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I saw in the paper How to Use a Short Basis: Trapdoors for Hard Lattices and New Cryptographic Constructions at page 29 that key generation algorithm of PKE can use a common random matrix $A$.

  • Is it OK to add a setup algorithm that generates some common public parameters?
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  • $\begingroup$ To get better answers you might consider expanding on why you considered it a potential problem. $\endgroup$ – Maeher Jan 9 at 15:56
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Yes.

There are a lot of precedents, for example DSA of FIPS 186-4 has a setup algorithm, described in appendix B.1.

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