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Reading the Schnorr signature Wikipedia page, I stumbled upon the following statement:
All users agree on a cryptographic hash function $H:\{0,1\}^*\to\mathbb{Z}_q$.
What do these curly brackets mean here and how exactly is the hash function's input domain defined? Normally, you can use whatever input you want for a CHF/ PRF.
This has little to do with cryptography or hash functions. It's slightly abused standard mathematical notation.
$\{0,1\}$ is the set consisting of $0$ and $1$, so the set of all single bits. For any set $S$, $S^n$ for any natural number $n$ refers to the set of $n$-tuples of Elements from $S$, e.g., $S^2 = S \times S$. So strictly speaking $\{0,1\}^n$ refers to the set of $n$-tuples of bits, however we generally call these "bitstrings of length $n$".
Finally, $\{0,1\}^*$ is defined as $$\{0,1\}^*=\bigcup_{n\in\mathbb{N}_0}\{0,1\}^n.$$ I.e. it refers to the (infinite) set of all finite length bitstrings.
