コード例 #1
0
ファイル: yashe.cpp プロジェクト: sportdeath/YASHE
/**
 * Precomputation on the evaluation key
 * allows for faster key switching
 */
void YASHE::dotEval(NTL::ZZ_pX& output, 
                    const std::vector<NTL::ZZ_pX>& a) {
  long n = cycloMod.n;
  long da = maxDegree;

  NTL::FFTRep fftOutput(NTL::INIT_SIZE, cycloMod.k);

  ToFFTRep(fftOutput, NTL::ZZ_pX(0), cycloMod.k);

  NTL::ZZ_pX P1(NTL::INIT_SIZE, n), P2(NTL::INIT_SIZE, n);
  NTL::FFTRep R1(NTL::INIT_SIZE, cycloMod.l), R2(NTL::INIT_SIZE, cycloMod.l);

  for (long i = 0; i < decompSize; i++) {
    ToFFTRep(R1, a[i], cycloMod.l);
    mul(R2, R1, evalKeyMult[i].B1);
    FromFFTRep(P1, R2, n-1, 2*n-3);
    reduce(R1, R1, cycloMod.k);
    mul(R1, R1, evalKeyMult[i].B2);
    ToFFTRep(R2, P1, cycloMod.k);
    mul(R2, R2, cycloMod.FRep);
    sub(R1, R1, R2);

    add(fftOutput, R1, fftOutput);
  }

  FromFFTRep(output, fftOutput, 0, n-1);
}
コード例 #2
0
ファイル: yashe.cpp プロジェクト: sportdeath/YASHE
void YASHE::roundMultiply(NTL::ZZ_pX& output,
                          const NTL::ZZ_pXMultiplier& a,
                          const NTL::ZZ_pXMultiplier& b) {
  // maximum is q^2 * (maxDegree + 1)
  NTL::ZZ_pPush push((cModulus * cModulus)/pModulus);

  long n = bigCycloMod.n;
  NTL::ZZ_pX product, P1(NTL::INIT_SIZE, n), P2(NTL::INIT_SIZE, n);
  NTL::FFTRep R1(NTL::INIT_SIZE, bigCycloMod.l), R2(NTL::INIT_SIZE, bigCycloMod.l);

  ToFFTRep(R1, a.val(), bigCycloMod.l);
  mul(R2, R1, b.B1);
  FromFFTRep(P1, R2, n-1, 2*n-3);

  mul(R1, a.B2, b.B2);
  ToFFTRep(R2, P1, bigCycloMod.k);
  mul(R2, R2, bigCycloMod.FRep);
  sub(R1, R1, R2);

  FromFFTRep(product, R1, 0, n-1);

  output.SetLength(maxDegree + 1);
  NTL::ZZ quotient, remainder;

  for (long i = 0; i <= maxDegree; i++) {
    DivRem(quotient, remainder, pModulus * rep(product[i]), cModulus);

    // Rounding using remainder
    if (remainder * 2 > cModulus) {
      quotient += 1;
    }

    output[i] = NTL::conv<NTL::ZZ_p>(quotient);
  }
}
コード例 #3
0
static
void ComputeTraceVec(vec_ZZ_p& S, const ZZ_pXModulus& F)
{
   if (!F.UseFFT) {
      PlainTraceVec(S, F.f);
      return;
   }

   long i;
   long n = F.n;

   FFTRep R;
   ZZ_pX P, g;

   g.rep.SetLength(n-1);
   for (i = 1; i < n; i++)
      mul(g.rep[n-i-1], F.f.rep[n-i], i); 
   g.normalize();

   ToFFTRep(R, g, F.l);
   mul(R, R, F.HRep);
   FromFFTRep(P, R, n-2, 2*n-4);

   S.SetLength(n);

   S[0] = n;
   for (i = 1; i < n; i++)
      negate(S[i], coeff(P, n-1-i));
}
コード例 #4
0
void FFTMulTrunc(ZZ_pX& x, const ZZ_pX& a, const ZZ_pX& b, long n)
{
   if (IsZero(a) || IsZero(b)) {
      clear(x);
      return;
   }

   long d = deg(a) + deg(b);
   if (n > d + 1)
      n = d + 1;

   long k = NextPowerOfTwo(d + 1);
   FFTRep R1(INIT_SIZE, k), R2(INIT_SIZE, k);

