What is Discrete logarithm?

In mathematics, for given real numbers a and b, the logarithm logb a is a number x such that b = a. Analogously, in any group G, powers b can be defined for all integers k, and the discrete logarithm logb a is an integer k such that b = a. In number theory, the more commonly used term is index: we can write x = indr a for r ≡ a if r is a primitive root of m and gcd = 1.

Discrete logarithms are quickly computable in a few special cases. However, no efficient method is known for computing them in general. Several important algorithms in public-key cryptography, such as ElGamal base their security on the assumption that the discrete logarithm problem over carefully chosen groups has no efficient solution.