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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

$$H1 : \{0, 1\}^∗ \rightarrow Z^∗_p,$$ $$H2 : G_T \rightarrow Z^∗_p$$ 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 $\operatorname{SHA-256}$ (for example) to implement both of them? If No, please recommend me cryptographic hash algorithms for them.

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    $\begingroup$ Voted to migrate to cryptoSE $\endgroup$ – wireghoul Jun 26 '16 at 11:31