Number Field Sieve Method In Polynomial Choice

As we know, the key of polynomial selection in NFS are size and root properties. In this thesis we deeply discuss and study these two factors. On the basis of knowing those knowledge, we apply L function to get the asymptotical consuming time in NFS. Then from the expression of the time, we obtain the relation between the optimal degree and the large number. With that, the paper give some methons to produce good functions and isolate the best function from a collection of many good polynomial. Considering these methons in practice, the thesis bring forward a general parameter. And from practice ,we solve the key problems in polynomial selection for NFS. Finally, it points out some questions those are left over and need further consideration.