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arXiv:1306.6531 · PLoS ONE

Critical Analysis of the Bennett–Riedel Attack on Secure Cryptographic Key Distributions via the Kirchhoff-Law–Johnson-Noise Scheme

László B. Kish, Derek Abbott, Claes G. Granqvist

Published Dec 16, 2013• 53 citations
arXivHTMLPDF

Abstract

Recently, Bennett and Riedel (BR) (http://arxiv.org/abs/1303.7435v1) argued that thermodynamics is not essential in the Kirchhoff-law-Johnson-noise (KLJN) classical physical cryptographic exchange method in an effort to disprove the security of the KLJN scheme. They attempted to demonstrate this by introducing a dissipation-free deterministic key exchange method with two batteries and two switches. In the present paper, we first show that BR's scheme is unphysical and that some elements of its assumptions violate basic protocols of secure communication. All our analyses are based on a technically unlimited Eve with infinitely accurate and fast measurements limited only by the laws of physics and statistics. For non-ideal situations and at active (invasive) attacks, the uncertainly principle between measurement duration and statistical errors makes it impossible for Eve to extract the key regardless of the accuracy or speed of her measurements. To show that thermodynamics and noise are essential for the security, we crack the BR system with 100% success via passive attacks, in ten different ways, and demonstrate that the same cracking methods do not function for the KLJN scheme that employs Johnson noise to provide security underpinned by the Second Law of Thermodynamics. We also present a critical analysis of some other claims by BR; for example, we prove that their equations for describing zero security do not apply to the KLJN scheme. Finally we give mathematical security proofs for each BR-attack against the KLJN scheme and conclude that the information theoretic (unconditional) security of the KLJN method has not been successfully challenged.

