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The ideal encryption scheme $E$ would be one that, for every ciphertext $C=E(K, M)$, if the key remains secret for the adversary, the probability of identifying $M$ is negligible. Since that is not possible in practice, the second most reasonable approach is to define constraints strong enough to satisfy some definition of security. The $IND-$ notation ...


[Note: This answer is based on k being generated by applying a pseudorandom function to a unique message-ID (counter) each time.] It depends how many times you want to encrypt with it. If you want it as a complicated OTP, then it's secure. In order to see this, just ignore the x parts and note that $s_1m \bmod p$ and $s_2m \bmod p$ are to independent ...

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