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.
1- How can I do that? 2- Same question with proof about $A$
I thought about: -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 it value.