void transpose(mat_ZZ& X, const mat_ZZ& A)
{
long n = A.NumRows();
long m = A.NumCols();
long i, j;
if (&X == & A) {
if (n == m)
for (i = 1; i <= n; i++)
for (j = i+1; j <= n; j++)
swap(X(i, j), X(j, i));
else {
mat_ZZ tmp;
tmp.SetDims(m, n);
for (i = 1; i <= n; i++)
for (j = 1; j <= m; j++)
tmp(j, i) = A(i, j);
X.kill();
X = tmp;
}
}
else {
X.SetDims(m, n);
for (i = 1; i <= n; i++)
for (j = 1; j <= m; j++)
X(j, i) = A(i, j);
}
}
void mul_aux(mat_ZZ& X, const mat_ZZ& A, const mat_ZZ& B)
{
long n = A.NumRows();
long l = A.NumCols();
long m = B.NumCols();
if (l != B.NumRows())
Error("matrix mul: dimension mismatch");
X.SetDims(n, m);
long i, j, k;
ZZ acc, tmp;
for (i = 1; i <= n; i++) {
for (j = 1; j <= m; j++) {
clear(acc);
for(k = 1; k <= l; k++) {
mul(tmp, A(i,k), B(k,j));
add(acc, acc, tmp);
}
X(i,j) = acc;
}
}
}
void gen_svpchallenge(mat_ZZ& B,int n,ZZ seed,int bit=10) {
vec_ZZ v;
generate_random_HNF(v,n,bit,seed);
B.SetDims(n,n); clear(B);
B(1,1) = v(1);
for (int i=2; i<=n; i++)
{
B(i,1)=v(i);
B(i,i)=1;
}
}
void mul(mat_ZZ& X, const mat_ZZ& A, long b)
{
long n = A.NumRows();
long m = A.NumCols();
X.SetDims(n, m);
long i, j;
for (i = 0; i < n; i++)
for (j = 0; j < m; j++)
mul(X[i][j], A[i][j], b);
}
void ident(mat_ZZ& X, long n)
{
X.SetDims(n, n);
long i, j;
for (i = 1; i <= n; i++)
for (j = 1; j <= n; j++)
if (i == j)
set(X(i, j));
else
clear(X(i, j));
}
void negate(mat_ZZ& X, const mat_ZZ& A)
{
long n = A.NumRows();
long m = A.NumCols();
X.SetDims(n, m);
long i, j;
for (i = 1; i <= n; i++)
for (j = 1; j <= m; j++)
negate(X(i,j), A(i,j));
}
void diag(mat_ZZ& X, long n, const ZZ& d_in)
{
ZZ d = d_in;
X.SetDims(n, n);
long i, j;
for (i = 1; i <= n; i++)
for (j = 1; j <= n; j++)
if (i == j)
X(i, j) = d;
else
clear(X(i, j));
}
void gen_randlat(mat_ZZ& basis, ZZ determinant, int dim) {
basis.SetDims(dim, dim);
ZZ s;
s= time(NULL);
SetSeed(s);
for(int i= 0; i < dim; i++) {
basis[i][0]= RandomBnd(determinant);
basis[i][i]= 1;
}
basis[0][0]= determinant;
}
void sub(mat_ZZ& X, const mat_ZZ& A, const mat_ZZ& B)
{
long n = A.NumRows();
long m = A.NumCols();
if (B.NumRows() != n || B.NumCols() != m)
Error("matrix sub: dimension mismatch");
X.SetDims(n, m);
long i, j;
for (i = 1; i <= n; i++)
for (j = 1; j <= m; j++)
sub(X(i,j), A(i,j), B(i,j));
}
void HNF(mat_ZZ& W, const mat_ZZ& A_in, const ZZ& D_in)
{
mat_ZZ A = A_in;
long n = A.NumRows();
long m = A.NumCols();
ZZ D = D_in;
if (D < 0)
negate(D, D);
if (n == 0 || m == 0 || D == 0)
Error("HNF: bad input");
W.SetDims(m, m);
clear(W);
long i, j, k;
ZZ d, u, v, c1, c2;
k = n;
for (i = m; i >= 1; i--) {
for (j = k-1; j >= 1; j--) {
