As computational ghost imaging is widely used in the military, radar, and other fields, its security and efficiency became more and more important. In this paper, we propose a compressive ghost imaging encryption scheme based on the hyper-chaotic system, DNA encoding, and KSVD algorithm for the first time. First, a 4-dimensional hyper-chaotic system is used to generate four long pseudorandom sequences and diffuse the sequences with DNA operation to get the phase mask sequence, and then

In recent years, with the rapid development of computer network and communication technology, information security issues have become more and more important. As an emerging optical imaging technology [

CGI is developed based on ghost imaging technology [

CGI encryption scheme.

Then, Durfin et al. proposed a CSGI encryption scheme [

Chaos has many excellent characteristics, such as pseudorandomness, ergodicity, and sensitivity to initial points and parameters [

The rest of this paper is organized as follows. In section

In CGI, as shown in Figure

The basic theory of CGI.

Through Fresnel diffraction, the light field distribution of signal light in front of object plane is the same as reference light, the light travels to the object plane which is

To construct the object’s transmission function

In our proposed CSGI encryption scheme, the phase mask matrix required on the SLM is generated by the hyper-chaotic system:

By setting parameters

Phase portraits. (a)

DNA is a long-chain polymer, and the basic elements are four nucleic acid bases, namely,

DNA encode rule.

Rule | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|

00 | 00 | 01 | 01 | 10 | 10 | 11 | 11 | |

11 | 11 | 10 | 10 | 01 | 01 | 00 | 00 | |

01 | 10 | 00 | 11 | 00 | 11 | 01 | 10 | |

10 | 01 | 11 | 00 | 11 | 00 | 10 | 01 |

DNA encode rule.

Addition | A | C | G | T | Subtraction | A | C | G | T |
---|---|---|---|---|---|---|---|---|---|

A | C | G | T | A | A | T | G | C | |

C | G | T | A | C | C | A | T | G | |

G | T | A | C | G | G | C | A | T | |

T | A | C | G | T | T | G | C | A |

DNA encode rule.

Complement | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

T | T | C | C | G | G | |

C | G | G | A | C | A | |

G | A | T | G | A | T | |

A | C | A | T | T | C |

Compressed sensing technology uses sparse basis such as DCT or DFT to represent the signal sparsely, measures the signal based on Gaussian random matrix, and then reconstructs the signal based on

Suppose a signal is

Sparse operation and the measurement matrix must satisfy restricted isometry property (RIP). Discrete cosine transform, fast-Fourier transform, etc. are common sparse operations.

During measuring

In the end, use the compressed sensing reconstruction algorithm to reconstruct

The approximate solution vector can be obtained by applying inverse transformation for

Suppose a real matrix

Decomposing

The proposed encryption scheme of CSGI includes three main parts: the generated of the phase mask

Chaotic systems have some significant features, such as deterministic, pseudorandomness, and ergodicity, and they are sensitive to initial points and parameters. Supposing that the original image is denoted as

Use the initial values

Define two

Convert sequences

According to the DNA complement rule and

the new sequence

Convert the sequence

Transform the sequence

Set

Suppose the original signal (image) is a matrix

In order to simplify the optimization problem,

So, the main problem is converted to

Suppose the sparse matrix

Through SVD, we can get

Replace

Repeat the above steps to update each column of dictionary, and then we can gain the final dictionary matrix

Figure

The phase masks matrices

The sparse matrix

The sparse matrix

The total light intensity

The initial values of the chaotic system and dictionary matrix

CSGI encryption.

Figure

The transmission key is received through the private channel

The same computed intensity patterns

The computed intensity patterns

According to

CSGI encryption.

In this part, the proposed scheme is simulated with MATLAB R2016a to verify the feasibility.

As shown in Figure

(a) The original image. (b) The random phase mask matrix. (c) The spares matrix. (d) The reconstructed image.

In generation of phase mask matrix, the size of gray image is

During the encryption of the CSGI, the wavelength of the plane wave is selected 0.532

If the cryptographic scheme has enough large key space, it can resist brute-force attacks. Here, the transmission keys are

A highly secure computation ghost imaging system must be sensitive to the key. To verify the security performance of our proposed scheme, a security test is carried out. The private keys are set as

Reconstructed images for the sample object. (a) The original image. The reconstructed image with (b) the correct keys and (c) the incorrect keys.

