I want to ask: How to show that a result of hash function and a random is computationally indistinguishable

If we denote $H(): \mathcal{X} \rightarrow \mathcal{Y}$ is a secure hash function, $m$ is a fixed message, and $r$ is chosen randomly.

Let $c_1 = H(m \mathbin\| r)$ and $c_2 \in \mathcal{Y}$ chosen randomly.

Is there any method to show the $c_1 = H(m \mathbin\| r)$ and $c_2$ is computationally indistinguishable?

  • 2
    $\begingroup$ In fact you need something more than "secure hash function" here, you need "$H$ is a random function / random oracle" which by design always outputs a fresh random value for a fresh input, so you'd have to argue why $H$'s input never repeats (or bound the probability thereof). $\endgroup$
    – SEJPM
    Oct 4, 2019 at 10:31
  • $\begingroup$ @SEJPM Thanks your reply. I will go further to study! $\endgroup$ Oct 4, 2019 at 10:53


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