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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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If the file has been crafted deliberately to survive this form of damage then yes you should be able to recover your data. There are many quite simple methods from adding CRCs to replicating the data multiple times. There are other possible routes to recovery. If for example the file was an ASCII text file then it may be possible to recover something close ...


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This cipher is called a one-time pad. It is unbreakable ("perfect secrecy") assuming that: The pad (the collection of random bits) really is truly random The pad is never reused to encrypt other messages So, no information can be extracted from $\text{file} \oplus \text{random bits}$. The basic idea of the proof is that an attacker can test every ...


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The One-Time Pad employs neither confusion nor diffusion, as defined by Shannon: "Two methods (other than recourse to ideal systems) suggest themselves for frustrating a statistical analysis. These we may call the methods of diffusion and confusion. In the method of diffusion the statistical structure of $M$ which leads to its redundancy is “dissipated” ...


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I believe you need a few clarifications to answer this question yourself. The first is the one time pad (OTP). This is the only truly unbreakable system if it's used correctly. Using correctly means that for every symbol of the message there is exactly one truly random symbol in the key. Specifically, this means that there is no chosen symbol of the key ...


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In a lot of cases OTP will be completely impractical. If instead of a truly random pad you use a pseudo random pad, you will have something a lot more practical. But it is no longer OTP, and the security proofs about OTP means nothing in that case. I think this is the essence of the Bruce Schneier quote you mention. If we for a moment ignore the impractical ...



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