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hash function notations and existing cryptographic hash algorithms

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 H1 and H2 during the setup H1 : {0, 1}^∗ → Z^∗_p, H2 : 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 H1 and H2 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.