Extending Seysen's Algorithm

The description Seysen gave in [38] of his algorithm was only an outline of a lattice basis reduction technique. We have tried in this chapter to give both theoretical and empirical reasons for the choices made in implementing Seysen's algorithm. However, we have only touched upon a few of the many possible combinations of techniques. As the next chapter shows, these choices are effective as reducing lattice bases derived from subset sum problems. For other lattices, their effectiveness may be in question. We briefly mention here some of the other possible choices for the various components of Seysen's algorithm.