In a forthcoming paper in IEE Proceedings Information Security, Feng Hao claims that temperature inaccuracies make the key exchange scheme based on Kirchhoff Loop with Johnson-like Noise insecure. First we point out that this claim is irrelevant for the security of the idealized/mathematical communicator because it violates basic assumptions. Furthermore, in general practical applications, as it has been pointed out in the very first paper, the use of thermal noise is disadvantageous therefore the issue of temperature and its accuracy is unimportant even for the security of common practical realizations. It is important to emphasize that any deviation from the idealized scheme can lead to a finite level of security. Thus, if the above-mentioned author had stressed the inaccuracy of the resistor values; his claim would have been practically valid. However the impact of such systematic errors can be kept under control. Here we cite our relevant analysis (Phys. Lett. A359, (2006) 741-744) of 1% voltage inaccuracy along the line due to wire resistance effects, which can be considered as a general result for inaccuracies of this order. The necessity to build a statistics to extract information during the properly chosen clock time leads to extremely poor eavesdropper statistics and this situation provides a good practical raw bit security that can be orders of magnitude beyond the raw bit security of idealized quantum communicators.
In a forthcoming paper in IEE Proceedings Information Security, Feng Hao claims that temperature inaccuracies make the key exchange scheme based on Kirchhoff Loop with Johnson-like Noise insecure. First we point out that this claim is irrelevant for the security of the idealized/mathematical communicator because it violates basic assumptions. Furthermore, in general practical applications, as it has been pointed out in the very first paper, the use of thermal noise is disadvantageous therefore the issue of temperature and its accuracy is unimportant even for the security of common practical realizations. It is important to emphasize that any deviation from the idealized scheme can lead to a finite level of security. Thus, if the above-mentioned author had stressed the inaccuracy of the resistor values; his claim would have been practically valid. However the impact of such systematic errors can be kept under control. Here we cite our relevant analysis (Phys. Lett. A359, (2006) 741-744) of 1% voltage inaccuracy along the line due to wire resistance effects, which can be considered as a general result for inaccuracies of this order. The necessity to build a statistics to extract information during the properly chosen clock time leads to extremely poor eavesdropper statistics and this situation provides a good practical raw bit security that can be orders of magnitude beyond the raw bit security of idealized quantum communicators.
This is the longer (partially unpublished) version of response; the shorter version (http://arxiv.org/abs/physics/0605013) is published in Physics Letters A. We point out that the claims in the comment-paper of Scheuer and Yariv are either irrelevant or incorrect. We first clarify what the security of a physically secure layer means. The idealized Kirchoff-loop-Johnson-like-noise (KLJN) scheme is totally secure therefore it is more secure than idealized quantum communication schemes which can never be totally secure because of the inherent noise processes in those communication schemes and the statistical nature of eavesdropper detection based on error statistics. On the other hand, with sufficient resources, a practical/non-ideal realization of the KLJN cipher can arbitrarily approach the idealized limit and outperform even the idealized quantum communicator schemes because the non-ideality-effects are determined and controlled by the design. The cable resistance issue analyzed by Scheuer and Yariv is a good example for that because the eavesdropper has insufficient time window to build a sufficient statistics and the actual information leak can be designed. We show that Scheuer's and Yariv's numerical result of 1% voltage drop supports higher security than that of quantum communicators. Moreover, choosing thicker or shorter wires can arbitrarily reduce this voltage drop further; the same conclusion holds even according to the equations of Scheuer and Yariv.
Very recently, it has been shown that Gaussian thermal noise and its artificial versions (Johnson-like noises) can be utilized as an information carrier with peculiar properties therefore it may be proper to call this topic Thermal Noise Informatics. Zero Power (Stealth) Communication, Thermal Noise Driven Computing, and Totally Secure Classical Communication are relevant examples. In this paper, while we will briefly describe the first and the second subjects, we shall focus on the third subject, the secure classical communication via wire. This way of secure telecommunication utilizes the properties of Johnson(-like) noise and those of a simple Kirchhoff's loop. The communicator is unconditionally secure at the conceptual (circuit theoretical) level and this property is (so far) unique in communication systems based on classical physics. The communicator is superior to quantum alternatives in all known aspects, except the need of using a wire. In the idealized system, the eavesdropper can extract zero bit of information without getting uncovered. The scheme is naturally protected against the man-in-the-middle attack. The communication can take place also via currently used power lines or phone (wire) lines and it is not only a point-to-point communication like quantum channels but network-ready. We report that a pair of Kirchhoff-Loop-Johnson(-like)-Noise communicators, which is able to work over variable ranges, was designed and built. Tests have been carried out on a model-line with ranges beyond the ranges of any known direct quantum communication channel and they indicate unrivalled signal fidelity and security performance. This simple device has single-wire secure key generation/sharing rates of 0.1, 1, 10, and 100 bit/second for copper wires with diameters/ranges of 21 mm / 2000 km, 7 mm / 200 km, 2.3 mm / 20 km, and 0.7 mm / 2 km, respectively and it performs with 0.02% raw-bit error rate (99.98 % fidelity). The raw-bit security of this practical system significantly outperforms raw-bit quantum security. Current injection breaking tests show zero bit eavesdropping ability without setting on the alarm signal, therefore no multiple measurements are needed to build an error statistics to detect the eavesdropping as in quantum communication. Wire resistance based breaking tests of Bergou-Scheuer-Yariv type give an upper limit of eavesdropped raw bit ratio is 0.19 % and this limit is inversely proportional to the sixth power of cable diameter. Hao's breaking method yields zero (below measurement resolution) eavesdropping information.
