# Parallel Crossed Chaotic Encryption for Hyperspectral Images

^{*}

## Abstract

**:**

## Featured Application

**This work presents a time-efficient and parallel encryption algorithm that is suitable for encrypting a significant amount of data, and that could be used to encrypt Hyperspectral Images and Hyperspectral video in real-time for remote sensing, classification, object recognition, earth monitoring, security and medical applications.**

## Abstract

## 1. Introduction

**Security**: The required level of security of encrypting passwords or other structured data could differ than the one required for visual data. A more secure algorithm could impact with a high computational cost.**Speed**: A significant difference between visual data encryption and text-based encryption is that visual data is usually much larger. If we consider a time constraint or real-time execution requirements, the speed of encryption is an important issue.**Bitstream compliance**: Visual data could have a specific data format. Algorithms for raw data such as AES do not take data format into account and this could cause unexpected crashes in the image decoding.

## 2. Chaotic Systems and Chaotic Encryption

#### 2.1. Chaotic Systems

**Deterministic**: There is no randomness involved in the system evolution, then if we know the initial condition and parameters, we will be able to predict the system.**Sensitive to initial conditions**: A chaotic system is exponentially sensitive to an initial condition, in other words, a small change in the initial condition provokes a big difference in the evolution of the system.**Aperiodic**: There is no periodicity in a chaotic system.**Bounded**: The state of a chaotic system is bounded, and it maintains chaotic inside this bounded limits.

#### 2.2. Chaotic Encryption

#### 2.3. Chaotic Image Encryption Performance

#### 2.4. Piecewise Linear Chaotic Map

## 3. Encryption for Hyperspectral Images

Algorithm 1: Parallel Crossed Chaotic Encryption. |

Data: Hyperspectral Image I |

Result: Encrypted Image ${I}_{c}$ |

Simulate all chaotic systems $\{{c}_{1},{c}_{2},{c}_{3},{c}_{s}\}$ in parallel for $max(n,m,l)$ iterations; |

Generate S-box with ${c}_{s}$; |

Upload I to GPU memory; |

In parallel apply ${I}_{c}(i,j,k)={S}_{box}\left[{c}_{3}\left(k\right)\oplus {c}_{2}\left(j\right)\oplus {c}_{1}\left(i\right)\oplus I(i,j,k)\right]$; |

Download ${I}_{c}$ to CPU memory; |

## 4. Results

^{®}E31225 3.10 GHz, with a 16 GB of RAM and a GTX 1050Ti. The algorithm was implemented in Matlab

^{®}programming language and with GPU computing support for Nvidia CUDA

^{®}. The GTX 1050Ti have 768 cores and 4 GB of memory.

^{®}(Database from http://www.imageval.com). The image size is $702\times 1000\times 148$ (we show in Figure 5 the layer 50) and the light-wave is 415–915 nm. The entropy of the original image is 6.1057 and the encrypted entropy is 7.99997, very close to the theoretical maximum entropy.

^{®}(Taken from http://www.imageval.com/scene-database/)). The dataset consists of 12 portraits of women and 12 of men with a light-wave spectrum of 415–915 nm. We show the file size and the image size.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Female Dataset | Male Dataset | ||||||||
---|---|---|---|---|---|---|---|---|---|

Name | Size (MB) | Dimensions | Name | Size (MB) | Dimensions | ||||

n | m | l | n | m | l | ||||

Female01 | 922 | 1403 | 975 | 29 | Male01 | 993 | 1349 | 965 | 41 |

Female02 | 820 | 1169 | 912 | 42 | Male02 | 974 | 1294 | 969 | 43 |

Female03 | 993 | 1346 | 935 | 46 | Male03 | 949 | 1337 | 948 | 39 |

Female04 | 906 | 1279 | 912 | 43 | Male04 | 927 | 1322 | 981 | 35 |

Female05 | 802 | 1260 | 904 | 33 | Male05 | 851 | 1379 | 969 | 24 |

Female06 | 651 | 1237 | 855 | 21 | Male06 | 894 | 1317 | 1066 | 24 |

Female07 | 1014 | 1368 | 942 | 45 | Male07 | 986 | 1447 | 1044 | 26 |

Female08 | 883 | 1322 | 955 | 33 | Male08 | 1013 | 1423 | 1059 | 30 |

Female09 | 952 | 1323 | 1043 | 31 | Male09 | 920 | 1366 | 938 | 35 |

Female10 | 763 | 1197 | 970 | 27 | Male10 | 1085 | 1271 | 1038 | 50 |

Female11 | 867 | 1213 | 929 | 42 | Male11 | 1105 | 1414 | 975 | 47 |

Female12 | 771 | 1214 | 914 | 32 | Male12 | 937 | 1317 | 981 | 36 |

Name | Serial Time (s) | Parallel Time(s) | Entropy | ||||
---|---|---|---|---|---|---|---|

