## 1 Introduction
### On the KLJN Secure Key Distribution  
The KLJN scheme [30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52] utilizes the thermal noise of resistors (or the emulation of that by a specific hardware). In the core scheme [PERSON] and [PERSON] have two identical pairs of resistors, \(R_{\rm L}\) and \(R_{\rm H}\) (\(R_{\rm L}<R_{\rm H}\)), respectively (see Figure 1). The key exchange protocol of a single secure bit is as follows: [PERSON] and [PERSON] randomly pick one of their resistors (\(R_{\rm L}\) or \(R_{\rm H}\)), connect it to the wire channel, and keep them there during the bit exchange period while they execute voltage and/or current measurements to learn the resistor value at the other end (see below). The noise voltage generators shown in Figure 1 with each resistor can be the resistors' own thermal noise, or an external noise generator emulating a much higher, common _noise-temperature_ that is publicly agreed. The power density spectra of the voltage and current in the channel are given by the Johnson-Nyquist formulas [11]  
\[S_{u}(f)=\frac{4 kTR_{\rm A}R_{\rm B}}{R_{\rm A}+R_{\rm B}}, \tag{1}\]  
\[S_{i}(f)=\frac{4 kT}{R_{\rm A}+R_{\rm B}} \tag{2}\]  
where \(k\) is the Boltzmann's constant, \(T\) is the common temperature, and \(R_{\rm A}\) and \(R_{\rm B}\) are the actually connected resistances at [PERSON]'s and [PERSON]'s ends, respectively, with \(R_{\rm A},R_{\rm B}\in\{R_{\rm L},R_{\rm H}\}\). After the measurement and spectral analysis, Equations (1) and (2) have two unknown variables, namely,the values of \(R_{\rm A}\) and \(R_{\rm B}\), and thus [PERSON] can find the values of the connected resistors, but not necessarily their locations, by solving these equations. We can represent the four different situations of the connected resistors (\(R_{\rm L}\) and/or \(R_{\rm H}\)) at [PERSON]'s and [PERSON]'s ends by the indices of the connected resistors, LL, LH, HL, and HH, respectively. As all the resistors have the same (noise) temperature, the ideal system is in thermal equilibrium, where the second law of thermodynamics guarantees zero net power-flow. Hence, [PERSON] cannot use the evaluation of power flow to determine the locations of the momentarily connected resistors unless they have the same resistance values. On the other hand, [PERSON] and [PERSON] can determine the connected resistor values by using Equations (1) or (2) since they know the value of their own connected resistors. When \(R_{\rm A}=R_{\rm B}\), which happens at 50% of the bit exchange attempts, the results are discarded. On Former Attacks Against the KLJN Secure Key Distribution  
Several attacks have been proposed but no attack has been able to compromise the unconditional security of the KLJN scheme because each known attack can efficiently be nullified by a corresponding defense scheme. The attacks can be categorized into two classes:  
(i) Passive attacks that utilize the non-ideal or parasitic features in a practical KLJN system for information leaks. Non-zero wire resistance (see [37; 38]) poses the greatest known threat, and the most efficient attack is power balance measurement (Second Law Attack) [39]. An efficient defense is based on a proper temperature-offset [39; 40]. Temperature-inaccuracies [41] and resistance-inaccuracies [42] can also cause information leaks. On the other hand, these inaccuracies can compensate for each other [43] if used in a creative way. Non-zero cable capacitance [44] or cable inductance can also yield information leaks that can be fixed by specific designs including the proper choice of frequency range and privacy amplification. Transients can also be utilized for attack [45] but there are various means of defense against these [46; 47]. The newest KLJN system, the random-resistor-random-temperature KLJN (RRRT-KLJN) scheme [48], is robust against the above vulnerabilities, or at least, no known attack exists against it yet. (ii) Active attacks, where [PERSON] either modifies the information channel or she injects an extra current into it.