What kind of noise guarantees security for the Kirchhoff-Loop-Johnson-Noise key exchange?

TL;DR

This paper mathematically proves that only normally distributed noise with specific scaling guarantees security in the Kirchhoff-Loop-Johnson-Noise key exchange system, supported by numerical simulations showing insecurity with improper noise choices.

Contribution

It provides a rigorous mathematical proof that normal distribution with special scaling is necessary for security in KLJN key exchange, complementing earlier physical assumptions.

Findings

Normal distribution with specific scaling guarantees security

Numerical simulations confirm insecurity with improper noise properties

Supports earlier physical assumptions about noise in KLJN system

Abstract

This article is a supplement to our recent one about the analysis of the noise properties in the Kirchhoff-Law-Johnson-Noise (KLJN) secure key exchange system [Gingl and Mingesz, PLOS ONE 9 (2014) e96109, doi:10.1371/journal.pone.0096109]. Here we use purely mathematical statistical derivations to prove that only normal distribution with special scaling can guarantee security. Our results are in agreement with earlier physical assumptions [Kish, Phys. Lett. A 352 (2006) 178-182, doi: 10.1016/j.physleta.2005.11.062]. Furthermore, we have carried out numerical simulations to show that the communication is clearly unsecure for improper selection of the noise properties. Protection against attacks using time and correlation analysis is not considered in this paper.