# A Static-loop-current Attack Against the Kirchhoff-Law-Johnson-Noise (KLJN) Secure Key Exchange System

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. On Secure Communications

#### 1.1.1. Secure Key Exchange

#### 1.1.2. Conditional Security

#### 1.1.3. Unconditional (Information-Theoretic) Security

#### 1.2. On the KLJN Secure Key Distribution

#### On Former Attacks Against the KLJN Secure Key Distribution

## 2. The New Attack Scheme Utilizing Deterministic Loop Currents

#### 2.1. The Situation that Eve Utilizes for the Attack

_{DC}is its DC component

_{DCw}and U

_{ACw}(t) represent the DC and AC voltage components in the wire, respectively. The DC component can be written as

_{H}> R

_{L}, in this particular situation

#### 2.2. The Attack Scheme

## 3. Simulation Results

## 4. Some of the Possible Defense Techniques Against the Attack

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The core of the Kirchhoff-Law-Johnson-Noise (KLJN) system. ${U}_{\mathrm{HAn}}(t)$, ${U}_{\mathrm{LAn}}(t)$, ${U}_{\mathrm{HBn}}(t)$, and ${U}_{\mathrm{LBn}}(t)$ are the (thermal) noise voltage generators for the related resistances ${R}_{\mathrm{H}}$ and ${R}_{\mathrm{L}}$, respectively. $U(t)$ and $I(t)$ are the measured noise voltage and the current in the wire that are used to evaluate the power density spectra ${S}_{u}(f)$ and ${S}_{i}(f)$, respectively.

**Figure 2.**The KLJN system with ground loop voltage. Here ${U}_{\mathrm{An}}\in \{{U}_{\mathrm{LAn}};{U}_{\mathrm{HAn}}\}$ and ${U}_{\mathrm{Bn}}\in \{{U}_{\mathrm{LBn}};{U}_{\mathrm{HBn}}\}$ are the voltage noises belonging to the randomly chosen resistors, ${R}_{\mathrm{A}}\&{R}_{\mathrm{B}}\in \{{R}_{\mathrm{L}};{R}_{\mathrm{H}}\}$, belonging to Alice and Bob, respectively. ${U}_{\mathrm{DC}}$ is the ground loop DC voltage source and $U(t)$ and $I(t)$ are the voltage and current on the wire, respectively.

**Figure 4.**Eve’s correct guessing probability (p) of key bits versus temperatures at bandwidth $\Delta f$ equals 10

^{6}Hz, for key length 700 bits, and duration/bit (number of samples/bit) 200, 500, and 1000, respectively. The limit p = 0.5 stands for perfect security.

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**MDPI and ACS Style**

Melhem, M.Y.; Kish, L.B. A Static-loop-current Attack Against the Kirchhoff-Law-Johnson-Noise (KLJN) Secure Key Exchange System. *Appl. Sci.* **2019**, *9*, 666.
https://doi.org/10.3390/app9040666

**AMA Style**

Melhem MY, Kish LB. A Static-loop-current Attack Against the Kirchhoff-Law-Johnson-Noise (KLJN) Secure Key Exchange System. *Applied Sciences*. 2019; 9(4):666.
https://doi.org/10.3390/app9040666

**Chicago/Turabian Style**

Melhem, Mutaz Y., and Laszlo B. Kish. 2019. "A Static-loop-current Attack Against the Kirchhoff-Law-Johnson-Noise (KLJN) Secure Key Exchange System" *Applied Sciences* 9, no. 4: 666.
https://doi.org/10.3390/app9040666