Kirchhoff's Law and Johnson's Noise: A Reliable Bit Detection Method and System for Secure Key Change Schemes

Abstract

This invention describes a Kirchhoff-Law-Johnson-Noise switch switching scheme in which a cable line (KH) connects a first terminal (Tr1) to a second terminal (Tr2), where if the first terminal bit is 0, the second terminal bit is determined by current measurements across the cable line (KH); and if the first terminal bit is 1, the second terminal bit is determined by voltage measurements across the cable line (KH).This relates to a reliable bit determination method for Kirchhoff's Law-Johnson Noise switch-exchange schemes involving steps and a reliable bit determination system for Kirchhoff's Law-Johnson Noise switch-exchange schemes involving a detector or processing unit that determines the second terminal bit by current measurements in the cable line (KH) if the first terminal bit is 0, and the second terminal bit by voltage measurements in the cable line (KH) if the first terminal bit is 1, in a Kirchhoff's Law-Johnson Noise switch-exchange scheme involving a cable line (KH) connecting a first terminal (Tr1) to a second terminal (Tr2).

Description

21644.53 1 TARIFF KIRCHHOFF-LAW-JOHNSON-NOISE SAFETY SWITCH A RELIABLE BIT DETERMINATION FOR CHANGE SCHEMES METHOD AND SYSTEM Technical Area 5 This invention relates to Kirchhoff's Law-Johnson Noise secure key exchange schemes. It relates to a reliable bit determination method and system. Before the Invention Today, data transmission is essential for industry, the defense industry, the economy, education, 10 It has become an integral part of entertainment and personal life. Therefore How to ensure secure data transmission is clearly one of the most important issues today. This is one of the problems. There are many methods and algorithms in technology for secure data transmission. It has been improved. The methods currently used are today's transaction processes. Encrypting the data with a code of such complexity that it is practically unbreakable given their capabilities. 15 It is then based on the principle of data transmission. However, the current process Data encryption-based data is becoming increasingly common as their capacities are growing exponentially. Transmission security methods are increasingly losing their reliability. Today's quantum computers will have processing capabilities far exceeding their current capacity With the introduction of these encryption methods into our lives, data security has increased by 20 It is considered almost certain that it will not be able to provide this. Therefore, the data... Apart from conditional methods such as encryption principles, data transmission security Alternative methods for providing this have become necessary. These alternative methods include: One of them is quantum encryption. Here, malicious actors want to listen to the communication line. Eavesdroppers (Eve)) can be identified. Thus, an eavesdropper can be identified up to 25 times. When detected, data transmission is interrupted and redirected to a different secure channel. It is continued. However, because quantum encryption methods involve high technology... And therefore, because it is a costly solution, it is not used in most daily life. 21644.53 2 It is not feasible to use it in practice. Another alternative method is... Kirchhoff-Law-Johnson-Noise (KLJN) It is referred to as the KLJN method / system. The KLJN method / system is used in classical physics. It is based on simplicity and includes a few resistors, a switch, and a communication line (cable). Therefore, the KLJN method is an effective, simple, and inexpensive way to secure data transmission. By offering a solution, it provides the most important methods for future data security. It is a strong candidate. Thermal noise of resistors (Johnson) in the method / system (noise) is used as a signal source between the parties (in the literature, Alice (and referred to as Bob) a secure communication is established. Each of the transmission lines There are two pairs of identical resistors at each end, called RL and RH. It receives this information for each condition at both ends of the transmission line (RL-RL, RL-RH, RH-RL, RH- RH) a pair of bits (00, 01, 10, 11) are transferred. The two transmission lines... in cases where the parties at the ends (Alice and Bob) choose different resistances (RL-RH, (RH-RL conditions) a medium mean square noise voltage level on the line (intermediate mean-square noise voltage level) occurs. Malicious listeners 15 When they want to listen to the transmission line, this is the mean square noise on the