arXiv:cs/0112014cs.CR
Guaranteeing the diversity of number generators
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Abstract
A major problem in using iterative number generators of the form x_i=f(x_{i-1}) is that they can enter unexpectedly short cycles. This is hard to analyze when the generator is designed, hard to detect in real time when the generator is used, and can have devastating cryptanalytic implications. In this paper we define a measure of security, called_sequence_diversity_, which generalizes the notion of cycle-length for non-iterative generators. We then introduce the class of counter assisted generators, and show how to turn any iterative generator (even a bad one designed or seeded by an adversary) into a counter assisted generator with a provably high diversity, without reducing the quality of generators which are already cryptographically strong.
> Assuming its a permutation and you output the whole thing. I'm assuming the state-mixing function is a permutation (i.e. the counter affects the whole state in a reversible way), but it is not required that the whole state is outputted. > However, you wouldn't output the whole…
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