Pairing based cryptography schemes such as identity-based encryption or different attribute-based encryption schemes (CP-ABE, KP-ABE etc.) often make use of a hash function defined as $H_1:\{0,1\}^* \rightarrow \mathbb{G}_1$. Where, $\mathbb{G}_1$ is a multiplicative group of some large prime order $p$. Then, the function $e:\mathbb{G}_1 \times \mathbb{G}_2 \rightarrow \mathbb{G}_T$ is called a bilinear pairing if it has bilinearity, non-degeneracy and computability properties. Here, $\mathbb{G}_2$ and $\mathbb{G}_T$ are also groups. Now, my question is, how such a hash function $H_1$ is constructed?
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