computing frobenius maps and factoring polynomials
A new probabilistic algorithm for factoring univariate polynomials over finite fields is presented whose asymptotic running time improves upon previous results. To factor a polynomial of degree n over F q , the algorithm uses O (( n 2 + n log q )(log n ) 2 log log n ) arithmetic operations in F q . The main technical innovation is a new way to compute Frobenius and trace maps in the ring of polynomials modulo the polynomial to be factored.
computation maps factor polynomial probabilistic algorithm algorithm finite field timing log operability innovating traces