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I have two secret numbers $A$ and $B$. Both are uniformly-distributed 32-bit numbers.

I need a deterministic function $f(x)$ such that $f(A) = B$. $f(x)$ must not leak any information about $A$ or $B$.

Naively, what if $f(x) = x + C$, where $C = B - A$. What information is leaked, if any, in this case, and what would be a better $f(x)$?

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  • $\begingroup$ How many times are you planning on invoking a given $ f(x) $ for different $ x $? Also, be aware that 32-bit numbers are typically small enough to brute-force, so the security here is not very substantial. $\endgroup$
    – bk2204
    Commented Dec 1, 2023 at 20:25
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    $\begingroup$ Does $f$ need to be pseudorandom? If you don't want "information to leak" then you have to be specific about what the adversary is allowed to do/see. Also note that you can "translate" any function $f$ into $f'(x) = f(x) + B - f(A)$ so that $f'(A)= B$. $\endgroup$
    – Mikero
    Commented Dec 1, 2023 at 20:43
  • $\begingroup$ Your naive example leaks at least $B-A$ by evaluating $f$ on $x=0$. $\endgroup$
    – lamontap
    Commented Dec 1, 2023 at 20:51

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