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Suppose I have the following hash function: $\newcommand{\md}[1]{\text{md#1}} \newcommand{\H}{\text{H}}$

$$\H(x, y) = \md{5}(x) \oplus \md{4}(y)$$

How can I prove it's collision proof?

I tried to say "lets assume we have an oracle which know how to find a collision/pre image of $\H$" and find an algorithm to find $\md5$ collision. I didn't manage to find such algorithm.

How can it be proved?

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    $\begingroup$ Actually, a standard birthday attack would take circa $2^{64}$ hash evaluations - plausible for some real-world entities... $\endgroup$
    – poncho
    Commented Dec 11, 2019 at 15:26
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    $\begingroup$ Hint: when asked to prove something, first question if it is true or false. That'll get you a grasp on the problem. $\endgroup$
    – fgrieu ♦
    Commented Dec 11, 2019 at 15:34
  • $\begingroup$ I couldn't find a way to make a collision. Thus, the hint isn't usefull for me $\endgroup$
    – MyNick
    Commented Dec 11, 2019 at 16:29
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    $\begingroup$ You seem to think that md5 is collision resistant. I have bad news for you. $\endgroup$
    – Maeher
    Commented Dec 11, 2019 at 17:37
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    $\begingroup$ Well then fix $x$. Finding collisions in md4 is even simpler. It apparently takes less than 2 md4 invocations to find fresh md4 collisions. $\endgroup$
    – Maeher
    Commented Dec 11, 2019 at 18:03

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