I am implementing Role-based access control by referencing the paper Enforcing Role-Based Access Control for Secure Data Storage in the Cloud. In page 6, they have mentioned to choose hash functions $H_1$ and $H_2$ during the setup $$ H_1 : \{0, 1\}^∗ → Z^∗_p, H_2 : G_T →Z^∗_p $$ where $G_T$ be a cyclic multiplicative group

Can anyone please explain me the notation of the two hash functions? Should the two hash functions $H_1$ and $H_2$ be implemented using different cryptographic hash algorithms? Or can I use SHA-256 (for example) to implement both of them? If No, please recommend me cryptographic hash algorithms for them.


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