I was reading Ring LWE homomorphic encryption scheme referred in http://www.wisdom.weizmann.ac.il/~zvikab/localpapers/IdealHom.pdf
But this encryption scheme provides security mostly in the semi-honest model.
Consider a scenario of the protocol is in the semi-honest model. Say, Alice has little computation capability who wants to some equality comparison with the party Charlie. But no one wants to disclose their message if they are not equal. So another party Bob is doing blindly the comparison computation using Homomorphic encryption on behalf of them. Alice and Charlie encrypt their message using the public key and sends it to Bob. Bob does the computation of equality which requires using Hamming distance computation which requires one decryption to decide. Bob sends the encrypted result to Alice and Alice decrypts using her secret key and sends the result back to Bob. Bob decides the equality depending on the feedback from Alice.
But the problem of this protocol is not secure against a malicious adversary or some collision attacks between parties.
How can I make the protocol secure against a malicious adversary or prevent some collision attacks?