Guaranteeing the diversity of number generators

TL;DR

This paper introduces a new measure called sequence diversity to ensure the unpredictability of number generators, and presents counter assisted generators that guarantee high diversity even if the original generator is weak or compromised.

Contribution

It defines sequence diversity as a security measure and proposes counter assisted generators that enhance diversity without compromising strong generators.

Findings

Counter assisted generators achieve high sequence diversity.

The measure generalizes cycle-length for non-iterative generators.

Any iterative generator can be transformed into a high-diversity generator.

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.