Proof of using a literal from known set, inside a computed formula Suppose I have publicly revealed the value of  $\phi(u) = A+Bu$,
where A, B, u are private values from a large group, that I want to keep in secret.

Furthermore, I want to add proof that the value $u$ is from a publicly known set of values, without revealing its real value.


How can I do that?
Same question with proof about $A$


I thought about:


A zero-knowledge scheme, but it seems to be inadequate to that purpose because the value $u$ is publicly known.
Private set intersection - But since $u$ is from a publicly known set I might reveal its value.
In Crypto 94, Cramer, Damgård and Schoenmakers proposed Proofs of Partial Knowledge and Simplified Design of Witness Hiding Protocols with abstract below:
Suppose we are given a proof of knowledge $P$ in which a prover demonstrates that he knows a solution to a given problem instance. Suppose also that we have a secret sharing scheme $S$ on $n$ participants. Then under certain assumptions on $P$ and $S,$ we show how to transform $P$ into a witness indistinguishable protocol, in which the prover demonstrates knowledge of the solution to some subset of $n$ problem instances out of a collection of subsets defined by $S.$
For example, using a threshold scheme, the prover can show that he knows at least $d$ out of $n$ solutions without revealing which $d$ instances are involved. If the instances are independently generated, we get a witness hiding protocol, even if $P$ did not have this property.
Our results can be used to efficiently implement general forms of group oriented identification and signatures. Our transformation produces a protocol with the same number of rounds as $P$ and communication complexity $n$ times that of $P.$ Our results use no unproven complexity assumptions.
The authors also state:

Our techniques are to some extent related to those of De Santis et al. The models are quite different, however: They consider non-interactive proofs of membership, while we consider interactive proofs of knowledge.

The paper is available here