Improved Techniques for Factoring Univariate Polynomials

The paper describes improved techniques for factoring univariate polynomials over the integers. The authors modify the usual linear method for lifting modular polynomial factorizations so that efficient early factor detection can be performed. The new lifting method is universally faster than the classical quadratic method, and is faster than a linear method due to Wang, provided we lift sufficiently high. Early factor detection is made more effective by also testing combinations of modular factors, rather than just single modular factors. Various heuristics are presented that reduce the cost of the factor testing or that increase the chance of successful testing. Both theoretical and empirical computing times are presented.