These are some of the things that can be done to improve the code, when times permit I will work on some of them.

Possible improvements:

• Sieving experiments in the polynomial selection step.
• Try lattice sieving in the sieving step.
• Implement the Block Lanczos algorithm to replace the rather primitive Gaussian Elimination.
• Implement Montgomery's algorithm for computing the algebraic square root.
• Find better format for storing temporary files and base files both for saving storage space and for doing faster reading/writing of data.