transmission line. voltage level using the current and voltage values ​​on the line They will be able to measure it. However, malicious listeners may notice the middle ground between the parties (Alice and Bob). Since they could not determine the contribution of mean square noise to the voltage level, RL- RH and RH-RL states cannot be distinguished from each other. Thus, the data on the communication line is 20 A one-bit, unconditional security is ensured during the transfer. KLJN-based methods and systems that utilize these methods represent the future of data transmission. While they may seem like suitable options for security, they are not perfect. Line current and voltage variances and the correlation between them, bit errors This gives rise to the reason. KLJN-based methods and 25 researchers using these methods. systems must ensure both data transmission security and data transmission reliability. For this, the probability of bit errors (BEM) needs to be reduced or eliminated. Therefore... Error-free data transmission is ensured. 21644.53 3 Therefore, in KLJN-based methods and systems that use these methods a reliable bit determination method to ensure data reliability and The system is technically required. Detailed Description of the Invention The Kirchhoff-Johnson Law was implemented to achieve the purpose of this invention. Determining a trusted bit for noise-based secure key exchange schemes. The method and system are shown in the attached figures, and the details of the invention are in section 10 of the description. All aspects should be considered during the evaluation; Figure 1. Secure key exchange based on Kirchhoff's Law and Johnson's Noise. This is a flowchart representation of an example application for diagrams. Figure 2. Threshold-based noise for KLJN diagrams used prior to this technique. 15 This is a schematic representation of voltage difference detection. Figure 3. Threshold-based noise for KLJN diagrams used prior to this technique. This is a schematic representation of current difference sensing. Figure 4. The inventive reliable bit determination method and inventive bit determination method in a KLJN schematic. BHO 20 uses a system that measures both voltage and current. BHO's performance, considering only voltage measurements. It is a graphical representation comparing performance. The elements in the figures are individually numbered, and each number corresponds to a specific element. given below. 25 Tr1: First terminal (Alice or Bob) Tr2: Second terminal (Bob or Alice) KH: Cable line 21644.53 4 00, 10, 11, 01: Binary bit states RL: Low resistance RH: High resistance v(t): Voltage change waveform i(t): Current change waveform example 5 σ002, σ102, σ112, σ012: Bit state variances 2TbΔf: Maximum number of samples per bit. The invention is a secure key based on Kirchhoff's Law-Johnson Noise (KLJN). It relates to a reliable bit determination method and system for exchange schemes. 10 Here, key exchange is also called bit exchange, i.e., data transfer. It should be read. For a better understanding of the invention, the Kirchhoff-Johnson Law should be considered. Here's how noise-based secure key exchange schemes work. This is explained. Kirchhoff's Law-Johnson Noise based secure key. An example diagram illustrating the change is shown in Figure 1. Figure 1 shows the invention as early as 15 This is given as an example for better understanding, and the scope of the invention is defined by this example. should not be restricted. A secure key exchange scheme based on Kirchhoff's Law and Johnson's Noise, two terminal (communicating parties: Alice and Bob) (hereinafter referred to as Alice and Bob) (will pass) As explained before, the technique will ensure secure data transmission 20 The diagram was created with a couple on Alice's side and a couple on Bob's side. There are pairs of resistors (RL and RH) that are identical to each other. Alice and Bob are one They are connected to each other via cable lines (CC). Communication (bit transfer) is Johnson- Nyquist noise (thermal noise, Johnson noise, or Nyquist noise) (thermal noise, Johnson noise, or Nyquist noise) based on the use of voltages 25 It is based on. Here, for each bit duration (bit change period) of Tb per second, Alice And Bob chooses one of the resistors with RL or RH ohms based on the information bits. Alice The resistors chosen by Bob are represented by RA and RB, respectively. So, bit 0. and bit 1 are connected by resistors RL, which is a low-resistance resistor, and RH, which is a high-resistance resistor, respectively. 