The Kirchhoff-Law-Johnson-Noise unconditionally secure key exchanger is a promising, surprisingly simple, very low cost and efficient electronic alternative to quantum key distribution. A few resistors, switches, and interconnecting cables can provide unconditionally secure data transmission in the ideal case by utilizing the thermal noise of the resistors. The key problems regarding practical realizations are related to the resistance tolerance, finite cable resistance, and other non-ideal properties that can cause information leak. In this paper, we present robust protection from cable resistance and resistance mismatch attacks against the system. Our theoretical results show that all resistive inaccuracies, parasitic resistances, cable resistance, and temperature dependence can be compensated; therefore, the practical implementation becomes much easier. The generalized method provides inherent protection against the so-called second law attack as well.
The Kirchhoff’s-Law-Johnson-Noise (KLJN) secure key exchanger is a simple, low-cost scheme that provides symmetric encryption with unconditional security in electronic communication. The key bits are generated based on measurements of the mean-square value of the noise voltage and/or current of the channel between the two communicating parties. In this work, a combined current–voltage measurement mode scenario and an error removal method for the ideal, symmetric KLJN secure key exchanger that uses an identical pair of resistors at both ends of the communication line were considered, which improves the fidelity and reduces the bit error probability compared to the schemes when either voltage or current measurement are being used. It has been shown in previous works that the error probability of the original, symmetric KLJN secure key exchanger decays exponentially with parameters such as the time window for performing the key exchange and other relevant criteria used in the interpretation of the key bits. The objective of this work is to develop optimization strategies for the ideal, symmetric KLJN secure key exchanger in order to obtain optimal values of these parameters while ensuring that errors are kept within acceptable values. For those strategies, closed-form solutions to the optimal values were derived by solving the Karush–Kuhn–Tucker (KKT) conditions. Numerical results show that the proposed optimization techniques not only ensure that the bit probability error remains within the desired limit, but also provide more flexibility to define the thresholds values, reduce the bit exchange period needed to guarantee an acceptable bit error probability, weaken Eve’s statistics, and improve the system resource managing.
In (Nature) Science Report 5 (2015) 13653, Vadai, Mingesz and Gingl (VMG) introduce a new Kirchhoff-law-Johnson-noise (KLJN) secure key exchanger that operates with 4 arbitrary resistors (instead of 2 arbitrary resistance values forming 2 identical resistor pairs in the original system). They state that in this new, VMG-KLJN, non-equilibrium system with nonzero power flow, the security during the exchange of the two (HL and LH) bit values is as strong as in the original KLJN scheme. Moreover, they claim that, at practical conditions, their VMG-KLJN protocol “supports more robust protection against attacks”. First, we investigate the power flow and thermal equilibrium issues of the VMG-KLJN system with 4 arbitrary resistors. Then we introduce a new KLJN protocol that allows the arbitrary choice of 3 resistors from the 4, while it still operates with zero power flow during the exchange of single bits by utilizing a specific value of the 4th resistor and a binary temperature set for the exchanged (HL and LH) bit values. Then we show that, in general, the KLJN schemes with more than 2 arbitrary resistors (including our new protocol mentioned above) are prone to 4 new passive attacks utilizing the parasitic capacitance and inductance in the cable, while the original KLJN scheme is naturally immune against these new attacks. The core of the security vulnerability exploited by these attacks is the different line resistances in the HL and LH cases. Therefore, on the contrary of the statement and claim cited above, the practical VMG-KLJN system is less secure than the original KLJN scheme. We introduce another 2, modified, non-equilibrium KLJN systems to eliminate the vulnerability against some - but not all - of these attacks. However the price for that is the loss of arbitrariness of the selection of the 4th resistor and the information leak still remains greater than zero.
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.