Suppose I have a function that accepts vector input $x$ and outputs vector $y=f(x)$. I want to protect the output $y$ through shuffling numbers in it. I hope the shuffling can confuse the attacker by hiding the position information. The ability of hiding position is indeed true when shuffling random numbers. However, the outputs $y$ is not uniform. A possible attack, for example, when $x_1$ and $x_2$ only differ a little, the $y_1$ and $y_2$ also differ a little. When receiving two outputs $shuffle(y_1)$ and $shuffle(y_2)$ that are shuffled differently, the attacker may match the order of $shuffle(y_1)$ and $shuffle(y_2)$ through the correlation of numbers.
I want to ask is there any similar known attack that can restore the shuffling?
