// Find A^{-1}
public static Matrix Invert(Matrix A)
{
Matrix E = new Matrix(A.size[0], A.size[0]);
for (int i = 0; i < A.size[0]; ++i)
{
E.data[i][i] = 1;
}
return(MatrixFuncs.SolveEq(A, E));
}
public double AttackHam(out Matrix N1, out Matrix P1)
{
int k = Gp.size[0], n = Gp.size[1];
N1 = new Matrix(k, k); P1 = new Matrix(n, n);
Code code = new Code(Gp);
// compute r
int r = 0;
while ((1 << r) - 1 < n)
{
++r;
}
Stopwatch t = new Stopwatch(); t.Start();
// Matrix P
Ham ham = new Ham(r);
IEnumerable <int> tmp1, tmp2;
Matrix P1_inv = new Matrix(n, n);
for (int j = 0; j < n; ++j)
{
tmp1 = code.H.data.Select(x => x[j]);
for (int jj = 0; jj < n; ++jj)
{
tmp2 = ham.H.data.Select(x => x[jj]);
if (tmp1.SequenceEqual(tmp2))
{
P1.data[jj][j] = 1;
P1_inv.data[j][jj] = 1;
break;
}
}
}
// Matrix N
code.G = code.G * P1_inv;
N1 = MatrixFuncs.Transp(MatrixFuncs.SolveEq(MatrixFuncs.Transp(ham.G), MatrixFuncs.Transp(code.G)));
t.Stop();
return(t.ElapsedMilliseconds / 1000.00);
}
public double AttackHam(out List <Matrix> Nlist, out Matrix P1)
{
int k = Gp.size[0], nn = Gp.size[1];
Nlist = new List <Matrix>(); P1 = new Matrix(nn, nn);
int r = (int)Math.Log((nn + 2) / 2, 2);
int tmp = nn % ((1 << r) - 1), s;
while (tmp != 0)
{
--r;
tmp = nn % ((1 << r) - 1);
}
s = nn / ((1 << r) - 1); int n = nn / s;
Matrix Ni = new Matrix(k, k); P1 = new Matrix(nn, nn); Matrix P1_inv = new Matrix(nn, nn);
Code code = new Code(Gp);
Ham ham = new Ham(r);
Stopwatch t = new Stopwatch(); t.Start();
// Matrix P1
List <int>[] ham_idx = GetHamIndices(code, ham, r, s, n, k);
Matrix Zero = new Matrix(k, n - k);
BigInteger iter_count = 0, max_iter_num = 1, ind_count = 0;
List <int>[] idx_copy = new List <int> [n]; int[][] indices = new int[s][];
for (int i = 0; i < s; ++i)
{
indices[i] = new int[n];
max_iter_num = BigInteger.Multiply(max_iter_num, BigInteger.Pow(s - i, n));
}
do
{
++iter_count; ++ind_count;
if (iter_count > max_iter_num)
{
ham_idx = GetHamIndices(code, ham, r, s, n, k);
for (int i = 0; i < s; ++i)
{
indices[i] = new int[n];
}
iter_count = 1; ind_count = 1;
}
idx_copy = ham_idx.Select(x => new List <int>(x)).ToArray();
P1 = new Matrix(nn, nn); P1_inv = new Matrix(nn, nn);
for (int i = 0; i < s; i++)
{
for (int j = 0; j < n; ++j)
{
P1.data[i * n + j][idx_copy[j][indices[i][j]]] = 1;
P1_inv.data[idx_copy[j][indices[i][j]]][i * n + j] = 1;
idx_copy[j].RemoveAt(indices[i][j]);
}
}
Common.NextSet(indices[0], s, n);
if (ind_count == BigInteger.Pow(s, n))
{
indices[0] = new int[n];
Common.NextSet(indices[1], s - 1, n);
ind_count = 0;
}
} while (checkP(Gp, P1_inv, ham, Zero, s, n) == false);
// Matrices N
Matrix NG = Gp * P1_inv;
for (int i = 0; i < s; ++i)
{
Ni = MatrixFuncs.SolveEq(MatrixFuncs.Transp(ham.G), MatrixFuncs.Transp(MatrixFuncs.SubMatrix(NG, i * n, (i + 1) * n)));
var ttt = MatrixFuncs.Transp(Ni) * ham.G == MatrixFuncs.SubMatrix(NG, i * n, (i + 1) * n);
Nlist.Add(MatrixFuncs.Transp(Ni));
}
NG = new Matrix();
for (int i = 0; i < Nlist.Count; ++i)
{
NG |= Nlist[i] * ham.G;
}
t.Stop();
return(t.ElapsedMilliseconds / 1000.00);
}
public double AttackRM(out Matrix N1, out Matrix P1)
{
int k = Gp.size[0], n = Gp.size[1];
N1 = new Matrix(k, k); P1 = new Matrix(n, n);
Code code = new Code(Gp); Code Gp_reduced;
// Compute r, m
int r = -1, m = (int)Math.Log(n, 2), k1 = 0;
while (k1 < k)
{
++r;
k1 += Common.C(m, r);
}
RM rm = new RM(r, m);
Stopwatch t = new Stopwatch(); t.Start();
// Reduction
//2 * r >= m => reduction on dual code
if (2 * r < m || m - r == 1)
{
Gp_reduced = new Code(code.G);
}
else
{
Gp_reduced = new Code(code.H);
r = m - r - 1;
}
while (r > 1)
{
Gp_reduced = AttackFuncs.Reduction(Gp_reduced, r, m);
--r;
}
// Matrix P
Matrix Tmp; int idx = -1;
Vector e = new Vector(Enumerable.Repeat(1, n).ToList());
do
{
++idx;
Tmp = (new Matrix(Gp_reduced.G) - idx) & e;
}while (MatrixFuncs.Gauss(Tmp) < m + 1);
Tmp = Gp_reduced.G; Tmp -= idx; Matrix RM_1 = (new RM(1, m)).G -= 0;
IEnumerable <int> tmp1, tmp2;
Matrix P1_inv = new Matrix(n, n);
for (int j = 0; j < n; ++j)
{
tmp1 = Tmp.data.Select(x => x[j]);
for (int jj = 0; jj < n; ++jj)
{
tmp2 = RM_1.data.Select(x => x[jj]);
if (tmp1.SequenceEqual(tmp2))
{
P1.data[jj][j] = 1;
P1_inv.data[j][jj] = 1;
break;
}
}
}
// Matrix N
code.G = code.G * P1_inv;
N1 = MatrixFuncs.Transp(MatrixFuncs.SolveEq(MatrixFuncs.Transp(rm.G), MatrixFuncs.Transp(code.G)));
t.Stop();
return(t.ElapsedMilliseconds / 1000.00);
}
