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Hashing a single message say $H(M)$ is vulnerable to a birthday attack. But what if a combination is hashed, such has $H(M,R)$? Is it still vulnerable to the attack?

I think it is because $M, R$ can be assumed to be as $X$, so in essence $H(X)$ is being hashed and the birthday attack possibility still exists. Is this logic correct?

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    $\begingroup$ Why shouldn't this logic be correct? $\endgroup$
    – SEJPM
    Sep 25, 2016 at 21:59
  • $\begingroup$ Well, I was wondering if there was any other perspective to approach this problem. $\endgroup$
    – saahil24
    Sep 25, 2016 at 22:31
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    $\begingroup$ That problem can be modeled as randomized hashing. ​ For candidate-eTCR hashes, the analogue of the birthday attack requires that the adversary submit lots of messages to honest parties, rather than just do offline computation. ​ ​ ​ ​ $\endgroup$
    – user991
    Sep 25, 2016 at 22:47

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I think so cause $M, R$ can be assumed to be as $X$, so in essence $H(X)$ is being hashed and the birthday attack possibility still exists.

Yes, that's correct.

Note that there is no such function as $H(M, R)$, you'd need some way of combining the values; lets assume concatenation though (so $H(M | R)$).

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    $\begingroup$ Concatenation of variable-length input is a bad idea in general, tho. For a message $110$ and random value $11$, I can find a collision with the message $11$ and random value $011$. $\endgroup$
    – tylo
    Oct 26, 2016 at 15:57
  • $\begingroup$ True, this was just for sake of answering the question though. You could use an ASN1 SEQUENCE and DER encoding instead. $\endgroup$
    – Maarten Bodewes
    Oct 26, 2016 at 16:40

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