# An Image Encryption Algorithm Based on Time-Delay and Random Insertion

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Proposed Cryptosystem

#### 2.1. Image Cryptosystem

#### 2.2. Encryption Steps

- Step 1.
- Read the plain-image as P and obtain its size $m\times n$.
- Step 2.
- Compute the sum s over the plain-image.
- Step 3.
- Generate the two sets H and L by simulating a time-delay phenomena.
- Step 4.
- Apply circular permutation to both rows and columns, and obtain T.
- Step 5.
- Insert random numbers into the permuted image T and obtain B by simulating a one-time pad.
- Step 6.
- Iterate the chaotic map again and obtain matrix M.
- Step 7.
- Apply the diffusion operation to revise the gray distribution, on both row and column dimensions.
- Step 8.
- Obtain the cipher-image E.

#### 2.3. Decryption

## 3. Experimental Results

## 4. Security Analyses

#### 4.1. Key Space Analysis

#### 4.2. Histogram Analysis

#### 4.3. Information Entropy Analysis

#### 4.4. Key Sensitivity Analysis

#### 4.5. Differential Analysis

#### 4.6. Run Test for Randomness

#### 4.7. Comparisons

## 5. Discussion and Conclusions

- (1)
- High sensitivity to keys and the plain-image.
- (2)
- Time-delay phenomenon is simulated according to outputs of the chaotic map.
- (3)
- One-time pad is designed by inserting random numbers before diffusion.
- (4)
- The keystream used in the diffusion stage is affected by keys assigned in the permutation stage.
- (5)
- Faster speed to implement the encryption.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Experimental tests: (

**a**) plain-image of Tree; (

**b**) cipher-image of Tree; (

**c**) decrypted image of Tree; (

**d**) plain-image of Lake; (

**e**) cipher-image of Lake; (

**f**) decrypted image of Lake; (

**g**) plain-image of Building; (

**h**) cipher-image of Building; (

**i**) decrypted image of Building.

**Figure 3.**Histograms of: (

**a**) the plain-image of Lena; (

**b**) the cipher-image of Lena; (

**c**) the plain-image of Baboon; (

**d**) the cipher-image of Baboon; (

**e**) the plain-image of Boat; (

**f**) the cipher-image of Boat; (

**g**) the plain-image of Peppers; (

**h**) the cipher-image of Peppers.

**Figure 5.**Key sensitivity tests for Lena: (

**a**) decryption with ${x}_{0}+{10}^{-14}$; (

**b**) decryption with ${y}_{0}+{10}^{-14}$; (

**c**) decryption with ${\widehat{x}}_{0}+{10}^{-14}$; (

**d**) decryption with ${\widehat{y}}_{0}+{10}^{-14}$.

Test Images | Plain-Image | Cipher-Image |
---|---|---|

Lena | 7.4532 | 7.9970 |

Boat | 7.1238 | 7.9993 |

Peppers | 7.5715 | 7.9992 |

Baboon | 7.3579 | 7.9993 |

Test Images | UACI | NPCR |
---|---|---|

Lena | 33.3537 | 99.6109 |

Boat | 33.4899 | 99.5900 |

Peppers | 33.5186 | 99.6044 |

Baboon | 33.5280 | 99.6136 |

Images | Lena | Peppers | Boat | Baboon |
---|---|---|---|---|

Results | 0 | 0 | 0 | 0 |

Randomness | Pass | Pass | Pass | Pass |

Channels | R | G | B | Average |
---|---|---|---|---|

Ref. [1] | 7.9903 | 7.9890 | 7.9893 | 7.9895 |

Ref. [38] | 7.9871 | 7.9881 | 7.9878 | 7.9877 |

Ref. [40] | 7.9278 | 7.9744 | 7.9705 | 7.9576 |

Ref. [46] | 7.9969 | 7.9974 | 7.9970 | 7.9971 |

Ref. [47] | 7.9895 | 7.9897 | 7.9893 | 7.9895 |

Ref. [48] | 7.9968 | 7.9970 | 7.9972 | 7.9970 |

Ours | 7.9977 | 7.9973 | 7.9975 | 7.9975 |

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**MDPI and ACS Style**

Huang, X.; Ye, G.
An Image Encryption Algorithm Based on Time-Delay and Random Insertion. *Entropy* **2018**, *20*, 974.
https://doi.org/10.3390/e20120974

**AMA Style**

Huang X, Ye G.
An Image Encryption Algorithm Based on Time-Delay and Random Insertion. *Entropy*. 2018; 20(12):974.
https://doi.org/10.3390/e20120974

**Chicago/Turabian Style**

Huang, Xiaoling, and Guodong Ye.
2018. "An Image Encryption Algorithm Based on Time-Delay and Random Insertion" *Entropy* 20, no. 12: 974.
https://doi.org/10.3390/e20120974