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arXiv:2110.03088 · Fluctuation and Noise Letters

Statistical Random Number Generator Attack Against the Kirchhoff-Law-Johnson-Noise (KLJN) Secure Key Exchange Protocol

Christiana Chamon, Shahriar Faysal Ferdous, László B. Kish

Published Feb 25, 2022• 8 citations
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Abstract

This paper introduces and demonstrates four new statistical attacks against the Kirchhoff-Law-Johnson-Noise (KLJN) secure key exchange scheme. The attacks utilize compromised random number generators (RNGs) at Alice’s/Bob’s site(s). The case of partial correlations between Alice’s/Bob’s and Eve’s probing noises is explored, that is, Eve’s knowledge of Alice’s and Bob’s noises is limited but not zero. We explore the bilateral situation where Eve has partial knowledge of Alice’s and Bob’s RNGs. It is shown that in this situation Eve can crack the secure key bit by taking the highest cross-correlation between her probing noises and the measured voltage noise in the wire. She can also crack the secure key bit by taking the highest cross-correlation between her noise voltages and her evaluation of Alice’s/Bob’s noise voltages. We then explore the unilateral situation in which Eve has partial knowledge of only Alice’s RNG thus only those noises (of Alice and Eve) are correlated. In this situation, Eve can still crack the secure key bit, but for sufficiently low error probability, she needs to use the whole bit exchange period for the attack. The security of the KLJN key exchange scheme, similarly to other protocols, necessitates that the RNG outputs are truly random for Eve.

DOI
10.1142/s0219477522500274

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•Jun 1, 2014•0 citations
This paper introduces and demonstrates four new statistical attacks against the Kirchhoff-Law-Johnson-Noise (KLJN) secure key exchange scheme. The attacks utilize compromised random number generators (RNGs) at Alice’s/Bob’s site(s). The case of partial correlations between Alice’s/Bob’s and Eve’s probing noises is explored, that is, Eve’s knowledge of Alice’s and Bob’s noises is limited but not zero. We explore the bilateral situation where Eve has partial knowledge of Alice’s and Bob’s RNGs. It is shown that in this situation Eve can crack the secure key bit by taking the highest cross-correlation between her probing noises and the measured voltage noise in the wire. She can also crack the secure key bit by taking the highest cross-correlation between her noise voltages and her evaluation of Alice’s/Bob’s noise voltages. We then explore the unilateral situation in which Eve has partial knowledge of only Alice’s RNG thus only those noises (of Alice and Eve) are correlated. In this situation, Eve can still crack the secure key bit, but for sufficiently low error probability, she needs to use the whole bit exchange period for the attack. The security of the KLJN key exchange scheme, similarly to other protocols, necessitates that the RNG outputs are truly random for Eve.
This paper introduces and demonstrates two new attacks against the Kirchhoff-Law-Johnson-Noise (KLJN) secure key exchange scheme. The attacks are based on random number generators with compromised security. First we explore the situation in which Eve knows the seed of both Alice's and Bob's random number generators. We show that in this situation Eve can crack the secure key bit within a fraction of the bit exchange period even if her current and voltage measurements have only a single bit of resolution. In the second attack, we explore the situation in which Eve knows the seed of only Alice's random number generator. We show that in this situation Eve can still crack the secure key bit but she needs to use the whole bit exchange period for the attack. The security of the KLJN key exchange scheme, similarly to other protocols, necessitates that the random number generator outputs are truly random for Eve.
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.
This paper demonstrates the vulnerability of the Kirchhoff-Law-Johnson-Noise (KLJN) secure key exchanger to compromised random number generator(s) even if these random numbers are used solely to generate the noises emulating the Johnson noise of Alice’s and Bob’s resistors. The attacks shown are deterministic in the sense that Eve’s knowledge of Alice’s and/or Bob’s random numbers is basically deterministic. Moreover, no statistical evaluation is needed, except for rarely occurring events of negligible, random waiting time and verification time. We explore two situations. In the first case, Eve knows both Alice’s and Bob’s random noises. We show that, in this situation, Eve can quickly crack the secure key bit by using Ohm’s Law. In the other situation, Eve knows only Bob’s random noise. Then Eve first can learn Bob’s resistance value by using Ohm’s Law. Therefore, she will have the same knowledge as Bob, thus at the end of the bit exchange period, she will know Alice’s bit.
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.
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.