21644.53 It is represented. Here we can consider the relationship RH=αRL. From this point of view, The KLJN scheme, based on the incoming information bits, simultaneously transmits a signal on both sides of the connection. an example of index modulation (IM) where the resistance index is selected It is possible to consider the bit transmission operation of the KLJN scheme, noise power. spectral density level, that is, a kind of 5 for the square of the average noise voltage. Modulation of noise fluctuations on the channel where IM is performed. It can be thought of as follows: The resistor selection process here is like Alice and Bob choosing a resistor based on a common voltage and... Current measurements are repeated every Tb per second. Each discrete time interval... The process of selecting a resistor in this situation is simply done randomly on the cable line (KH). It takes samples from fluctuating voltage v(t) or current i(t) waveforms. Another 10 In other words, Alice and Bob use a system to take samples of noise voltage and current. It is equipped with sampling devices. As shown in Figure 2, only noise While sampling their voltages is a simple way to detect bits, 00 and Due to the proximity of voltage-noise variances for 01 / 10 cases, in the system Statistical decision errors may occur. This situation arises when noise voltages are 15. This significantly reduces the quality and reliability of the determination. On the other hand, as shown in Figure 3, noise is the inverse of voltage-based sensing. In the case of noise current-based variance detection, which has an effect on nearby locations Due to this, error events of 11 and 1 / 10 are dominant. The invention addresses this critically unreliable bit detection. This was done to resolve their problems. 20 The first and second bits represent the bits chosen by Alice and Bob, respectively. The variance values ​​of the following four selected binary bit states (00, 01, 10, 11) as indicated below. Here, the voltage waveform on the cable line (KH) is shown. The samples taken are based on Kirchhoff's law and Johnson's thermal noise formula. The distribution will be Gaussian with the following variance values: 25 21644.53 6 Here are examples taken from the voltage waveform on the σi2 cable line (KH). noise variance values, Δf noise bandwidth, k Boltzmann constant and T The temperature is shown in Kelvin, and α represents the ratio of the large and small resistance values. The KLJN scheme takes a limited number of samples during a specified bit duration. It therefore has random bit errors. Similarly, noise stream samples The noise variances for are obtained as follows: Here are 10 examples taken from the current waveform on the s2 cable line (KH). It expresses variance values. Alice and Bob depend on each other's choice. They are susceptible to certain bit errors. Due to symmetry, Alice and Bob share the same bit. It has a probability of error (BHO). For ease of explanation, here's Alice. We are focusing. Selected Bits (Alice / Bob) 00 01 10 11 Decisions 00 Alice True Mistake PA (01 00) - - Bob Doğru - Mistake PB (10 00) - 01 Alice Mistake PA (00 01) TRUE - - E1 E1' E1'' E2 E2' E2'' 21644.53 7 Bob - That's right - Mistake PB (11 01) Alice - - That's right Mistake PA (11 10) Bob Mistake PB (00 10) - TRUE - 11 Alice - - Mistake PA (00 11) TRUE Bob - Mistake PB (01 11) - TRUE Table 1. Voltage-based fault conditions. Table 1 shows all possible failures in four possible resistor selection scenarios for Alice and Bob. situations (situations where only voltage measurements are taken for ease of display) (considered) is shown. Here, possible resistance choices are “RL – The corresponding values ​​are "RL", "RL – RH", "RH – RL", "RH – RH". Here, the corresponding value for Alice and Bob is 5. The probabilities of the incoming error events are shown as PA(.) and PB(.) respectively. When evaluating BHO, all error conditions are considered as well as safe bit replacement. This should be taken into consideration. There are simply two reasons for this. Firstly, it is hidden and ultra-low. Under strong communication, the insecure bit exchange states 00 and 11 also occur. It can be used for secure data transmission. In terms of encryption, general standards include 10. and sufficiently long, such as 256-bit keys commonly used in protocols. decrypting messages transmitted with 50% compromised bits for the keys It will still be difficult to solve. The second is 00 and 11, which are insecure bit changes. These states can be confused with the safe bit changes of states 01 and 10. Or, conversely, the safe bit exchange cases 01 and 10 are valid in 15. It can be confused with the unsafe bit changes of the 00 and 11 states. Therefore, focusing