Suppose I have an arbitrary 256 bit number $m$ another secret number $k$ of the same bit length, and then I multiply them both modulo a 256 bit prime number $p$ to get $c$ as follows:
$$
c = (m\cdot k) \mod p
$$
Is there any way to get $m$ back without knowing $k$?
Is this problem as hard as the discrete log problem?
How can this task be made more computationally difficult?



Is there any way to solve this equation without knowing the inverse modulo?
$c$ represents a congruence class, and there are $p$ of them. However both $m$ and $k$ belong to the same [complete residue system](https://en.wikipedia.org/wiki/Modular_multiplicative_inverse), and so for any given $c$ there are $2^{256}$ pairs of $m,k$ that satisfy the equation. So, the answer is no.


