C++ vec_GF2E::SetLength方法代码示例

///////////////////////////////////////////////////////////////////////////
// PURPOSE:
// Computes the syndrome of a sparse vector
// of the binary BCH code of design distance d.
// The vector is viewed as a vector of 0's and 1's
// being indexed by all nonzero elements of GF2E; because
// it is sparse, it is given as the set a of 
// elements of GF2E where the coordinates of the vector are equal to 1.
// If used to compute the secure sketch, the sketch will
// tolerate symmetric difference of up to (d-1)/2
//
//
// ALGORITHM:
// The syndrome is computed as a vector of
// f(j) = (a_0)^j + (a_2)^j + ... + (a_s)^j
// for odd i from 1 do d-1, where a_i is the i-th component
// of the input vector A.
// (only the odd j are needed, because
// f(2j) is simply the square of f(j)).
// Because in C++ we number from 0, f(j) will reside
// in location (j-1)/2.
//
//
// ASSUMPTIONS:
// Let m=GF2E::degree() (i.e., the field is GF(2^m)).
// Assumes d is odd,
// greater than 1, and less than 2^m (else BCH codes don't make sense).
// Assumes the input set has no zeros (they will be ignored)
//
// 
// RUNNING TIME:
// Takes time O(len*d) operations in GF(2^m),
// where len is the length of the input vector
//
void BCHSyndromeCompute(vec_GF2E & ss, const vec_GF2E & a, long d)
{
	GF2E a_i_to_the_j, multiplier;
	long i, j;

	ss.SetLength((d-1)/2); // half the syndrome length, 
	                       // because even power not needed

	// We will compute the fs in parallel: first add
	// all the powers of a_1, then of a_2, ..., then of a_s
	for (i = 0; i < a.length(); ++i)
	{

		a_i_to_the_j = a[i];
                sqr(multiplier, a[i]); // multiplier = a[i]*a[i];

		// special-case 0, because it doesn't need to be multiplied
		// by the multiplier
		ss[0] += a_i_to_the_j; 

		for (long j = 3; j < d; j+=2)
		{
			a_i_to_the_j *= multiplier;
			ss[(j-1)/2] += a_i_to_the_j;

		}
	}
}

static
void RecFindRoots(vec_GF2E& x, const GF2EX& f)
{
   if (deg(f) == 0) return;

   if (deg(f) == 1) {
      long k = x.length();
      x.SetLength(k+1);
      x[k] = ConstTerm(f);
      return;
   }
      
   GF2EX h;

   GF2E r;

   
   {
      GF2EXModulus F;
      build(F, f);

      do {
         random(r);
         clear(h);
         SetCoeff(h, 1, r);
         TraceMap(h, h, F);
         GCD(h, h, f);
      } while (deg(h) <= 0 || deg(h) == deg(f));
   }

   RecFindRoots(x, h);
   div(h, f, h); 
   RecFindRoots(x, h);
}

void mul(vec_GF2E& x, const vec_GF2E& a, const GF2E& b_in)
{
   GF2E b = b_in;
   long n = a.length();
   x.SetLength(n);
   long i;
   for (i = 0; i < n; i++)
      mul(x[i], a[i], b);
}

void add(vec_GF2E& x, const vec_GF2E& a, const vec_GF2E& b)
{
   long n = a.length();
   if (b.length() != n) LogicError("vector add: dimension mismatch");

   x.SetLength(n);
   long i;
   for (i = 0; i < n; i++)
      add(x[i], a[i], b[i]);
}

void FindRoots(vec_GF2E& x, const GF2EX& ff)
{
   GF2EX f = ff;

   if (!IsOne(LeadCoeff(f)))
      Error("FindRoots: bad args");

   x.SetMaxLength(deg(f));
   x.SetLength(0);
   RecFindRoots(x, f);
}

///////////////////////////////////////////////////////////////////////////
// Produces a vector res such that res[2i]=ss[i]
// and res[2i+1]=ss[i]*ss[i]
//
// Used to recover the redundant representation
// of the BCH syndrome (which includes even values of j)
// from the representation produced by BCHSyndromeCompute
// Because C++ indexes from 0, the j-th coordinate of the syndrome
// will end up in location j-1.
//
// Takes time O(d) operations in GF2E, where d is the output length
//
static
void InterpolateEvens(vec_GF2E & res, const vec_GF2E & ss)
{
	// uses relation syn(j) = syn(j/2)^2 to recover syn from ss
	long i;

