, Volume 2, Issue 3, pp 187-224

Computing Frobenius maps and factoring polynomials

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A new probabilistic algorithm for factoring univariate polynomials over finite fields is presented. To factor a polynomial of degreen overF q , the number of arithmetic operations inF q isO((n 2+nlogq). (logn)2 loglogn). 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.