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 … See more

Powers obey the usual algebraic identity b = b  b . In other words, the function
$${\displaystyle f\colon \mathbf {Z} \to G}$$ See more

The discrete logarithm problem is considered to be computationally intractable. That is, no efficient classical algorithm is known … See more

There exist groups for which computing discrete logarithms is apparently difficult. In some cases (e.g. large prime order subgroups of … See more

Let G be any group. Denote its group operation by multiplication and its identity element by 1. Let b be any element of G. For any positive … See more

Powers of 10
The powers of 10 are
$${\displaystyle \ldots ,0.001,0.01,0.1,1,10,100,1000,\ldots .}$$
For any number a in this list, one can compute log10 a. For example, log10 10000 = 4, and … See more

While computing discrete logarithms and integer factorization are distinct problems, they share some properties:
• both … See more