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No. There is a difference between the type of a cipher and the construction of a cipher. If a cipher is of a specific type for which there are known IND-CPA secure constructions then that doesn't mean that an entirely different construction is secure. There are known attacks on stream ciphers, including "modern" stream ciphers such as RC4. If the generated ...

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No. Indeed, as in the answer by Maarten, it depends on the security and strength of the stream cipher. However, even if the stream cipher is a secure pseudorandom generator (which is its proper modeling), encryption is not necessarily CPA-secure when XORing the pad with the plaintext. This is also explained in great detail in Katz-Lindell. In fact, it is ...

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To make notations simpler, I note $R_i = F(k_i, IV_i)$. Then: $$C_1 = P \oplus R_1$$ $$C_2 = P \oplus R_1 \oplus R_2$$ $$C_3 = P \oplus R_2$$ Therefore: $$C_1 \oplus C_2 \oplus C_3 = P \oplus R_1 \oplus P \oplus R_1 \oplus R_2 \oplus P \oplus R_2 = P$$ Your protocol looks like Shamir's three-pass protocol but it requires a bit more than mere commutativity, ...

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Yes it is possible for a passive eavesdropper to recover the secret $P$. Here's how: The attacker observes $C_1,C_2,C_3$ and formes the XOR of all those values. That's it, the result of $C_1\oplus C_2 \oplus C_3=P\oplus F(K_1,IV_1)\oplus P \oplus F(K_1,IV_1) \oplus F(K_2,IV_2) \oplus P \oplus F(K_2,IV_2)=P$ yields the desired plaintext.

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