One important application of Berlekamp's algorithm is in computing [[discrete logarithm]]s over finite fields of<math>\mathbb{F}_{p^n}</math>, where <math>p</math> is prime-powerorderand <math>n\geq 2</math>. Computing discrete logarithms is an important problem in [[public key cryptography]]. For a finite field of prime-power order, the fastest known method is the [[index calculus|index calculus method]], which involves the factorisation of field elements. If we represent the prime-powerfield order field<math>\mathbb{F}_{p^n}</math> in the usual way - that is, as polynomials over the prime order base field <math>\mathbb{F}_{p}</math>, reduced modulo an irreducible polynomial of appropriate degree <math>n</math> - then this is simply polynomial factorisation, as provided by Berlekamp's algorithm.
