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Suppose the attacker knows $X, Z$ such that

$H(X || Y) = Z$

If bit-length(Y) < 60 then a brute force attack is possible.

What if bit-length(Z) = 256 (such as in SHA-256), bit-length(X) = 128, or bit-length(Y) = 256? Are there any published paper with results/experiments with SHA-256/512 in full or reduced rounds? Are there specific known attack techniques?

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I'm pretty confident there is nothing out there allowing a preimage attack of this kind on SHA-256 with full rounds. –  fgrieu Feb 23 '13 at 16:46
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