Is this formula/problem hard to crack? I have a simple calculation. Its inputs should be very hard to discover, but I want to be certain, hence the question.
Start with value $A$, a known 1024-bit number.
Input $I_1$ and $I_2$ are 512-bit numbers, and their hashes are known as $h_1 =Hash(I_1),  h_2=Hash(I_2)$.
Output $O$ is the result of $O=(A\cdot I_1)+I_2$.
Given $A,O,h_1$, and $h_2$, is it feasible to brute force $I_1$ and $I_2$?
$$O=(A\cdot I_1)+I_2$$
Take $\mod A$ of the equation.
$$O \bmod A=\left( ( A\cdot I_1)+I_2 \right) \bmod A = I_2 \bmod A$$
So we get the $I_2$. the rest is substructing the $I_2$
$$O - I_2 = A\cdot I_1$$ and the final is simply dividing by A.
$$I_1 = \frac{O - I_2}{A} $$
The given $h_1$ and $h_2$ are not used! One may argue to use the hashes to identify the multiple solutions, however, the Euclidean division says they are unique since $A$ is a 1024-bit number and $I_i$'s are 512-bit numbers.