[Resource Topic] 2003/132: Guaranteeing the diversity of number generators

Welcome to the resource topic for 2003/132

Guaranteeing the diversity of number generators

Authors: Adi Shamir, Boaz Tsaban


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 \emph{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.

ePrint: https://eprint.iacr.org/2003/132

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