A new efficient factorization algorithm for polynomials over small finite fields
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We present a new deterministic factorization algorithm for polynomials over a finite prime fieldF p . As in other factorization algorithms for polynomials over finite fields such as the Berlekamp algorithm, the key step is the “linearization” of the factorization problem, i.e., the reduction of the problem to a system of linear equations. The theoretical justification for our algorithm is based on a study of the differential equationy(p−1)+y p =0 of orderp−1 in the rational function fieldFp(x). In the casep=2 the new algorithm is more efficient than the Berlekamp algorithm since there is no set-up cost for the coefficient matrix of the system of linear equations.
KeywordsFactorization of polynomials over finite fields Differential equations over rational function fields
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