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A cryptographic hash algorithm is a function which takes a variable size input and produces a fixed size output. The algorithm makes it difficult to find two inputs with the same output or reconstruct the input from the output.
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Rewarding the finding of zeroes of a hash function
We have an arbitrary and public hash function $\text{Hash}$. … Could I possibly publish a function $F$ (that is, publish an algorithm that returns $F(M)$ given $M$) such that
$F(M)=K$ whenever $\text{Hash}(M)=0$, where $K$ is a previously defined private key that …