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1

This is the pre-image attack on hash functions, i.e. pre-image attack : given a hash value $y$ find a pre-image $x$ such that $y=h(x)$. Good designed cryptographic hash functions have $\mathcal{O}(2^{n})$ classical pre-image resistance for $n$-bit output. The classical attack tries all possible input space to find a $x$ that hashes the target hash value. ...


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I disregard the perfect hash requirement. In the application asking for preimage-resistance with a narrow hash, one should use a purposely-slow memory-hard hash (as used for passwords, also known as key-streching or password-based hash). This greatly reduces the number of bits needed for preimage resistance. More precisely, we want to build a hash that ...


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