only on the 00 / 11  01 / 10 error case is generally recommended. It can be misleading. During each bit of time, both Alice and Bob use the cable as shown in Figure 1. Thermal noise voltage v(t) and thermal noise current 20 on both sides of the line (KH) Thermal noise on cable line (KH) to determine i(t) variances 21644.53 8 They took samples of the voltage v(t) and the thermal noise current i(t). It is assumed. To simplify the analysis, let's first look at voltage examples. Zero k-th independent samples following a Gaussian distribution with zero mean and variance 𝜎2 where the noise sample is denoted by xk, [where the variance σi2 has three possible values ​​5 [low σ002, medium σ012, high σ112)]. Accordingly, the noise variance estimate is as follows: It is obtained as follows: Considering the central limit theorem (CLT), The sample variance given above is distributed with a mean σi2 and a variance of 2σi4 / N. It is becoming Guassian. External noise generators and / or band-limited cable lines The band-limited nature of noise that may result from the use of (KH), Alice and There is no definite limit to the number of N samples that Bob can take from his line. It states that, assuming a noise bandwidth of Δf Hz, Wiener-Khinchin The theorem requires a maximum of 15 bits per bit to provide statistically independent samples. It indicates that N=2TbΔf can be sampled. Using a very similar methodology, N Current noise variance estimation can also be obtained using the current sample. As shown in Figure 2, in the case of voltage-based measurement, the noise variance considering statistical decision errors arising from the randomness of the estimation When present, the corresponding error event for states 00, 11, 01, and 11 is 20. The probabilities are obtained as follows: E3 21644.53 9 Here, ϒi represents the selected threshold values, Q(.), represents the Gaussian Q function, and 00 Error events involving the state are dominant. In light of these, the generation of bit 0 and bit 1... Given a 50% probability for each, voltage measurements alone are 5 Taking this into consideration, the BHO of the KLJN scheme is obtained as follows: E4 E4' E4'' E4. 21644.53 Here, β represents the threshold normalization, and the threshold values ​​are as follows: It is normalized as follows: ϒ1=βσ2 and ϒ2=κσ2 for variance σ002= σ2. Similarly, KLJN The BHO of the diagram is obtained as follows, taking into account only the current measurements: 5 is done: Here, the new normalized thresholds for noise stream samples are ϒ3=ηs2 and 10 ϒ4 is defined as ξs2, and in the voltage case where N samples are used. It means a sample size defined in a very similar way. The invention concerns a reliable bit determination method and system for voltage and current. on the fact that error events of 00 and 11 were dominant in the measurements, respectively It has been established. Therefore, in the reliable bit determination method and system, 15 Alice and Bob are allowed to choose the types of measurements based on their own bits. In other words, in the invention, if Alice's (or Bob's) own bit is 0... Current measurements are considered, or voltage measurements are considered if its own bit is 1. This is because Alice's current measurements are for error condition 00  01 and 10  11. The reason for the error is that Alice's voltage measurements are less likely to be accurate. This 20 From that point of view, Alice and Bob's own reliable bit determination method and system. By using the information from their bits, they can get information from the other side (Alice from Bob, Bob from...). The probability of error in detecting the transmitted bit (by Alice) is minimized. E5 E6 21644.53 11 Positions 00 11 01 10 Alice Current Measurement Voltage Measurement Current Measurement Voltage Measurement Bob Current Measurement Voltage Measurement Voltage Measurement Current Measurement Mistake Their situations P̃A (00 01) P̃B (00 10) P̃A (11 10) P̃B (11 01) P̃A (01 00) P̃B (01 11) P̃A (10 11) P̃B (10 00) Table 2. Positions used in the reliable bit determination method and system. The procedure shows which measurement values ​​to use. Based on this information, Alice and Bob made their decisions according to the procedures in Table 2. They will provide. Accordingly, a reliable bit determination method and system. The BHO of the KLJN scheme used is as follows: Here, BHO can be distinguished from the probabilities of voltage-based fault events. The probability expression P̃(.) is used for the name. Here, κ and ξ are normalized thresholds. It expresses their values. As can be seen from this expression, the probability of bit