   ToFFTRep(R1, a, k);
   ToFFTRep(R2, b, k);
   mul(R1, R1, R2);
   FromFFTRep(x, R1, 0, n-1);
}
コード例 #5
0
void mul(ZZ_pXMatrix& A, ZZ_pXMatrix& B, ZZ_pXMatrix& C)
// A = B*C, B and C are destroyed
{
   long db = deg(B(1,1));
   long dc = deg(C(1,1));
   long da = db + dc;

   long k = NextPowerOfTwo(da+1);

   FFTRep B00, B01, B10, B11, C0, C1, T1, T2;
   
   ToFFTRep(B00, B(0,0), k); B(0,0).kill();
   ToFFTRep(B01, B(0,1), k); B(0,1).kill();
   ToFFTRep(B10, B(1,0), k); B(1,0).kill();
   ToFFTRep(B11, B(1,1), k); B(1,1).kill();

   ToFFTRep(C0, C(0,0), k);  C(0,0).kill();
   ToFFTRep(C1, C(1,0), k);  C(1,0).kill();

   mul(T1, B00, C0);
   mul(T2, B01, C1);
   add(T1, T1, T2);
   FromFFTRep(A(0,0), T1, 0, da);

   mul(T1, B10, C0);
   mul(T2, B11, C1);
   add(T1, T1, T2);
   FromFFTRep(A(1,0), T1, 0, da);

   ToFFTRep(C0, C(0,1), k);  C(0,1).kill();
   ToFFTRep(C1, C(1,1), k);  C(1,1).kill();

   mul(T1, B00, C0);
   mul(T2, B01, C1);
   add(T1, T1, T2);
   FromFFTRep(A(0,1), T1, 0, da);

   mul(T1, B10, C0);
   mul(T2, B11, C1);
   add(T1, T1, T2);
   FromFFTRep(A(1,1), T1, 0, da);
}
コード例 #6
0
void FFTSqrTrunc(ZZ_pX& x, const ZZ_pX& a, long n)
{
   if (IsZero(a)) {
      clear(x);
      return;
   }

   long d = 2*deg(a);
   if (n > d + 1)
      n = d + 1;

   long k = NextPowerOfTwo(d + 1);
   FFTRep R1(INIT_SIZE, k);

   ToFFTRep(R1, a, k);
   mul(R1, R1, R1);
   FromFFTRep(x, R1, 0, n-1);
}
コード例 #7
0
void BuildFromRoots(ZZ_pX& x, const vec_ZZ_p& a)
{
   long n = a.length();

   if (n == 0) {
      set(x);
      return;
   }

   long k0 = NextPowerOfTwo(NTL_ZZ_pX_FFT_CROSSOVER);
   long crossover = 1L << k0;

   if (n <= crossover) {
      x.rep.SetMaxLength(n+1);
      x.rep = a;
      IterBuild(&x.rep[0], n);
      x.rep.SetLength(n+1);
      SetCoeff(x, n);
      return;
   }

   long k = NextPowerOfTwo(n);

   long m = 1L << k;
   long i, j;
   long l, width;

   ZZ_pX b(INIT_SIZE, m+1);

   b.rep = a;
   b.rep.SetLength(m+1);
   for (i = n; i < m; i++)
      clear(b.rep[i]);

   set(b.rep[m]);
   
   FFTRep R1(INIT_SIZE, k), R2(INIT_SIZE, k);


   ZZ_p t1, one;
   set(one);

   vec_ZZ_p G(INIT_SIZE, crossover), H(INIT_SIZE, crossover);
   ZZ_p *g = G.elts();
   ZZ_p *h = H.elts();
   ZZ_p *tmp;
   
   for (i = 0; i < m; i+= crossover) {
      for (j = 0; j < crossover; j++)
         negate(g[j], b.rep[i+j]);

      if (k0 > 0) {
         for (j = 0; j < crossover; j+=2) {
            mul(t1, g[j], g[j+1]);
            add(g[j+1], g[j], g[j+1]);
            g[j] = t1;
         }
      }
   
      for (l = 1; l < k0; l++) {
         width = 1L << l;

