Is it possible to find the product of two numbers without knowing the two numbers? I'm doing a thought experiment:

Alice chooses a number $a$ and Bob $b$. They send $A(a)$ and $B(b)$ to Charlie. He performs $C(A(a), B(b))$ and gets $ab$.

Do there exist not easily reversible functions $A, B, C$ for which the above is true?

I'm a beginner so I'd be all the more grateful if somebody knows :)

Thank you!
In the way you setup the problem the answer is No.

As Charlie can perform $C(A(1),B(b))$.