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The following three attacks come to mind: It would be trivial to forge the encryption of any message $m'$ by choosing $r=0$ and outputting $(m', 0)$. The scheme makes no mention of padding, so for short plaintexts and low values of $e$, it could be very easy to retrieve $r$ from $(r^e \text{ mod } N)$. And if a known ciphertext/plaintext pair $(c,m)$ is ...


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First things first: a PRNG (Pseudo Random Number Generator) can not provide a one-time pad. As a reminder: a one-time pad… has to be truly random, must be at least as long as the plaintext, is never reused in whole or in part, and is kept completely secret. Only when all four points are met, we´re talking about OTP. Your PRNG idea fails to meet those ...


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The security notion one usually considers for OTP is perfect secrecy, which informally means that the ciphertext does not reveal any information about the original message, regardless of the computational power of the adversary. It is already known that this requires that the key size must be equal to the plaintext size and that all keys are equiprobable. ...


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[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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