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We simply strive for crypto that's as close as possible to ideal. Indistinguishably is the strongest property we can demand from a PRNG/streamcipher. It's hard to predict which non ideal properties will lead to problems at some point in the future. For example the non ideal properties that lead to padding oracles, BEAST, CRIME or the RC4 biases were known ...


If you can distinguish a source from true random, then that can directly translate into less guesses required in order to brute force a decryption - recovering the internal RNG state, which may lead to further attacks into decryption or key recovery, depending on what other resources an attacker can control. If I know probabilities of some output bits are ...


A PRNG must be indistinguishable from a true RNG only in a complexity theoretic sense. No polynomial (efficient) algorithm must be able to distinguish both. The fact that a true RNG has more collisions (by the birthday paradox) then a PRNG (say, running in counter mode) is not distinguishable by a polynomial algorithm.


What you are essentally describing is a Pseudo-Random Generator in which the base numbers act as the seed. This does not make a good method for generating OTPs because if you know the seed then you just work from there and crack the message.

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