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Yes, ofcourse it is possible. Let's consider with below example: Our compression function: f : {0, 1}^(128+512+1) → {0, 1}^(128) Message x has 1000 bits: (yi's are our input blocks and zis are output blocks, considered Mekle-Damgard schema) y1 is first 512 bits of x y2 is last 488 bits of x||0^24 y3 is 0^480||32-bit binary representation of 24 ...


Ok, here's how it is supposed to work: we take the function (which maps a string of $n$ bits to a string of $n$ bits), and iterate it repeatedly. After some amount of time, we'll run into a loop (that is, we'll evaluate to a value that we visited before, and there after, we'll repeatedly run through the loop). And, we'll run the function iteration twice, ...

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