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The term super-logarithmic in the paper you cite has nothing to do with the notion of a super-logarithm in Wikipedia. Rather, the intention is simply a function that is asymptotically larger than the $\log$ function. Formally, $f$ is super-logarithmic if $f(n)=\omega(\log n)$. The formal definition of "little-omega" appears in the Wikipedia entry on big-O ...

8

A circuit is a representation of a (computable) function. There are many other ways to represent a function (mathematical notation, Turing machines, pseudo-code, etc.), but for some purposes it happens that circuits are the most convenient one.

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Does many:1 mean two different inputs would have the same hash outputs? Yes. This is a consequence of the pidgeonhole principle: as MD5 has a much larger number of potential inputs ($2^{2^{64}}$ or so) than outputs ($2^{128}$), some inputs must lead to the same output, i.e. collide. Cryptographic hashes all have this "limitation", because they have a ...

1

Number of inputs Hashing algorithms usually take more than one input. For instance, SCrypt takes 5, but only one field represents data to be hashed. The rest are salt and hardness configuration values. It doesn't really makes sense to have more than one data field to be hashed, because most modern hashing algorithms require a unique value (salt) to be ...

3

The standard definition of a hash function is from arbitrary length bitstrings to a constant length bitstring. That is, there is only one input. Password hashes, like keyed hashes (MACs, more or less), have more than one input. There is no contradiction there, since password hashes are not cryptographic hashes - thought they may be built from cryptographic ...

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I believe the concept you're looking for is a cryptographical hash. This is a function that takes a (potentially) long input, produces a short (fixed length) output, and for which it is impractical to find two different inputs that generate the same output. It is a fixed function; anyone (including your customer) can generate a hash for any input. How it ...

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