         for (j = 0; j < crossover; j += 2*width)
            mul(&h[j], &g[j], &g[j+width], width);
      
         tmp = g; g = h; h = tmp;
      }

      for (j = 0; j < crossover; j++)
         b.rep[i+j] = g[j];
   }

   for (l = k0; l < k; l++) {
      width = 1L << l;
      for (i = 0; i < m; i += 2*width) {
         t1 = b.rep[i+width];
         set(b.rep[i+width]);
         ToFFTRep(R1, b, l+1, i, i+width);
         b.rep[i+width] = t1;
         t1 = b.rep[i+2*width];
         set(b.rep[i+2*width]);
         ToFFTRep(R2, b, l+1, i+width, i+2*width);
         b.rep[i+2*width] = t1;
         mul(R1, R1, R2);
         FromFFTRep(&b.rep[i], R1, 0, 2*width-1);
         sub(b.rep[i], b.rep[i], one);
      }
   }

   x.rep.SetLength(n+1);
   long delta = m-n;
   for (i = 0; i <= n; i++)
     x.rep[i] = b.rep[i+delta];

   // no need to normalize
}
コード例 #8
0
void mul(ZZ_pX& U, ZZ_pX& V, const ZZ_pXMatrix& M)
// (U, V)^T = M*(U, V)^T
{
   long d = deg(U) - deg(M(1,1));
   long k = NextPowerOfTwo(d - 1);

   // When the GCD algorithm is run on polynomials of degree n, n-1, 
   // where n is a power of two, then d-1 is likely to be a power of two.
   // It would be more natural to set k = NextPowerOfTwo(d+1), but this
   // would be much less efficient in this case.

   // We optimize this case, as it does sometimes arise naturally
   // in some situations.

   long n = (1L << k);
   long xx;
   ZZ_p a0, a1, b0, b1, c0, d0, u0, u1, v0, v1, nu0, nu1, nv0;
   NTL_ZZRegister(t1);
   NTL_ZZRegister(t2);

   if (n == d-1)
      xx = 1;
   else if (n == d)
      xx = 2;
   else 
      xx = 3;

   switch (xx) {
   case 1:
      GetCoeff(a0, M(0,0), 0);
      GetCoeff(a1, M(0,0), 1);
      GetCoeff(b0, M(0,1), 0);
      GetCoeff(b1, M(0,1), 1);
      GetCoeff(c0, M(1,0), 0);
      GetCoeff(d0, M(1,1), 0);

      GetCoeff(u0, U, 0);
      GetCoeff(u1, U, 1);
      GetCoeff(v0, V, 0);
      GetCoeff(v1, V, 1);

      mul(t1, rep(a0), rep(u0));
      mul(t2, rep(b0), rep(v0));
      add(t1, t1, t2); 
      conv(nu0, t1);

      mul(t1, rep(a1), rep(u0));
      mul(t2, rep(a0), rep(u1));
      add(t1, t1, t2);
      mul(t2, rep(b1), rep(v0));
      add(t1, t1, t2);
      mul(t2, rep(b0), rep(v1));
      add(t1, t1, t2);
      conv(nu1, t1);

      mul(t1, rep(c0), rep(u0));
      mul(t2, rep(d0), rep(v0));
      add (t1, t1, t2);
      conv(nv0, t1);
   
      break;

   case 2:
      GetCoeff(a0, M(0,0), 0);
      GetCoeff(b0, M(0,1), 0);

      GetCoeff(u0, U, 0);
      GetCoeff(v0, V, 0);

      mul(t1, rep(a0), rep(u0));
      mul(t2, rep(b0), rep(v0));
      add(t1, t1, t2); 
      conv(nu0, t1);

      break;

   case 3:
      break;

   }

   FFTRep RU(INIT_SIZE, k), RV(INIT_SIZE, k), R1(INIT_SIZE, k), 
          R2(INIT_SIZE, k);

   ToFFTRep(RU, U, k);  
   ToFFTRep(RV, V, k);  

   ToFFTRep(R1, M(0,0), k);
   mul(R1, R1, RU);
   ToFFTRep(R2, M(0,1), k);
   mul(R2, R2, RV);
   add(R1, R1, R2);
   FromFFTRep(U, R1, 0, d);

