This is a further question to the one reached here Homomorphic encryption and approximated GCD.

I am now thinking about a symmetric cipher in which the plaintext set is integers, illustrated as follows. For an integer $m_i$, the encryption is $c_i=pq_i+m_i$ and the decryption is $m_i=c_i\mod p$, where $p$ is the key and $q_i$ is some randomly chosen integer. I know that this cipher is not semantically secure since it cannot resist known plaintext attack or chosen plaintext attack. My question now is whether it is secure under ciphertext only attack? If so, what security definition I should use?


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