What Is Discrete Logarithm Problem (DLP)

This section describes what is Discrete Logarithm Problem (DLP), which is the reverse operation of an exponentiation (or scalar multiplication) operation in an Abelian group.

What Is Discrete Logarithm Problem (DLP)? DLP in an Abelian Group can be described as the following:

For a given element, P, in an Abelian Group, the resulting point of an exponentiation operation, Q = Pn, in multiplicative notation is provided. The problem of finding the smallest exponent, n, such that Pn = Q, is called Discrete Logarithm Problem (DLP).

In other words, the reverse operation of an exponentiation is called DLP, which can be expressed as the following using the "Logarithm" function, log(). This is where the "Discrete Logarithm Problem (DLP)" name comes from:

```Given P and (Q = Pn), find the smallest n:
n = logP(Q)
```

In additive notation, Discrete Logarithm Problem (DLP) can be expressed as the following using the "division" operation:

```Given P and (Q = nP), find the smallest n:
n = Q/P
```

Last update: 2019.