod;
decryptVector[i] = bigInt;
}
string messageBinary = "";
for (int i = 0; i < decryptVector.Length; i++)
{
string blockPart = "";
for (int j = privateKey.dim - 1; j >= 0; j--)
{
if (decryptVector[i] >= privateKey.values[j])
{
decryptVector[i] -= privateKey.values[j];
blockPart += "1";
}
else
{
blockPart += "0";
}
}
//Beim letzten Block kürzen
if (i == decryptVector.Length - 1)
{
int redudandBits = (messageBinary.Length + blockPart.Length) % maxBitLength;
if (redudandBits > 0)
{
blockPart = blockPart.Remove(0, redudandBits);
}
if (blockPart.Length >= maxBitLength && blockPart.Substring(0, maxBitLength).IndexOf('1') == -1)
{
blockPart = blockPart.Remove(0, maxBitLength);
}
}
blockPart = new string(blockPart.Reverse().ToArray());
messageBinary += blockPart;
}
List <byte> bytes = new List <byte>();
for (int i = 0; i < messageBinary.Length; i += maxBitLength)
{
bytes.Add(Convert.ToByte(messageBinary.Substring(i, maxBitLength), 2));
}
return(Encoding.UTF8.GetString(bytes.ToArray()));
}
private void ComputePublicKey()
{
publicKey = new VectorND(dim);
for (int i = 0; i < dim; i++)
{
BigInteger bigInt = (privateKey.values[i] * r) % mod;
publicKey.values[i] = bigInt;
}
Debug.WriteLine(publicKey);
}
public LatticeND(int n, int m, bool transpose)
{
Vectors = new VectorND[n];
ReducedVectors = new VectorND[n];
N = n;
M = m;
for (int i = 0; i < N; i++)
{
Vectors[i] = new VectorND(M);
}
UseRowVectors = transpose;
}
public void GaussianReduce()
{
ReductionMethod = ReductionMethods.reduceGauss;
VectorND v1 = Vectors[0];
VectorND v2 = Vectors[1];
ReductionSteps = new List <VectorND[]>();
UnimodTransVectors = new VectorND[2];
VectorND u1 = new VectorND(new BigInteger[] { 1, 0 });
VectorND u2 = new VectorND(new BigInteger[] { 0, 1 });
BigInteger rem;
do
{
if (v1.Length > v2.Length)
{
Util.Swap(ref v1, ref v2);
Util.Swap(ref u1, ref u2);
ReductionSteps.Add(new[] { v1, v2 });
}
BigInteger t = BigInteger.DivRem(v1 * v2, v1.LengthSquared, out rem);
//Bei der Division von BigIntegers muss noch auf korrektes Runden geprüft werden
if (BigInteger.Abs(rem) > v1.LengthSquared / 2)
{
t += rem.Sign;
}
v2 = v2 - v1 * t;
u2 = u2 - u1 * t;
ReductionSteps.Add(new[] { v1, v2 });
} while (v1.Length > v2.Length);
//Damit ein spitzer Winkel entsteht
if (Settings.Default.forceAcuteAngle)
{
BigInteger.DivRem(v1 * v2, v1.LengthSquared, out rem);
if (rem.Sign == -1)
{
v2 = v2 * -1;
u2 = u2 * -1;
ReductionSteps.Add(new[] { v1, v2 });
}
}
ReducedVectors[0] = v1;
ReducedVectors[1] = v2;
UnimodTransVectors = new[] { u1, u2 };
AngleReducedVectors = ReducedVectors[0].AngleBetween(ReducedVectors[1]);
CalculateDensity();
}
public void GenerateErrorVector()
{
Random random = new Random();
errorVector = new VectorND(dim);
errorVectorIntern = new MatrixND(dim, 1);
for (int i = 0; i < dim; i++)
{
int randomSigma = random.NextDouble() < 0.5 ? sigma : -sigma;
errorVector.values[i] = randomSigma;
errorVectorIntern[i, 0] = randomSigma;
}
}
public LatticeND(VectorND[] vectors, bool useRowVectors)
{
Vectors = vectors;
UseRowVectors = useRowVectors;
N = vectors.Length;
M = vectors[0].dim;
ReducedVectors = new VectorND[N];
if (N == M)
{
Determinant = CalculateDeterminant(Vectors);
}
if (Vectors.Length == 2)
{
AngleBasisVectors = Vectors[0].AngleBetween(Vectors[1]);
}
}
public void GenerateLattice()
{
lattice = new LatticeND(dim, dim, false);
//Umwandlung der Matrizeneinträge von double zu BigInt und damit Umwandlung der Matrizen zu einem Gitter
VectorND[] privateVectors = new VectorND[dim];
for (int i = 0; i < dim; i++)
