Random Number Generators Founded on Signal and Information Theory

Abstract

The strength of a cryptographic function depends on the amount of entropy in the cryptovariables that are used as keys. Using a large key length with a strong algorithm is false comfort if the amount of entropy in the key is small. Unfortunately the amount of entropy driving a cryptographic function is usually overestimated, as entropy is confused with much weaker correlation properties and the entropy source is difficult to analyze. Reliable, high speed, and low cost generation of non-deterministic, highly entropic bits is quite difficult with many pitfalls. Natural analog processes can provide non-deterministic sources, but practical implementations introduce various biases. Convenient wide-band natural signals are typically 5 to 6 orders of magnitude less in voltage than other co-resident digital signals such as clock signals that rob those noise sources of their entropy. To address these problems, we have developed new theory and we have invented and implemented some new techniques. Of particular interest are our applications of signal theory, digital filtering, and chaotic processes to the design of random number generators. Our goal has been to develop a theory that will allow us to evaluate the effectiveness of our entropy sources. To that end, we develop a Nyquist theory for entropy sources, and we prove a lower bound for the entropy produced by certain chaotic sources. We also demonstrate how chaotic sources can allow spurious narrow band sources to add entropy to a signal rather than subtract it. Armed with this theory, it is possible to build practical, low cost random number generators and use them with confidence.