Show The function $mult(a,b)$ is weak one way if the Integer Factorization Assumption is true.
I am read the proof of this enunciated but I want know if I understand this in my way. The proof use the lemma:
For $k$ big, the probability for one number with $k$ bits, choosen in random form, is prime is greater than $1/k$.
If I choose two numbers the probability that they are prime is $1/k^2$. Using this fact, I will be able to say given the fact that for the probability $ 1 / k ^ 2 $ a mult function is difficult to invert, then to $1/k^2$ cases the mult function will fail, then as $1 / k ^ 2$ is not negligence. The proof is completed.