&quot;Define a function h such that h(f(x), f(y)) is true iff x = y&quot;<p>If an attacker can compute such a function then any cryptosystem would be broken because of the attack you give. The Goldwasser,Micali paper &quot;Probabalistic Encryption&quot; is a very important early result in cryptography about this fact.<p>The attack implies that no deterministic encryption scheme is secure.<p>&quot;By our assumptions, the attacker knows f(1)&quot;.<p>There will not be a single value f(1) as secure encryption schemes cannot be deterministic.<p>There is nothing special about knowing one of the values of f(1) because modern cryptography assumes that the encryption algorithm is public.