Inverting a ZZ_p matrix in NTL - linear-algebra

Question

I am trying to generate a random binary matrix and its inverse mod q where q is a power of 2. Sometimes when the determinant of my matrix is invertible modulo q (so the matrix over Z_q is invertible), I am getting the error "InvMod:inverse undefined Aborted (core dumped)" and other times the inverse is computed. What am I doing incorrectly?
#include <iostream>
//NTL files
#include <NTL/ZZ_p.h>
#include <NTL/vec_vec_ZZ_p.h>
#include <NTL/LLL.h>
#include <NTL/matrix.h>
#include <NTL/vector.h>
#include <NTL/tools.h>
#include <NTL/ZZ.h>
#include <NTL/vec_vec_ZZ.h>
using namespace std;
using namespace NTL;
int main(){//task generate a random matrix S with 0/1 entries stored as a ZZ_p matrix, then generate a random, invertible S
int nn = 8;
ZZ n = ZZ(nn);
ZZ N = ZZ(0);
ZZ q; power2(q, 4);
ZZ_p::init(q);
mat_ZZ S; S.SetDims(nn,nn);
for(int i = 0; i<nn; i++){
for(int j = 0; j<nn; j++){
S[i][j] = RandomBits_ZZ(1);
}
}
mat_ZZ_p S1; S1.SetDims(nn,nn);//copy to ZZ_P
mat_ZZ_p R; R.SetDims(nn,nn);//will set to inverse if
cout<<"The random matrix is S = "<<endl; //print S
for(int i = 0; i<nn; i++){
for(int j=0; j<n;j++){
cout<<S[i][j]<<", ";
} cout<<endl;
}
ZZ d; determinant(d,S); ZZ_p d1; conv(d1, d % q);
if(GCD(q,d) == 1){//convert to mod q datatype
for(int i = 0; i<nn; i++){
for(int j = 0; j<nn; j++){
conv(S1[i][j], S[i][j]);
}
}
//let's invert the matrix and print it!
cout<<"The random matrix is R = "<<endl; //print R
R = inv(S1); //mul(R,R,S1);
for(int i = 0; i<nn; i++){
for(int j=0; j<n;j++){
cout<<R[i][j]<<", ";
} cout<<endl;
}
}
cout<<endl<<"det of S is "<<d<<" and this mod q is "<<d1<<endl;
cout<<"Our modulus is "<< q <<endl;
return 0;
}

Answer 1

If the determinant is invertable mod q this only means that there exists an inverse matrix. But the algorithm that computes this matrix can still come to a point where it would need to calculate the inverse of an element that don't has one.
You don't have this problem if q is prime.
By the way, here is a simplified version of your code.
#include <iostream>
//NTL files
#include <NTL/mat_ZZ_p.h>
using namespace std;
using namespace NTL;
int main()
{//task generate a random matrix S with 0/1 entries stored as a ZZ_p matrix, then generate a random, invertible S
int nn = 8;
ZZ q;
power2(q, 4);
ZZ_p::init(q);
mat_ZZ_p S;
S.SetDims(nn, nn);
for(int i = 0; i < nn; i++)
{
for(int j = 0; j < nn; j++)
{
S[i][j] = conv<ZZ_p>(RandomBits_ZZ(1));
}
}
mat_ZZ_p R;
R.SetDims(nn, nn);//will set to inverse if
cout << "The random matrix is S = " << endl << S;
ZZ_p d;
determinant(d, S);
cout << endl << "det(S) = " << d << endl;
cout << "q = " << q << endl;
if(GCD(conv<ZZ>(d), q) == 1)
{
// let's invert the matrix and print it!
R = inv(S);
cout << "The random matrix is R = " << R << endl;
}
return 0;
}