	res.SetLength(2*ss.length());
	// odd coordinates (which, confusingly, means even i)
	// are just copied from the input
	for (i = 0; i < ss.length(); ++i)
		res[2*i] = ss[i];
	// even coordinates (odd i) are computed via squaring.
	for (i = 1; i < res.length(); i+=2)
		sqr(res[i], res[(i-1)/2]); // square
}

void VectorCopy(vec_GF2E& x, const vec_GF2E& a, long n)
{
   if (n < 0) LogicError("VectorCopy: negative length");
   if (NTL_OVERFLOW(n, 1, 0)) ResourceError("overflow in VectorCopy");

   long m = min(n, a.length());

   x.SetLength(n);

   long i;

   for (i = 0; i < m; i++)
      x[i] = a[i];

   for (i = m; i < n; i++)
      clear(x[i]);
}

static
void mul_aux(vec_GF2E& x, const mat_GF2E& A, const vec_GF2E& b)  
{  
   long n = A.NumRows();  
   long l = A.NumCols();  
  
   if (l != b.length())  
      LogicError("matrix mul: dimension mismatch");  
  
   x.SetLength(n);  
  
   long i, k;  
   GF2X acc, tmp;  
  
   for (i = 1; i <= n; i++) {  
      clear(acc);  
      for (k = 1; k <= l; k++) {  
         mul(tmp, rep(A(i,k)), rep(b(k)));  
         add(acc, acc, tmp);  
      }  
      conv(x(i), acc);  
   }  
}  

static
void solve_impl(GF2E& d, vec_GF2E& X, const mat_GF2E& A, const vec_GF2E& b, bool trans)

{
   long n = A.NumRows();
   if (A.NumCols() != n)
      LogicError("solve: nonsquare matrix");

   if (b.length() != n)
      LogicError("solve: dimension mismatch");

   if (n == 0) {
      set(d);
      X.SetLength(0);
      return;
   }

   long i, j, k, pos;
   GF2X t1, t2;
   GF2X *x, *y;

   const GF2XModulus& p = GF2E::modulus();

   vec_GF2XVec M;

   M.SetLength(n);

   for (i = 0; i < n; i++) {
      M[i].SetSize(n+1, 2*GF2E::WordLength());

      if (trans) 
         for (j = 0; j < n; j++) M[i][j] = rep(A[j][i]);
      else
         for (j = 0; j < n; j++) M[i][j] = rep(A[i][j]);

      M[i][n] = rep(b[i]);
   }

   GF2X det;
   set(det);

   for (k = 0; k < n; k++) {
      pos = -1;
      for (i = k; i < n; i++) {
         rem(t1, M[i][k], p);
         M[i][k] = t1;
         if (pos == -1 && !IsZero(t1)) {
            pos = i;
         }
      }

      if (pos != -1) {
         if (k != pos) {
            swap(M[pos], M[k]);
         }

         MulMod(det, det, M[k][k], p);

         // make M[k, k] == -1 mod p, and make row k reduced

         InvMod(t1, M[k][k], p);
         for (j = k+1; j <= n; j++) {
            rem(t2, M[k][j], p);
            MulMod(M[k][j], t2, t1, p);
         }

         for (i = k+1; i < n; i++) {
            // M[i] = M[i] + M[k]*M[i,k]

            t1 = M[i][k];   // this is already reduced

            x = M[i].elts() + (k+1);
            y = M[k].elts() + (k+1);

            for (j = k+1; j <= n; j++, x++, y++) {
               // *x = *x + (*y)*t1

               mul(t2, *y, t1);
               add(*x, *x, t2);
            }
         }
      }
      else {
         clear(d);
         return;
      }
   }

   X.SetLength(n);
   for (i = n-1; i >= 0; i--) {
      clear(t1);
      for (j = i+1; j < n; j++) {
         mul(t2, rep(X[j]), M[i][j]);
         add(t1, t1, t2);
      }
      add(t1, t1, M[i][n]);
      conv(X[i], t1);
   }

   conv(d, det);
//.........这里部分代码省略.........