{
BigInteger[] privateBigInts = new BigInteger[dim];
for (int j = 0; j < dim; j++)
{
privateBigInts[j] = new BigInteger(privateKeyR[j, i]);
}
privateVectors[i] = new VectorND(privateBigInts);
}
lattice.ReducedVectors = privateVectors;
VectorND[] publicVectors = new VectorND[dim];
for (int i = 0; i < dim; i++)
{
BigInteger[] publicBigInts = new BigInteger[dim];
for (int j = 0; j < dim; j++)
{
publicBigInts[j] = new BigInteger(publicKeyB[j, i]);
}
publicVectors[i] = new VectorND(publicBigInts);
}
lattice.Vectors = publicVectors;
if (transU == null)
{
return;
}
VectorND[] transVectors = new VectorND[dim];
for (int i = 0; i < dim; i++)
{
BigInteger[] transBigInts = new BigInteger[dim];
for (int j = 0; j < dim; j++)
{
transBigInts[j] = new BigInteger(transU[j, i]);
}
transVectors[i] = new VectorND(transBigInts);
}
lattice.UnimodTransVectors = transVectors;
}
public GGHModel(int dim, MatrixND privateKeyR, MatrixND publicKeyB, VectorND errorVector)
{
this.dim = dim;
this.privateKeyR = privateKeyR;
this.publicKeyB = publicKeyB;
privateKeyR1 = privateKeyR.Invert();
publicKeyB1 = publicKeyB.Invert();
GenerateLattice();
this.errorVector = errorVector;
errorVectorIntern = new MatrixND(dim, 1);
for (int i = 0; i < dim; i++)
{
errorVectorIntern[i, 0] = (double)errorVector.values[i];
}
}
public void GenerateRandomVectors(bool checkForGoodBasis, BigInteger codomainStart, BigInteger codomainEnd)
{
VectorND[] newVectorNds = new VectorND[N];
BigInteger det = 0;
int counter = 0;
while (true)
{
for (int i = 0; i < N; i++)
{
BigInteger[] vector = new BigInteger[M];
newVectorNds[i] = new VectorND(M);
for (int j = 0; j < M; j++)
{
vector[j] = Util.ComputeRandomBigInt(codomainStart, codomainEnd);
}
for (int k = 0; k < vector.Length; k++)
{
newVectorNds[i].values[k] = vector[k];
}
}
if (N == M)
{
det = CalculateDeterminant(newVectorNds);
}
if ((N != M || det != 0) && (!checkForGoodBasis || IsGoodBasis(newVectorNds)))
{
break;
}
counter++;
if (counter > 1024)
{
throw new Exception(Languages.errorFailedToGenerateLattice);
}
}
Vectors = (VectorND[])newVectorNds.Clone();
Determinant = det;
if (Vectors.Length == 2)
{
AngleBasisVectors = Vectors[0].AngleBetween(Vectors[1]);
}
}
public void Transpose()
{
VectorND[] tempVectors = (VectorND[])Vectors.Clone();
int tempN = N;
N = M;
M = tempN;
Vectors = new VectorND[N];
for (int i = 0; i < N; i++)
{
Vectors[i] = new VectorND(M);
for (int j = 0; j < M; j++)
{
Vectors[i].values[j] = tempVectors[j].values[i];
}
}
}
private void GenerateSuperincreasingSequence()
{
List <BigInteger> values = new List <BigInteger>(dim);
BigInteger tempGenMult = generatingMultiplicator;
bool sequenceFound = false;
while (!sequenceFound)
{
for (int i = 0; i < dim; i++)
{
BigInteger sum = Util.Sum(values);
if (sum == 0)
{
sum = 1;
}
values.Add(Util.ComputeRandomBigInt(sum + 1, sum * tempGenMult));
}
double density = dim / BigInteger.Log(values[dim - 1], 2);
if (density > 0.646 || !IsSuperincreasingSequence(values))
{
tempGenMult *= 2;
values = new List <BigInteger>(dim);
}
else
{
sequenceFound = true;
}
}
//Könnte hier weg und stattdessen in der dazugehörigen Test-Methode verwendet werden
//if (!IsSuperincreasingSequence(values))
// throw new Exception(Languages.errorGeneratingSuperincSequence);
privateKey = new VectorND(values.ToArray());
Debug.WriteLine(privateKey);
}
public string Cryptanalysis(VectorND cipher, Paragraph paragraph)
{
string messageBinary = "";
foreach (BigInteger value in cipher.values)
{
//BigInteger tempValue = value;
