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I know that when the domain is $\{0, 1\}^{m}$ in function $h(x)=Ax$ for $A \stackrel{\$}{\leftarrow} \mathbb{Z}^{n\times m}_{q}$, this function is called Ajtai hash function. So when the domain is extended to $\mathbb{Z}_{q}^{m}$, is it also called Ajtai hash function?

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István András Seres
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Alex Ideal
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  • When the domain is extended to $\mathbb{Z}_q^m$ it is no longer collision resistant, so one should be careful in what one means by "hash function". – Mark Schultz-Wu Apr 11 '20 at 03:26
  • @Mark Thanks for your reminding. I want to ask that if the domain is extended and at the same time the function is collision resistant. Is the function with extended domain also called Ajtai hash function? – Alex Ideal Apr 11 '20 at 03:38
  • I'm unaware of the particular name to use in this situation, but Peikert's answer to this question makes that seem appropriate (provided the domain is suitably restricted). – Mark Schultz-Wu Apr 11 '20 at 04:13

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