Computing Frobenius maps and factoring polynomials

A new probabilistic algorithm for factoring univariate polynomials over finite fields is presented. To factor a polynomial of degreen overFq, the number of arithmetic operations inFq isO((n2+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.

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