LatticeND lattice = TransformToLattice(value);
//Anmerkung: Der zweite Versuch nach LAGARIAS/ODLYZKO, S.232 funktioniert leider nicht,
//daher wurde dieser Teil auskommentiert
//for (int j = 0; j <= 1; j++)
//{
lattice.LLLReduce();
BigInteger[] vector = FindBinaryVector(lattice.ReducedVectors, value);
// if (vector != null)
// break;
// //Zweiter Versuch
// tempValue = Util.Sum(publicKey.ToList()) - tempValue;
// lattice = TransformToLattice(tempValue);
//}
if (vector == null)
{
throw new Exception();
}
if (paragraph != null)
{
paragraph.Inlines.Add("--------------------\r\n");
paragraph.Inlines.Add(new Bold(new Run(Languages.labelCurrentBlock)));
paragraph.Inlines.Add(" " + value + "\r\n");
paragraph.Inlines.Add(new Bold(new Run(Languages.labelLatticeBasis)));
paragraph.Inlines.Add(" " + lattice.LatticeToString() + "\r\n");
paragraph.Inlines.Add(new Bold(new Run(Languages.labelReducedLatticeBasis)));
paragraph.Inlines.Add(" " + lattice.LatticeReducedToString() + "\r\n");
paragraph.Inlines.Add(new Bold(new Run(Languages.labelFoundVector)));
paragraph.Inlines.Add(" " + new VectorND(vector) + "\r\n");
}
for (int k = 0; k < dim; k++)
{
messageBinary += vector[k];
}
}
int redudandBits = (messageBinary.Length) % maxBitLength;
if (redudandBits > 0)
{
messageBinary = messageBinary.Remove(messageBinary.Length - redudandBits);
}
if (messageBinary.Length >= maxBitLength && messageBinary.Substring(messageBinary.Length - maxBitLength).IndexOf('1') == -1)
{
messageBinary = messageBinary.Remove(messageBinary.Length - maxBitLength);
}
if (paragraph != null)
{
paragraph.Inlines.Add("--------------------\r\n");
paragraph.Inlines.Add(new Bold(new Run(Languages.labelPlainTextBinary)));
paragraph.Inlines.Add(" " + messageBinary + "\r\n");
}
List <byte> bytes = new List <byte>();
for (int i = 0; i < messageBinary.Length; i += maxBitLength)
{
bytes.Add(Convert.ToByte(messageBinary.Substring(i, maxBitLength), 2));
}
string messageUTF8 = Encoding.UTF8.GetString(bytes.ToArray());
if (paragraph != null)
{
paragraph.Inlines.Add(new Bold(new Run(Languages.labelPlainTextUTF8)));
paragraph.Inlines.Add(" " + messageUTF8 + "\r\n");
}
return(messageUTF8);
}
public double AngleBetween(VectorND v2)
{
return(Math.Acos(((double)Multiply(v2) / (Length * v2.Length))) * (180 / Math.PI));
}
public void LLLReduce()
{
ReductionMethod = ReductionMethods.reduceLLL;
BigInteger[,] basisArray = new BigInteger[N, M];
BigInteger[,] transArray = new BigInteger[N, N];
List <BigInteger[, ]> stepList = new List <BigInteger[, ]>();
for (int i = 0; i < N; i++)
{
for (int j = 0; j < M; j++)
{
basisArray[i, j] = Vectors[i].values[j];
}
}
using (var nativeObject = new NTL_Wrapper())
{
nativeObject.LLLReduce(basisArray, transArray, stepList, N, M, 0.99);
}
ReducedVectors = new VectorND[N];
for (int i = 0; i < N; i++)
{
ReducedVectors[i] = new VectorND(M);
for (int j = 0; j < M; j++)
{
ReducedVectors[i].values[j] = basisArray[i, j];
}
}
if (M == 2 && N == 2)
{
AngleReducedVectors = ReducedVectors[0].AngleBetween(ReducedVectors[1]);
CalculateDensity();
}
UnimodTransVectors = new VectorND[N];
for (int i = 0; i < N; i++)
{
UnimodTransVectors[i] = new VectorND(N);
for (int j = 0; j < N; j++)
{
UnimodTransVectors[i].values[j] = transArray[i, j];
}
}
ReductionSteps = new List <VectorND[]>();
foreach (var step in stepList)
{
VectorND[] stepVectors = new VectorND[N];
for (int i = 0; i < N; i++)
{
stepVectors[i] = new VectorND(M);
for (int j = 0; j < M; j++)
{
stepVectors[i].values[j] = step[i, j];
}
}
ReductionSteps.Add(stepVectors);
}
}