# What can attackers do to increase the rate of attempts in a brute-force attack as the number of attempts increases?

I am aware of this post (about Moore's Law and brute-force attack). Suppose $\inline y$ is the number of brute-force attempts, we have $\inline \frac{dy}{dt} = k \cdot 2^{\frac{t}{2}}$.

What I want to ask is the following: suppose an attacker started a brute-force attack. Can he/she increase the rate of attempts by making more attempts? In other words, is there any factor that contributes to a $\inline y$-term on $\inline RHS$?

The only thing that I can think of is to perform a reverse brute-force attack. The attacker continuously performs login trials on different systems (e.g. web server). It is expected that a small portion of them uses weak passwords, so when the number of brute-force attempts increases, the attacker gains more computational power by creating a botnet (the actual gain is related to the distribution of the level of security of web servers), helping him/her to brute-force.

Any other ideas? Thanks in advance.

• It would be naturally aymptotic because even if you subvert the machines with weak credentials, adding them to your effort isn't going to substantively speed up work on the hard credentials. Eventually in the best case scenario you have suborned every machine with weak credentials as soon as they are added to the universe, but you are still left with "Lifetime of the universe" creds to crack. – J Kimball Nov 20 '18 at 14:45