A BABYSTEP-GIANTSTEP METHOD FOR FASTER DETERMINISTIC INTEGER FACTORIZATION

In 1977, Strassen presented a deterministic and rigorous algorithm for solving the problem of computing the prime factorization of natural numbers N. His method is based on fast polynomial arithmetic techniques and runs in time (O ) over tilde (N-1/4), which has been state of the art for the last forty years. In this paper, we will combine Strassen's approach with a babystep-giantstep method to improve the currently best known bound by a superpolynomial factor. The runtime complexity of our algorithm is of the form (O) over tilde (N-1/4 exp(-C log N/log log N)).