for my undergraduate thesis I'm (pseudo) replicating algebraic attack on certain cryptosystem using gröbner basis approach. The heart of original attack was F5/2 algorithm (since the cryptosystem is defined over $GF(2)$), which I appear to have no access to - I am aware of no public implementation of this algorithm. As the original computation was pretty tough - 2 days on regular PC time, it is important to get as effective algorithm as possible for computing such a gröbner basis.
I'd be very pleased if any could provide advice in choosing fast implementation of algorithm for computing gröbner basis.
Thank you.
You can try Magma, which has special code for dense systems: http://magma.maths.usyd.edu.au/users/allan/densef4/