I am trying to understand why Merkle Tree doesn't suffer the birthday attack?
Can you help me?
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The birthday attack, birthday paradox or - probably most accurately - birthday problem does occur for Merkle-trees. This is both the case for the output of the hash algorithms used for the nodes, the in between hash values in the tree as well as the final hash value.
What's probably confusing you here is that the birthday attack isn't really a practical attack against secure hash functions unless the output size is not large enough. In other words, it is the output size of the hash values that protect against the birthday problem becoming a practical issue.