# hash function notations and existing cryptographic hash algorithms [duplicate]

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.

• Voted to migrate to cryptoSE
– wireghoul
Jun 26 '16 at 11:31