Upload | Encrypt | Download | Total | Original | Encrypted | ||

Female01 | 12.4671 | 0.0194 | 0.003338 | 0.0231 | 0.045838 | 7.6478 | 7.99995 |

Female02 | 14.5577 | 0.0220 | 0.003502 | 0.0259 | 0.051482 | 6.9685 | 7.99994 |

Female03 | 18.0801 | 0.0289 | 0.004160 | 0.0323 | 0.065360 | 7.7217 | 7.99994 |

Female04 | 15.3995 | 0.0249 | 0.003745 | 0.0290 | 0.057645 | 7.4850 | 7.99994 |

Female05 | 11.4269 | 0.0188 | 0.003177 | 0.0225 | 0.044477 | 6.9084 | 7.99994 |

Female06 | 6.6332 | 0.0129 | 0.002135 | 0.0139 | 0.028935 | 7.5043 | 7.99996 |

Female07 | 17.8849 | 0.0286 | 0.004158 | 0.0332 | 0.065958 | 7.7350 | 7.99997 |

Female08 | 12.8754 | 0.0208 | 0.003407 | 0.0249 | 0.049107 | 7.5038 | 7.99994 |

Female09 | 13.5488 | 0.0230 | 0.005120 | 0.0420 | 0.070120 | 6.0217 | 7.99995 |

Female10 | 10.5763 | 0.0164 | 0.003324 | 0.0186 | 0.038324 | 7.0142 | 7.99996 |

Female11 | 14.7164 | 0.0215 | 0.003804 | 0.0243 | 0.049604 | 6.9170 | 7.99994 |

Female12 | 11.4762 | 0.0145 | 0.002545 | 0.0194 | 0.036445 | 7.2636 | 7.99994 |

Name | Serial Time (s) | Parallel Time(s) | Entropy | ||||
---|---|---|---|---|---|---|---|

Upload | Encrypt | Download | Total | Original | Encrypted | ||

Male01 | 16.6417 | 0.0253 | 0.00353 | 0.0304 | 0.05923 | 7.6170 | 7.99994 |

Male02 | 16.9902 | 0.0249 | 0.00356 | 0.0301 | 0.05856 | 7.2491 | 7.99994 |

Male03 | 15.0768 | 0.0243 | 0.00346 | 0.0298 | 0.05756 | 7.4629 | 7.99994 |

Male04 | 14.8045 | 0.0239 | 0.00351 | 0.0301 | 0.05751 | 7.4662 | 7.99995 |

Male05 | 10.4175 | 0.0186 | 0.00295 | 0.0275 | 0.04905 | 7.3869 | 7.99995 |

Male06 | 9.8852 | 0.0187 | 0.00334 | 0.0256 | 0.04764 | 7.7191 | 7.99996 |

Male07 | 11.8605 | 0.0225 | 0.00421 | 0.0261 | 0.05281 | 7.0507 | 7.99995 |

Male08 | 14.7449 | 0.0246 | 0.00394 | 0.0311 | 0.05964 | 7.2739 | 7.99995 |

Male09 | 13.2484 | 0.0225 | 0.00284 | 0.0294 | 0.05474 | 7.2322 | 7.99994 |

Male10 | 22.14 | 0.0351 | 0.00353 | 0.0395 | 0.07813 | 7.4603 | 7.99996 |

Male11 | 20.9537 | 0.0346 | 0.00467 | 0.0481 | 0.08737 | 7.3924 | 7.99995 |

Male12 | 13.939 | 0.0253 | 0.00347 | 0.0331 | 0.06187 | 7.3524 | 7.99995 |

Input Images | NPCR | UACI |
---|---|---|

Female09 and Female10 | 99.6186 | 33.4595 |

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## Share and Cite

**MDPI and ACS Style**

Villaseñor, C.; Gutierrez-Frias, E.F.; Arana-Daniel, N.; Alanis, A.Y.; Lopez-Franco, C.
Parallel Crossed Chaotic Encryption for Hyperspectral Images. *Appl. Sci.* **2018**, *8*, 1183.
https://doi.org/10.3390/app8071183

**AMA Style**

Villaseñor C, Gutierrez-Frias EF, Arana-Daniel N, Alanis AY, Lopez-Franco C.
Parallel Crossed Chaotic Encryption for Hyperspectral Images. *Applied Sciences*. 2018; 8(7):1183.
https://doi.org/10.3390/app8071183

**Chicago/Turabian Style**

Villaseñor, Carlos, Eric F. Gutierrez-Frias, Nancy Arana-Daniel, Alma Y. Alanis, and Carlos Lopez-Franco.
2018. "Parallel Crossed Chaotic Encryption for Hyperspectral Images" *Applied Sciences* 8, no. 7: 1183.
https://doi.org/10.3390/app8071183