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Abstract: While factoring large polynomials over finite fields is (apparently) far easier than factoring large integers, it is still an open problem to give an algorithm that does it ``as fast as possible'' (roughly speaking, in time proportional to the length of the input data). We will explain a recent improvement in the complexity of factoring polynomials over finite fields, based on an asymptotically optimal solution of a related problem (the modular composition problem). Joint work with Chris Umans (Caltech).
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