I am implementing ID based encryption in c# right now i am having problem at the following mathematics
$$H_1: \{0,1 \}^n \times \{0,1 \}^n \to \mathbb{Z}^*_p, \text{ what does this expression mean?}$$ P is prime number. G's are groups of finite orders. H's are hash functions
What is the difference among the following expressions?
$$ \begin{align} H_2: & \{0,1\}^n \to G \\ H_3: & \{0,1\}^n \to \{0,1\}^n \\ H_4: & G_1 \to \{0,1\}^n . \end{align} $$
I am pretty new user dont even know how to format equation here?