cipher text only attacks on deterministic homomorphic encryption schemes If we consider a set of numbers say a set $s=\{a,b,c,d\}$ , where $a,b,c,d&gt;1$ and the numbers $a, b, c, d$ do not share any relation between them , i.e. for any two numbers,  $n_1,n_2\in s$ the following relations are guaranteed to hold: $n_1+n_2\neq 0$ and $n_1*n_2\neq 1$.

Is it possible to break the fully homomorphic encryption scheme on these set of numbers?

Note
This is a followup to this question which does not restrict the set $s$ is at all.
This is an interesting question. If the input set does not have any identity element (for both mul and add operations) then one cannot construct a field and subsequently there cannot be homomorphic operations.  More clearly, if the input plaintext elements do not form a field (and their respective ciphertext elements do not form a field either)  then there cannot be homomorphisms of operations. This is by definition of Field.

So if the input set contains identity elements (and other properties needed to become a field) then while the given set members may not have any obvious relation. There would be some constant $c$ for which  $enc(n_1) + c * enc(n_2) = enc(0) $ subsequently finding which attacks mentioned in previous question apply ! 

Also  an attacker could try to find random complex relations among them. For example is $ enc(a) + enc(a) = enc(b) $ or is $ enc(a) *enc( b) = enc(c) $ etc. revealing inferences.