Joined out of interest in One Time Pad for it's elegance, simplicity and perfect secrecy when done correctly. This interest originated when exposed to number stations while listening to shortwave radio. I enjoy that this method can be done with pencil, paper and basic math, and is not only practical for short messages (without assistance of computers), but for long messages as well with the help of computers.

I bring this interest to Crypto SE in order to try to understand the finer points of what makes OTP perfectly secret, and to learn of requirements that aren't usually specified in general descriptions of OTP. For example, a quick internet search on OTP usually yields that the key must be shared securely between Alice and Bob and that each element of the key must be used only once, that the key must be truly random, and that the key must be as long as the message.

But beyond that, there is not much explanation as to why these requirements are as they are. The general descriptions do not specify why modular math is necessary or why any given modulus is either necessary, allowed or disallowed, etc. I'm sure these questions are explained in textbooks about OTP and perfect secrecy, but as a layman who's math education stopped after algebra 1, some of the explanations there are beyond me.

So I come here mostly to try to understand the concepts in layman's terms to whatever extent possible. The most valuable answers to me are those who can take these mathematical concepts and explain them in language easily understood by someone who has a limited understanding of mathematics. Not always possible at some level, I understand, but that's where I am at the moment.

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