DOI
10.1371/journal.pone.0081810

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Recently, Bennett and Riedel (BR) (http://arxiv.org/abs/1303.7435v1) argued that thermodynamics is not essential in the Kirchhoff-law-Johnson-noise (KLJN) classical physical cryptographic exchange method in an effort to disprove the security of the KLJN scheme. They attempted to demonstrate this by introducing a dissipation-free deterministic key exchange method with two batteries and two switches. In the present paper, we first show that BR's scheme is unphysical and that some elements of its assumptions violate basic protocols of secure communication. All our analyses are based on a technically unlimited Eve with infinitely accurate and fast measurements limited only by the laws of physics and statistics. For non-ideal situations and at active (invasive) attacks, the uncertainly principle between measurement duration and statistical errors makes it impossible for Eve to extract the key regardless of the accuracy or speed of her measurements. To show that thermodynamics and noise are essential for the security, we crack the BR system with 100% success via passive attacks, in ten different ways, and demonstrate that the same cracking methods do not function for the KLJN scheme that employs Johnson noise to provide security underpinned by the Second Law of Thermodynamics. We also present a critical analysis of some other claims by BR; for example, we prove that their equations for describing zero security do not apply to the KLJN scheme. Finally we give mathematical security proofs for each BR-attack against the KLJN scheme and conclude that the information theoretic (unconditional) security of the KLJN method has not been successfully challenged.
Abstract We introduce two new Kirchhoff-law-Johnson-noise (KLJN) secure key distribution schemes which are generalizations of the original KLJN scheme. The first of these, the Random-Resistor (RR-) KLJN scheme, uses random resistors with values chosen from a quasi-continuum set. It is well-known since the creation of the KLJN concept that such a system could work in cryptography, because Alice and Bob can calculate the unknown resistance value from measurements, but the RR-KLJN system has not been addressed in prior publications since it was considered impractical. The reason for discussing it now is the second scheme, the Random Resistor Random Temperature (RRRT-) KLJN key exchange, inspired by a recent paper of Vadai, Mingesz and Gingl, wherein security was shown to be maintained at non-zero power flow. In the RRRT-KLJN secure key exchange scheme, both the resistances and their temperatures are continuum random variables. We prove that the security of the RRRT-KLJN scheme can prevail at a non-zero power flow, and thus the physical law guaranteeing security is not the Second Law of Thermodynamics but the Fluctuation-Dissipation Theorem. Alice and Bob know their own resistances and temperatures and can calculate the resistance and temperature values at the other end of the communication channel from measured voltage, current and power-flow data in the wire. However, Eve cannot determine these values because, for her, there are four unknown quantities while she can set up only three equations. The RRRT-KLJN scheme has several advantages and makes all former attacks on the KLJN scheme invalid or incomplete.
This dissertation demonstrates three new types of attacks against the KLJN scheme. The first attack type is based on compromised RNGs. The first RNG attacks are deterministic. First, Eve knows both noises. She can crack the bit via Ohm's Law and one-bit powers within a fraction of the bit exchange period. Second, Eve knows only Bob's noise, so she can learn Bob's resistance value via Ohm's Law and Alice's resistance at the end of the bit exchange period. She can also use a process of elimination. The second RNG attacks are statistical. First, Eve has partial knowledge of Alice's and Bob's noises. She can crack the bit by taking the highest cross-correlation between her noises and the measured noise in the wire, and by taking the highest cross-correlation between her noises and Alice's/Bob's noises. Second, Eve has partial knowledge of only Alice's noise. She can still crack the bit, but after the bit exchange period. The second attack type is based on thermodynamics. Previously, the KLJN scheme required thermal equilibrium. However, Vadai, et al, in (Nature) Science Reports shows a modified scheme, where there is a non-zero thermal noise, yet the system resists all the known attacks. We utilize coincidence events between the line current and voltage and show that there is non-zero information leak. As soon as thermal equilibrium is restored, the system is perfectly secure again. The final attack type is based on the nonlinearity of the noise generators. We explore the effect of distortion at the second and third orders. It is demonstrated that 1% distortion results in a significant information leak. We also show that decreasing the effective temperature results in the KLJN scheme approaching perfect security.
A secure key distribution (exchange) scheme is unconditionally secure if it is unbreakable against arbitrary technological improvements of computing power and/or any development of new algorithms. There are only two families of experimentally realized and tested unconditionally secure key distribution technologies: quantum key distribution (QKD), the base of quantum cryptography, which utilizes quantum physical photonic features, and the Kirchhoff-Law–Johnson-Noise (KLJN) system that is based on classical statistical physics (fluctuation–dissipation theorem). The focus topic of this paper is the thermodynamical situation of the KLJN system. In all the original works, the proposed KLJN schemes required thermal equilibrium between the devices of the communicating parties to achieve perfect security. However, Vadai et al., in (Nature) Sci. Rep. 5, 13653 (2015) show a modified scheme, where there is a non-zero thermal noise energy flow between the parties, yet the system seems to resist all the known attack types. We introduce an attack type against their system. The attack utilizes coincidence events between the line current and voltages. We show that there is a non-zero information leak toward the Eavesdropper, even under idealized conditions. As soon as the thermal equilibrium is restored, the system becomes perfectly secure again. In conclusion, perfect unconditional security requires thermal equilibrium.
We introduce the so far most efficient attack against the Kirchhoff-law-Johnson-noise (KLJN) secure key exchange system. This attack utilizes the lack of exact thermal equilibrium in practical applications and is based on cable resistance losses and the fact that the Second Law of Thermodynamics cannot provide full security when such losses are present. The new attack does not challenge the unconditional security of the KLJN scheme, but it puts more stringent demands on the security/privacy enhancing protocol than for any earlier attack. In this paper we present a simple defense protocol to fully eliminate this new attack by increasing the noise-temperature at the side of the smaller resistance value over the noise-temperature at the side with the greater resistance. It is shown that this simple protocol totally removes Eve’s information not only for the new attack but also for the old Bergou-Scheuer-Yariv attack. The presently most efficient attacks against the KLJN scheme are thereby completely nullified.
The Kirchhoff-Law-Johnson-(like)-Noise (KLJN) key exchange system is a promising low-cost alternative to the quantum key distribution and is based solely on the laws of classical physics. Although several papers have been published in the field, there is still an ongoing debate about the security of the method. In our paper we will give an overview the most important findings about the security of the KLJN system and show the effects of the non-idealities of the system on the information leak. We will also analyze different methods of proposed cracking the KLJN protocol, including the latest directional coupler attack.