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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You have recently asked a similar question. And you have accepted an answer, which is supposed to tell that you are satisfied. You even told so! At least, try to explain where your problem is: understanding the notation? Building the group G, or getting a representative? – fgrieu Dec 23 '20 at 11:30
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Thank you for closing the question. The other question's answer was satisfying in explaining the input of the hash function. What I mean now by the question is how the hashed value h can be in $\mathbb Z_q^*$ ? – Chai Ma Dec 23 '20 at 11:40
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I'll answer in your other question – fgrieu Dec 23 '20 at 11:51
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You had many comments under the question, if nothing was clear or something missing you can comment that too. – kelalaka Dec 23 '20 at 15:28
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@kelalaka thank you :) but it's okay now I got the answer and everything is clear – Chai Ma Dec 23 '20 at 15:38