In the same way that the usual logarithm is defined as the inverse of exponentiation in the real multiplicative group, discrete logarithms invert exponentiation in finite cyclic groups.

Computationally, discrete logarithms are interesting for similar reasons that prime factorization is: both problems are computationally difficult and both are utilized for cryptographic purposes. What´s more, methods for solving discrete logs are often adapted to prime factorization and vice versa.

We will talk about algorithms for computing discrete logs including a specialized algorithm for (the multiplicative group of) finite fields.