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arXiv:1509.08150 · Metrology and Measurement Systems

Random-Resistor-Random-Temperature Kirchhoff-Law-Johnson-Noise (RRRT-KLJN) Key Exchange

László B. Kish, Claes Goran Granqvist

Published Mar 1, 2016• 31 citations
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Abstract

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.

DOI
10.1515/mms-2016-0007

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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.
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.
The Kirchhoff-law–Johnson-noise (KLJN) secure key distribution system provides a way of exchanging theoretically secure keys by measuring random voltage and current through the wire connecting two different resistors at Alice's and Bob's ends. Recently new advanced protocols for the KLJN method have been proposed with enhanced performance. In this paper, we analyze the KLJN system and compare with the "intelligent" KLJN (iKLJN) scheme. That task requires determination of the applied resistors and identification of various superpositions of known and unknown noise components. Some statistical tools will be explored to determine how the duration of the bit exchange window (averaging time) influences the performance of the secure bit exchange.
The Kirchhoff-Law-Johnson-Noise (KLJN) secure key distribution system provides a way of exchanging theoretically secure keys by measuring random voltage and current through the wire connecting two different resistors at Alice's and Bob's ends. Recently new advanced protocols for the KLJN method have been proposed with enhanced performance. In this paper we analyze the KLJN system and compare with the intelligent KLJN (iKLJN) scheme. That task requires determination of the applied resistors and identification of various superpositions of known and unknown noise components. Some statistical tools will be explored to determine how the duration of the bit exchange window (averaging time) influences the performance of the secure bit exchange.
The Kirchhoff-Law-Johnson-Noise (KLJN) secure key distribution system provides a way of exchanging information theoretic secure keys by measuring the random voltage and current through the wire connecting two different resistors at Alice's and Bob's ends. Recently new advanced protocols for the KLJN method have been proposed with enhanced performance. In this paper we analyze the KLJN system and compare with “intelligent” KLJN (iKLJN) scheme. This task requires the determination of the applied resistors and the identification of the various superpositions of known and unknown noise components. Some statistical tools to determine how the duration of the bit exchange window (averaging time) influences the performance of secure bit exchange will be explored.
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.
Abstract We introduce seven new versions of the Kirchhoff-Law-Johnson-(like)-Noise (KLJN) classical physical secure key exchange scheme and a new transient protocol for practically-perfect security. While these practical improvements offer progressively enhanced security and/or speed for non-ideal conditions, the fundamental physical laws providing the security remain the same. In the "intelligent" KLJN (iKLJN) scheme, Alice and Bob utilize the fact that they exactly know not only their own resistor value but also the stochastic time function of their own noise, which they generate before feeding it into the loop. By using this extra information, they can reduce the duration of exchanging a single bit and in this way they achieve not only higher speed but also an enhanced security because Eve’s information will significantly be reduced due to smaller statistics. In the "multiple" KLJN (MKLJN) system, Alice and Bob have publicly known identical sets of different resistors with a proper, publicly known truth table about the bit-interpretation of their combination. In this new situation, for Eve to succeed, it is not enough to find out which end has the higher resistor. Eve must exactly identify the actual resistor values at both sides. In the "keyed" KLJN (KKLJN) system, by using secure communication with a formerly shared key, Alice and Bob share a proper time-dependent truth table for the bit-interpretation of the resistor situation for each secure bit exchange step during generating the next key. In this new situation, for Eve to succeed, it is not enough to find out the resistor values at the two ends. Eve must also know the former key. The remaining four KLJN schemes are the combinations of the above protocols to synergically enhance the security properties. These are: the "intelligent-multiple" (iMKLJN), the "intelligent-keyed" (iKKLJN), the "keyed-multiple" (KMKLJN) and the "intelligent-keyed-multiple" (iKMKLJN) KLJN key exchange systems. Finally, we introduce a new transient-protocol offering practically-perfect security without privacy amplification, which is not needed in practical applications but it is shown for the sake of ongoing discussions.