I am reading this explanation of zkSnark written by Maksym Petkus - http://www.petkus.info/papers/WhyAndHowZkSnarkWorks.pdf
From Section 3.5
Because verifier can extract knowledge about the unknown polynomial
$p(x)$ only from the data sent by the prover, let us consider those
provided values (the proof): $g^p$, $g^{p'}$, $g^h$. They participate in
the following checks:
$g^p = (g^{h})^{t(s)}$ (polynomial $p(x)$ has roots of $t(x)$)
$(g^p)^\alpha = g^{p'}$ (polynomial of a correct form is used)
The question is how do we alter the proof such that the checks still
hold, but no knowledge can be extracted? One answer can be derived
from the previous section: we can "shift" those values by some random
number $\delta$ (delta), e.g., $(g^p)^{\delta}$. Now, in order to
extract the knowledge, one first needs to find $\delta$ which is
considered infeasible. Moreover, such randomization is statistically
indistinguishable from random.
We already have Strong Homomorphic Encryption (as stated in Section 3.3.3),
$E(v) = g^v \pmod n$
The $g^p$, $g^{p'}$, $g^h$ are created as above. I mean how do you extract info about p, p' & h from $g^p$, $g^{p'}$, $g^h$ that the shift by $\delta$ is required?
So then why is the $\delta$ shift required for Zero Knowledge?