errors in this invention... (Pb) is not dependent on fragile thresholds, β and η, and is only a weaker probability. It consists of terms that minimize the probability of a bit error (Pb) for given α and N. The optimum κ and ξ values ​​can be determined by selecting them. E7' E7 21644.53 12 Figure 4 shows the KLJN schematic of the invented reliable bit determination method and system. BHO performance, which uses both voltage and current measurements, compared with BHO performance where only voltage measurements are considered A graph is included. The example shown in the graph is reliable bit identification. In the method and system, for the optimization of thresholds, κ=3.1512 and ξ=0.3148 5 N=100 was considered, satisfying the given values. As can be seen in Figure 4, the subject of the invention is a reliable bit determination method and Adaptive examples are shown between the voltage and current samples generated by the system. Much better BHO performance thanks to the ability to calculate variance. is provided. In this context, the subject of the invention is a reliable bit determination method and 10 a limited number of KLJN-based secure key exchange schemes through the system By using a noise sample, it obtains lower error probabilities. Thus, with the help of invention... Reliability and availability of KLJN-based secure key exchange schemes. Its potential has been increased. The subject of the invention is 15 Kirchhoff-Law-Johnson-Noise switch change schemes. A reliable bit determination method involves the following steps: - a cable line connecting a first terminal (Tr1) to a second terminal (Tr2) A Kirchhoff-Law-Johnson-Noise key change containing (KH). In the diagram, if the bit of the first terminal is 0, then the bit of the second terminal is on the cable line. (KH) determination by current measurements; 20 - If the bit of the first terminal is 1, then the bit of the second terminal is (KH) on the cable line. Determined by voltage measurements. The subject of the invention is Kirchhoff's Law-Johnson Noise switch change schemes. a reliable bit determination system, 25 a cable line (KH) connecting a first terminal (Tr1) to a second terminal (Tr2) the first in a Kirchhoff-Law-Johnson-Noise switchover scheme 21644.53 13 If the first terminal bit is 0, the second terminal bit is measured with current measurements (KH) in the cable line. If the bit of the first terminal is 1, then the bit of the second terminal is determined by the cable line (KH). It contains a detector that determines voltage through measurements. Here, the first terminal (Tr1) can be Alice or Bob. First terminal (Tr1) Alice If the second terminal (Tr2) is Bob, or if the first terminal (Tr1) is Bob, then the second 5 The terminal (Tr2) is Alice. As previously mentioned, the key exchange here... This expression should also be read as bit exchange, i.e., data transfer.

Claims

21644.53 14 REQUESTS 1. – a cable line connecting a first terminal (Tr1) to a second terminal (Tr2) A Kirchhoff-Law-Johnson-Noise key change containing (KH). In the diagram, if the bit of the first terminal is 0, then the bit of the second terminal is 5 on the cable line. (KH) determination by current measurements; - If the first terminal bit is 1, then the second terminal bit must be the voltage across the cable line (KH). determined by measurements; The Kirchhoff-Law-Johnson-Noise key change involves the following steps. A reliable bit determination method for schematics. 10 2. A cable line connecting a first terminal (Tr1) to a second terminal (Tr2). A Kirchhoff-Law-Johnson-Noise key change containing (KH). In the diagram, if the bit of the first terminal is 0, then the bit of the second terminal is in the cable line. (KH) determined by current measurements, if the bit of the first terminal is 1, the second terminal is 15 a detector that determines the bit by measuring the voltage in the cable line (KH) or Kirchhoff's Law-Johnson Noise switch containing a processing unit A reliable bit determination system for schematics.

3. A cable line connecting a first terminal (Tr1) to a second terminal (Tr2) 20 A Kirchhoff-Law-Johnson-Noise key change containing (KH). In the diagram, if the bit of the first terminal is 0, then the bit of the second terminal is in the cable line. (KH) Determination by current measurements, if the bit of the first terminal is 1, then the second terminal a bit adapted for determining voltage measurements in the cable line (KH) Kirchhoff's Law-Johnson Noise key exchange containing the processing unit 25 A reliable bit determination system for schematics.

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