It is arguably the dominant algorithm for solving the problem, having replaced the earlier Berlekamp's algorithm of 1967.

Over finite fields, Berlekamp's algorithm or Cantor-Zassenhaus algorithm is used.

E.g. Rabin proposes to find the square roots modulo primes by using a special case of Berlekamp's algorithm.

Berlekamp's algorithm finds polynomials suitable for use with the above result by computing a basis for the Berlekamp subalgebra.

One important application of Berlekamp's algorithm is in computing discrete logarithms over finite fields , where is prime and .

Berlekamp's algorithm may be accessed in the PARI/GP package using the factormod command.

In mathematics, particularly computational algebra, Berlekamp's algorithm is a well-known method for factoring polynomials over finite fields (also known as Galois fields).

If we represent the field in the usual way - that is, as polynomials over the base field , reduced modulo an irreducible polynomial of degree - then this is simply polynomial factorisation, as provided by Berlekamp's algorithm.

Berlekamp's algorithm takes as input a square-free polynomial (i.e. one with no repeated factors) of degree with coefficients in a finite field and gives as output a polynomial with coefficients in the same field such that divides .