Unformatted text preview: he computer’s current state. That means that any randomnumber generator on a computer (at least, on a finitestate machine) is, by definition, periodic. Anything that is periodic is, by definition, predictable. And if something is predictable, it can’t be random. A true randomnumber generator requires some random input; a computer can’t provide that. PseudoRandom Sequences
The best a computer can produce is a pseudorandomsequence generator. What’s that? Many people have taken a stab at defining this formally, but I’ll handwave here. A pseudorandom sequence is one that looks random. The sequence’s period should be long enough so that a finite sequence of reasonable length—that is, one that is actually used—is not periodic. If you need a billion random bits, don’t choose a sequence generator that repeats after only sixteen thousand bits. These relatively short nonperiodic subsequences should be as indistinguishable as possible from random sequences. For example, they should have about the same number of ones and zeros, about half the runs (sequences of the same bit) should be of length one, one quarter of length two, one eighth of length three, and so on. They should not be compressible. The distribution of run lengths for zeros and ones should be the same [643,863,99,1357]. These properties can be empirically measured and then compared to statistical expectations using a chisquare test. For our purposes, a sequence generator is pseudorandom if it has this property: 1. It looks random. This means that it passes all the statistical tests of randomness that we can find. (Start with the ones in [863].) A lot of effort has gone into producing good pseudorandom sequences on computer. Discussions of generators abound in the academic literature, along with various tests of randomness. All of these generators are periodic (there’s no escaping that); but with potential periods of 2256 bits and higher, they can be used for the largest applications. The problem is sti...
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 Fall '10
 ALIULGER
 Cryptography, Bruce Schneier, Applied Cryptography, EarthWeb, Search Search Tips

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