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Pseudorandomness and Cryptographic Applications (Princeton Computer Science Notes)
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This is the theme taken in this book, namely tha a proper concept of randomness is not an intrinsic property of a collection or a distribution, but rather is dependent of the tools and computing capabilities of the observer. The concept of a pseudorandom distribution is introduced as a distribution where no efficient procedure or program can distinguish it from a uniform distribution. Pseudorandom generators are polynomial-time deterministic programs that take a randomly selected seed and expand it into a pseudorandom bit sequence.
The preliminaries/introduction gives an overview of sets, set functions, big-O, little-o notation, and most importantly from the author's standpoint, function and probability ensembles. He defines what it means to have a source of random bits, but does not give algorithms on how to produce them. Complexity classes are also discussed for both the deterministic and probabilistic cases, along with a very brief review of probability.
Private key cryptosystems begin the next chapter with an example of a one-time-pad private key cryptosystems. Pseudorandom generators are introduced as a solution to the problem of sending secure messages that are longer than the private key.
The author does a good job of defining computational and statistical indistinguishability, and the connection between 1-way functions and pseudorandom generators.Read more ›