   ToFFTRep(R1, M(1,0), k);
   mul(R1, R1, RU);
   ToFFTRep(R2, M(1,1), k);
   mul(R2, R2, RV);
   add(R1, R1, R2);
   FromFFTRep(V, R1, 0, d-1);

   // now fix-up results

   switch (xx) {
   case 1:
      GetCoeff(u0, U, 0);
      sub(u0, u0, nu0);
      SetCoeff(U, d-1, u0);
      SetCoeff(U, 0, nu0);

      GetCoeff(u1, U, 1);
      sub(u1, u1, nu1);
      SetCoeff(U, d, u1);
      SetCoeff(U, 1, nu1);

      GetCoeff(v0, V, 0);
      sub(v0, v0, nv0);
      SetCoeff(V, d-1, v0);
      SetCoeff(V, 0, nv0);

      break;
      

   case 2:
      GetCoeff(u0, U, 0);
      sub(u0, u0, nu0);
      SetCoeff(U, d, u0);
      SetCoeff(U, 0, nu0);

      break;

   }
}
コード例 #9
0
ファイル: Poly3TimeTest.c プロジェクト: textbrowser/mcnoodle
int main()
{

#if (defined(NTL_CRT_ALTCODE) && !(defined(NTL_HAVE_LL_TYPE) && NTL_ZZ_NBITS == NTL_BITS_PER_LONG))

   {
      printf("999999999999999 ");
      print_flag();
      return 0;
   }


#endif

   SetSeed(ZZ(0));

   long n, k;

   n = 1024;
   k = 30*NTL_SP_NBITS; 

   ZZ p;

   RandomLen(p, k);
   if (!IsOdd(p)) p++;


   ZZ_p::init(p);         // initialization

   ZZ_pX f, g, h, r1, r2, r3;

   random(g, n);    // g = random polynomial of degree < n
   random(h, n);    // h =             "   "
   random(f, n);    // f =             "   "

   SetCoeff(f, n);  // Sets coefficient of X^n to 1

   // For doing arithmetic mod f quickly, one must pre-compute
   // some information.

   ZZ_pXModulus F;
   build(F, f);

   PlainMul(r1, g, h);  // this uses classical arithmetic
   PlainRem(r1, r1, f);

   MulMod(r2, g, h, F);  // this uses the FFT

   MulMod(r3, g, h, f);  // uses FFT, but slower

   // compare the results...

   if (r1 != r2) {
      printf("999999999999999 ");
      print_flag();
      return 0;
   }
   else if (r1 != r3) {
      printf("999999999999999 ");
      print_flag();
      return 0;
   }

   double t;
   long i;
   long iter;

   ZZ_pX a, b, c;
   random(a, n);
   random(b, n);
   long da = deg(a);
   long db = deg(b);
   long dc = da + db;
   long l = NextPowerOfTwo(dc+1);

   FFTRep arep, brep, crep;
   ToFFTRep(arep, a, l, 0, da);
   ToFFTRep(brep, b, l, 0, db);

   mul(crep, arep, brep);

   ZZ_pXModRep modrep;
   FromFFTRep(modrep, crep);

   FromZZ_pXModRep(c, modrep, 0, dc);

   iter = 1;

   do {
     t = GetTime();
     for (i = 0; i < iter; i++) {
        FromZZ_pXModRep(c, modrep, 0, dc);
     }
     t = GetTime() - t;
     iter = 2*iter;
   } while(t < 1);

   iter = iter/2;

   iter = long((3/t)*iter) + 1;

   double tvec[5];
   long w;

   for (w = 0; w < 5; w++) {
     t = GetTime();
     for (i = 0; i < iter; i++) {
        FromZZ_pXModRep(c, modrep, 0, dc);
     }
     t = GetTime() - t;
     tvec[w] = t;
   } 


   t = clean_data(tvec);

   t = floor((t/iter)*1e12);

   // The following is just to test some tuning Wizard logic --
   // be sure to get rid of this!!
#if (defined(NTL_CRT_ALTCODE))
   // t *= 1.12;
#endif

   if (t < 0 || t >= 1e15)
      printf("999999999999999 ");
   else
      printf("%015.0f ", t);

   printf(" [%ld] ", iter);

   print_flag();

   return 0;
}