martani / quadratic-sieve-cxx

A Quadratic Sieve implementation in C++

Quadratic Sieve C++

A simple Quadratic Sieve implementation in C++, this is an adaptation of the C version here https://github.com/martani/Quadratic-Sieve.

Status

The current version is fully working but have several performance issues compared to the C version. It does not play nice with small RSA integers (less than 50 bits) and natuarally with very large ones (more than 200 bits).

Compilling and testing the code

1. autoreconf -v
2. ./configure (if another compiler, clang for example use: CXX=clang ./configure)
3. cd tests/ && make
4. ./test-qs

Factoring RSA integers from C++ code

You can use the code as follows:

• Include the QS.h header file
• Initialize the Qudratic Sieve algorithm from the QS class

    //N represents the RSA integer you want to factor
    //NB_LINEAR_RELATIONS is a const (between 1..10 usually) indicating how much it is likely to find a factorization
    QS qs(N, NB_LINEAR_RELATIONS);

• Start factoring (this may take a while depending on the size of your RSA modulus)

    //Start factoring
    qs.Factor();

• Get the results back

    if(qs.GetFactor1 () == 1 || qs.GetFactor1 () == N)
    {
  		cout << ">>>> Failed to factor " << N << " <<<<\t"
  				<< "Try using more linear relations" << endl;
  	}
  	else
  	{
  		cout << endl << ">>>>>>> Factored " << N << endl;
  		cout << "\t Factor 1: " << qs.GetFactor1 () << endl;
  		cout << "\t Factor 2: " << qs.GetFactor2 () << endl;
  	}

Note If the algorithm fails to factor the RSA integer is returns the result (N, 1) as factors.

Check tests/test-qs.C for a complete example of how to use the QS class.