if (A(j, i) != 0) {
XGCD(d, u, v, A(k, i), A(j, i));
div(c1, A(k, i), d);
div(c2, A(j, i), d);
negate(c2, c2);
EuclUpdate(A(j), A(k), c1, c2, v, u, D);
}
}
XGCD(d, u, v, A(k, i), D);
FixDiag(W(i), u, A(k), D, i);
if (W(i, i) == 0) W(i, i) = D;
for (j = i+1; j <= m; j++) {
div(c1, W(j, i), W(i, i));
ReduceW(W(j), c1, W(i), D, i);
}
div(D, D, d);
k--;
}
}
NTL_START_IMPL
void add(mat_ZZ& X, const mat_ZZ& A, const mat_ZZ& B)
{
long n = A.NumRows();
long m = A.NumCols();
if (B.NumRows() != n || B.NumCols() != m)
LogicError("matrix add: dimension mismatch");
X.SetDims(n, m);
long i, j;
for (i = 1; i <= n; i++)
for (j = 1; j <= m; j++)
add(X(i,j), A(i,j), B(i,j));
}
//Ideal lattice challenge problem generator
//modified from generate_ideal.cpp in Ideal lattice Challenge web page
void gen_idealsvpchallenge(mat_ZZ& B,int index,ZZ seed,vec_ZZ& phivec) {
ZZX phi=find_cyclotomic(index);
long n=deg(phi);
ZZ det=find_determinant(index,10*n,seed);
ZZ alpha=find_unity_root(index,det,phi);
B.SetDims(n,n);
clear(B);
B(1,1) = det;
for (long i=2; i<=n; i++)
{
B(i,1)=det-PowerMod(alpha,i-1,det);
B(i,i)=1;
}
phivec.SetLength(n+1);
for (int i=0;i<=n;i++) phivec[i] = coeff(phi,i);
}
void inv(ZZ& d_out, mat_ZZ& x_out, const mat_ZZ& A, long deterministic)
{
long n = A.NumRows();
if (A.NumCols() != n)
Error("solve: nonsquare matrix");
if (n == 0) {
set(d_out);
x_out.SetDims(0, 0);
return;
}
zz_pBak zbak;
zbak.save();
ZZ_pBak Zbak;
Zbak.save();
mat_ZZ x(INIT_SIZE, n, n);
ZZ d, d1;
ZZ d_prod, x_prod;
set(d_prod);
set(x_prod);
long d_instable = 1;
long x_instable = 1;
long gp_cnt = 0;
long check = 0;
mat_ZZ y;
long i;
long bound = 2+DetBound(A);
for (i = 0; ; i++) {
if ((check || IsZero(d)) && !d_instable) {
if (NumBits(d_prod) > bound) {
break;
}
else if (!deterministic &&
bound > 1000 && NumBits(d_prod) < 0.25*bound) {
ZZ P;
long plen = 90 + NumBits(max(bound, NumBits(d)));
GenPrime(P, plen, 90 + 2*NumBits(gp_cnt++));
ZZ_p::init(P);
mat_ZZ_p AA;
conv(AA, A);
ZZ_p dd;
determinant(dd, AA);
if (CRT(d, d_prod, rep(dd), P))
d_instable = 1;
else
break;
}
}
zz_p::FFTInit(i);
long p = zz_p::modulus();
mat_zz_p AA;
conv(AA, A);
if (!check) {
mat_zz_p xx;
zz_p dd;
inv(dd, xx, AA);
d_instable = CRT(d, d_prod, rep(dd), p);
if (!IsZero(dd)) {
mul(xx, xx, dd);
x_instable = CRT(x, x_prod, xx);
}
else
x_instable = 1;
if (!d_instable && !x_instable) {
mul(y, x, A);
if (IsDiag(y, n, d)) {
d1 = d;
check = 1;
}
}
}
else {
zz_p dd;
determinant(dd, AA);
d_instable = CRT(d, d_prod, rep(dd), p);
}
}
if (check && d1 != d) {
mul(x, x, d);
ExactDiv(x, d1);
}
d_out = d;
if (check) x_out = x;
zbak.restore();
Zbak.restore();
}
