Cantor–Zassenhaus algorithm (Equal-degree Factorization of Polynomials Over Finite Fields)

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Time Complexity

$O(n^{3} \log n)$

Space Complexity

$O(n)$ words

(Keeps track of a set of factors, where sum of degrees of factors is O(n) so the total number of terms to keep track of is O(n). Also, computing h^{((q^d-1)/2)}-1 mod f only requires O(n) space)

Description

Approximate?

Exact

Randomized?

Yes, Monte Carlo

Model of Computation

Word RAM

Year

1981

Reference

https://www.ams.org/journals/mcom/1981-36-154/S0025-5718-1981-0606517-5/home.html