The basic idea of homomorphic MACs is that a user can use a secret key to generate a set of tags $σ_1 \dots σ_n$ authenticating values $D_1 \dots D_n$ respectively. so, anyone can homomorphically execute a program $P$ over $(σ_1 \dots σ_n)$ to generate a short tag σ that authenticates $m$ as the output of $P(m_1 \dots m_n)$. The authentication tag of a message $m \in Z^p$ is a degree-1 polynomial $y(z)$.

Could this tag be generated for message expressed as vector of $n$ scalars?

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    $\begingroup$ Please review your post before hitting the final button, there was a clear mistake in the title. We've got MathJax / $\LaTeX$ support on this site to help you format your questions (take a look at the edits). $\endgroup$ – Maarten Bodewes Sep 4 '19 at 14:18

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