void randomizePlaintext(Plaintext &ptxt, unsigned deg, unsigned p) {
ZZ_pX poly;
poly.rep.SetLength(deg);
for(unsigned i = 0; i < deg; i++) {
poly.rep[i] = RandomBnd(p);
}
poly.normalize();
ptxt.Init(poly);
}
static
void RandomBasisElt(ZZ_pX& g, const vec_long& D, const vec_ZZVec& M)
{
ZZ t1, t2;
long n = D.length();
long i, j, s;
g.rep.SetLength(n);
vec_ZZ_p& v = g.rep;
for (j = n-1; j >= 0; j--) {
if (D[j] == -1)
random(v[j]);
else {
i = D[j];
// v[j] = sum_{s=j+1}^{n-1} v[s]*M[i,s]
clear(t1);
for (s = j+1; s < n; s++) {
mul(t2, rep(v[s]), M[i][s]);
add(t1, t1, t2);
}
conv(v[j], t1);
}
}
g.normalize();
}
void InnerProduct(ZZ_pX& x, const vec_ZZ_p& v, long low, long high,
const vec_ZZ_pX& H, long n, ZZVec& t)
{
NTL_ZZRegister(s);
long i, j;
for (j = 0; j < n; j++)
clear(t[j]);
high = min(high, v.length()-1);
for (i = low; i <= high; i++) {
const vec_ZZ_p& h = H[i-low].rep;
long m = h.length();
const ZZ& w = rep(v[i]);
for (j = 0; j < m; j++) {
mul(s, w, rep(h[j]));
add(t[j], t[j], s);
}
}
x.rep.SetLength(n);
for (j = 0; j < n; j++)
conv(x.rep[j], t[j]);
x.normalize();
}
void RightShift(ZZ_pX& x, const ZZ_pX& a, long n)
{
if (IsZero(a)) {
clear(x);
return;
}
if (n < 0) {
if (n < -NTL_MAX_LONG) ResourceError("overflow in RightShift");
LeftShift(x, a, -n);
return;
}
long da = deg(a);
long i;
if (da < n) {
clear(x);
return;
}
if (&x != &a)
x.rep.SetLength(da-n+1);
for (i = 0; i <= da-n; i++)
x.rep[i] = a.rep[i+n];
if (&x == &a)
x.rep.SetLength(da-n+1);
x.normalize();
}
void diff(ZZ_pX& x, const ZZ_pX& a)
{
long n = deg(a);
long i;
if (n <= 0) {
clear(x);
return;
}
if (&x != &a)
x.rep.SetLength(n);
for (i = 0; i <= n-1; i++) {
mul(x.rep[i], a.rep[i+1], i+1);
}
if (&x == &a)
x.rep.SetLength(n);
x.normalize();
}
void ShiftSub(ZZ_pX& U, const ZZ_pX& V, long n)
// assumes input does not alias output
{
if (IsZero(V))
return;
long du = deg(U);
long dv = deg(V);
long d = max(du, n+dv);
U.rep.SetLength(d+1);
long i;
for (i = du+1; i <= d; i++)
clear(U.rep[i]);
for (i = 0; i <= dv; i++)
sub(U.rep[i+n], U.rep[i+n], V.rep[i]);
U.normalize();
}
static void ZZ_pX_conv_modulus(ZZ_pX &fout, const ZZ_pX &fin, const ZZ_pContext &modout)
{
// Changes the modulus of fin to modout, and puts the result in fout.
long i, n;
n = fin.rep.length();
fout.rep.SetLength(n);
ZZ_p* xp = fout.rep.elts();
const ZZ_p* ap = fin.rep.elts();
// I think it's enough to just restore modout once.
// This should be true as long as the function rep taking a ZZ_p as an argument
// and returning a ZZ works when the ZZ_p::modulus is incorrect.
modout.restore();
for (i = 0; i < n; i++)
{
conv(xp[i], rep(ap[i]));
}
// We may have set a leading coefficient to 0, so we have to normalize
fout.normalize();
}
void conv(ZZ_pX& x, const ZZX& a)
{
conv(x.rep, a.rep);
x.normalize();
}
NTL_START_IMPL
void CharPoly(ZZ_pX& f, const mat_ZZ_p& M)
{
long n = M.NumRows();
if (M.NumCols() != n)
Error("CharPoly: nonsquare matrix");
if (n == 0) {
set(f);
return;
}
ZZ_p t;
if (n == 1) {
SetX(f);
negate(t, M(1, 1));
SetCoeff(f, 0, t);
return;
}
mat_ZZ_p H;
H = M;
long i, j, m;
ZZ_p u, t1;
for (m = 2; m <= n-1; m++) {
i = m;
while (i <= n && IsZero(H(i, m-1)))
i++;
if (i <= n) {
t = H(i, m-1);
if (i > m) {
swap(H(i), H(m));
// swap columns i and m
for (j = 1; j <= n; j++)
swap(H(j, i), H(j, m));
}
for (i = m+1; i <= n; i++) {
div(u, H(i, m-1), t);
for (j = m; j <= n; j++) {
mul(t1, u, H(m, j));
sub(H(i, j), H(i, j), t1);
}
for (j = 1; j <= n; j++) {
mul(t1, u, H(j, i));
add(H(j, m), H(j, m), t1);
}
}
}
}
vec_ZZ_pX F;
F.SetLength(n+1);
ZZ_pX T;
T.SetMaxLength(n);
set(F[0]);
for (m = 1; m <= n; m++) {
LeftShift(F[m], F[m-1], 1);
mul(T, F[m-1], H(m, m));
sub(F[m], F[m], T);
set(t);
for (i = 1; i <= m-1; i++) {
mul(t, t, H(m-i+1, m-i));
mul(t1, t, H(m-i, m));
mul(T, F[m-i-1], t1);
sub(F[m], F[m], T);
}
}
f = F[n];
}
