Is it acceptable to add a setup algorithm in the public key encryption? 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?
Yes.

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