# Dynamic Secure Key Distribution Based on Dispersion Equalization and Cellular Automata for Optical Transmission

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## Abstract

**:**

## 1. Introduction

## 2. Operating Principle

#### 2.1. FDE Algorithm

#### 2.2. CA Iteration

## 3. Simulations and Discussions

#### 3.1. FDE Algorithm Performance

#### 3.2. Effective Elimination of Key Inconsistency

#### 3.3. Proof of Security under Eavesdropping Attack Situations

#### 3.4. Dynamic Key Generation

#### 3.4.1. Operation of Input Parameter Variation Interval

#### 3.4.2. Operation of Local Fiber

#### 3.4.3. Operation of CA Iteration

#### 3.5. Analysis of Security Enhancement

#### 3.6. Assessment of Overall Scheme

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**(

**a**) Effect of dispersion on signal before and after transmission. (

**b**) The first and last intercept length of overlap on each sub-block of FFT length. (

**c**) Overlapping FDE algorithm processing, FFT: Fast Fourier Transform, IFFT: Inverse Fast Fourier Transform.

**Figure 6.**The DECA key distribution scheme system setup based on bidirectional fiber link. CW: continuous wave; PRBS: pseudo random bit sequence; EDFA: Erbium-Doped Fiber Amplifier; OC: optical coupler; OBPF: optical band-pass filter.

**Figure 7.**(

**a**–

**d**) The BER changing trend with input parameter variation of FDE on different transmission lengths.

**Figure 8.**(

**a**) The optimal parameter with the variation of FDE input parameter interval where Alice and Bob start to reach the same from green line of interval 23. (

**b**) KER between Alice–Bob of different variation intervals.

**Figure 9.**(

**a**) Transmission fiber link where eavesdropping position variation ranges from point A to point B. (

**b**) Eve’s obtained optimal parameter with the eavesdropping position variation compared with Alice–Bob.

**Figure 10.**(

**a**,

**b**) The BER changing trend with different input parameter variation of FDE on Alice, Bob and Eve.

**Figure 11.**(

**a**) Optimal parameter with local fiber variation among Alice, Bob and Eve. (

**b**) KER with local fiber variation of Alice–Bob and Alice–Eve. (

**c**) Example of dynamic key generation with local fiber variation (The number in red represents an error).

**Figure 12.**(

**a**) Example of dynamic key generation with iteration times from 1 to 40 on the same key base (The number in red represents an error). (

**b**) KER with iteration times from 1 to 40 of Alice-Bob and Alice-Eve on the same key base.

**Table 1.**CA rule of k = 2 (${D}_{core}=440.016,\phantom{\rule{0.277778em}{0ex}}{D}_{rule}={\left(208\right)}_{10}={\left(11010000\right)}_{2}$).

$({\mathit{s}}_{\mathit{i}-1}^{\mathit{t}},{\mathit{s}}_{\mathit{i}}^{\mathit{t}},{\mathit{s}}_{\mathit{i}+1}^{\mathit{t}})$ | ${\mathit{s}}_{\mathit{i}}^{\mathit{t}+1}$ | $({\mathit{s}}_{\mathit{i}-1}^{\mathit{t}},{\mathit{s}}_{\mathit{i}}^{\mathit{t}},{\mathit{s}}_{\mathit{i}+1}^{\mathit{t}})$ | ${\mathit{s}}_{\mathit{i}}^{\mathit{t}+1}$ |
---|---|---|---|

000 | 1 | 100 | 0 |

001 | 1 | 101 | 0 |

010 | 0 | 110 | 0 |

011 | 1 | 111 | 0 |

**Table 2.**CA rule with k = 4 (${D}_{core}=440.016,\phantom{\rule{0.277778em}{0ex}}{D}_{rule}={\left(208\right)}_{10}={\left(11010000\right)}_{2}$).

$({\mathit{s}}_{\mathit{i}-1}^{\mathit{t}},{\mathit{s}}_{\mathit{i}}^{\mathit{t}},{\mathit{s}}_{\mathit{i}+1}^{\mathit{t}})$ | ${\mathit{s}}_{\mathit{i}}^{\mathit{t}+1}$ | ${\mathit{s}}_{\mathit{i}}^{\mathit{t}+1}$ | ${\mathit{s}}_{\mathit{i}}^{\mathit{t}+1}$ | ${\mathit{s}}_{\mathit{i}}^{\mathit{t}+1}$ | |||
---|---|---|---|---|---|---|---|

TTT | A | TTG | C | TTC | G | TTA | T |

TGT | C | TGG | A | TGC | T | TGA | G |

TCT | A | TCG | C | TCC | G | TCA | T |

TAT | C | TAG | A | TAC | T | TAA | G |

GTT | T | GTG | G | GTC | C | GTA | A |

GGT | G | GGG | T | GGC | A | GGA | C |

GCT | G | GCG | T | GCC | A | GCA | C |

GAT | T | GAG | G | GAC | C | GAA | A |

CTT | C | CTG | A | CTC | T | CTA | G |

CGT | A | CGG | C | CGC | G | CGA | T |

CCT | T | CCG | G | CCC | C | CCA | A |

CAT | G | CAG | T | CAC | A | CAA | C |

ATT | T | ATG | G | ATC | C | ATA | A |

AGT | G | AGG | T | AGC | A | AGA | C |

ACT | C | ACG | A | ACC | T | ACA | G |

AAT | A | AAG | C | AAC | G | AAA | T |

Index | p-Value |
---|---|

Frequency | 0.455228 |

Block frequency | 0.042503 |

Runs | 0.746962 |

Longest Run | 0.901933 |

Rank | 0.270256 |

FFT | 0.574617 |

Non-Overlapping Template | 0.999999 |

Overlapping Template | 0.592848 |

Universal | 0.638407 |

Linear Complexity | 0.704754 |

Serial | 0.959372 |

Approximate Entropy | 0.993281 |

Cumulative sum | 0.226876 |

Random Excursions | 0.390989 |

Random Excursion Variant | 0.114968 |

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**MDPI and ACS Style**

Cui, J.; Kong, W.; Liu, Z.; Ji, Y.
Dynamic Secure Key Distribution Based on Dispersion Equalization and Cellular Automata for Optical Transmission. *Photonics* **2023**, *10*, 1308.
https://doi.org/10.3390/photonics10121308

**AMA Style**

Cui J, Kong W, Liu Z, Ji Y.
Dynamic Secure Key Distribution Based on Dispersion Equalization and Cellular Automata for Optical Transmission. *Photonics*. 2023; 10(12):1308.
https://doi.org/10.3390/photonics10121308

**Chicago/Turabian Style**

Cui, Jiabin, Wei Kong, Zhaoyang Liu, and Yuefeng Ji.
2023. "Dynamic Secure Key Distribution Based on Dispersion Equalization and Cellular Automata for Optical Transmission" *Photonics* 10, no. 12: 1308.
https://doi.org/10.3390/photonics10121308