To evaluate the quality of the reconstructed image, the correlation coefficient between the reconstructed image

In order to get a good reconstruction result, we performed a lot of experiments by changing the measurement

Reconstructed images with different measurements. The measurement and

The comparison experiments for compressed sensing using different sparse basis such as DCT, DFT, and KSVD are conducted on Lena. Besides, simulation of QR-CGI-OE and XOR-LWT-OE is conducted in this experiment. Figure

The relation curve of correlation coefficient

Make measurement 3000 times on Lena, and the reconstructed images are shown in Figures

The reconstructed image based different sparse transformation. (a) The original image of Lena. (b–f) The reconstructed image based on DCT, DFT, and KSVD sparse representation, respectively, and QR-CGI-OE AND XOR-LWT-OE algorithms.

The best reconstructed

Sparse basis or algorithms | Max | Measurement |
---|---|---|

No sparse representation | 0.8243 | 18000 |

DCT | 0.8478 | 6400 |

DFT | 0.8439 | 5300 |

QR-CGI-OE | 0.8210 | 7100 |

XOR-LWT-OE | 0.9343 | 6200 |

In this paper, the NIST SP 800-22 test suite [

NIST statistical test result.

Statistical test | ||||||||
---|---|---|---|---|---|---|---|---|

Result | Result | Result | Result | |||||

Frequency | 0.105232 | Passed | 0.150434 | Passed | 0.200545 | Passed | 0.331051 | Passed |

Block frequency | 0.553902 | Passed | 0.426452 | Passed | 0.626177 | Passed | 0.788040 | Passed |

Runs | 0.873186 | Passed | 0.072802 | Passed | 0.893688 | Passed | 0.216107 | Passed |

Longest run | 0.713956 | Passed | 0.935258 | Passed | 0.497594 | Passed | 0.985966 | Passed |

Rank | 0.357115 | Passed | 0.437155 | Passed | 0.771378 | Passed | 0.193581 | Passed |

FFT | 0.291282 | Passed | 0.840006 | Passed | 0.186356 | Passed | 0.354010 | Passed |

Non-overlapping template | 0.263903 | Passed | 0.640982 | Passed | 0.886167 | Passed | 0.433739 | Passed |

Overlapping template | 0.121652 | Passed | 0.468763 | Passed | 0.969480 | Passed | 0.660406 | Passed |

Universal | 0.522018 | Passed | 0.532899 | Passed | 0.257854 | Passed | 0.881329 | Passed |

Linear complexity | 0.985256 | Passed | 0.847794 | Passed | 0.913437 | Passed | 0.824185 | Passed |

Serial test-1 | 0.271726 | Passed | 0.082269 | Passed | 0.368673 | Passed | 0.229263 | Passed |

Serial test-2 | 0.437868 | Passed | 0.130755 | Passed | 0.308462 | Passed | 0.182765 | Passed |

Approximate entropy | 0.992196 | Passed | 0.939959 | Passed | 0.214085 | Passed | 0.105079 | Passed |

Cumulative sums | 0.116982 | Passed | 0.083702 | Passed | 0.182438 | Passed | 0.182438 | Passed |

Random excursions | 0.030601 | Passed | 0.058385 | Passed | 0.054319 | Passed | 0.200294 | Passed |

Random excursions variant | 0.040671 | Passed | 0.470229 | Passed | 0.032714 | Passed | 0.042780 | Passed |

As the phase mask matrices may be attacked by noise, to test the robustness of this scheme, we add Gaussian noise, salt and pepper noise, and speckle noise on the phase mask matrices, respectively. As shown in Figure

The decrypted images when the phase mask matrices are attacked by noise, and the measurement is 3000. (a) Gaussian noise: mean value is zero, variance is 0.005 and

In this paper, a CSGI encryption scheme based on hyper-chaotic-system and DNA and KSVD technology is proposed for the first time. The hyper-chaotic system is used to generate four long pseudorandom sequences, the sequences are diffused with DNA operation, and then the phase mask matrices for encryption can be obtained. The original image is sparse by dictionary

The data used to support the findings of the study are available from the corresponding author upon request.

All authors declare that they have no conflicts of interest.

This work was supposed by the Science and Technology Project of Hunan Provincial Communications Department, China (Grant No.2018037), and the National Nature Science Foundation of China (Grant nos. 61674054 and 91964108).