In many cryptographic protocols design like this one, I have seen the statement 'Choose a Hash function for example: \begin{align} h&: \{0,1\}^*\times\mathbb G\to\mathbb Z_q^*\\ h_2&: \{0,1\}^*\times\{0,1\}^*\times\mathbb G\to\mathbb Z_q^*\\ \end{align} in which it takes as input a binary string and a random element of some group and outputs an element of multiplicative group of prime field. How could I construct such a hash function?
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