 Computing discrete logarithms is an important problem in public key cryptography and error-control coding.For a finite field, the fastest known method is the index calculus method, which involves the factorisation of field elements.If we represent the field formula_40 in the usual way - that is, as polynomials over the base field formula_44, reduced modulo an irreducible polynomial of degree formula_2 - then this is simply polynomial factorisation, as provided by Berlekamp's algorithm.