• Laser & Optoelectronics Progress
  • Vol. 58, Issue 4, 0410021 (2021)
Xue Wang1, Zhuhong Shao1、*, Yunfei Wang2, and Yuanyuan Shang1、2、3
Author Affiliations
  • 1Information Engineering College, Capital Normal University, Beijing 100048, China
  • 2Department of Physics, Capital Normal University, Beijing 100048, China
  • 3Beijing Advanced Innovation Center for Imaging Theory and Technology, Beijing 100048, China
  • show less
    DOI: 10.3788/LOP202158.0410021 Cite this Article Set citation alerts
    Xue Wang, Zhuhong Shao, Yunfei Wang, Yuanyuan Shang. Color Image Encryption Based on Symmetry of Fourier Transform and R-MRSVD[J]. Laser & Optoelectronics Progress, 2021, 58(4): 0410021 Copy Citation Text show less
    Flowchart of the proposed algorithm. (a) Encryption process; (b) decryption process
    Fig. 1. Flowchart of the proposed algorithm. (a) Encryption process; (b) decryption process
    Tested images. (a) Lena; (b) Elephant; (c) Grnpeace; (d) Peppers; (e) Butterfly
    Fig. 2. Tested images. (a) Lena; (b) Elephant; (c) Grnpeace; (d) Peppers; (e) Butterfly
    Results of encryption and decryption. (a) Cipherimages; (b) restituted images
    Fig. 3. Results of encryption and decryption. (a) Cipherimages; (b) restituted images
    Histogram results. (a) Plaintext images; (b) ciphertext images
    Fig. 4. Histogram results. (a) Plaintext images; (b) ciphertext images
    Correlation distribution of adjacent pixels. (a) Lena's plaintext image; (b) Lena's ciphertext image
    Fig. 5. Correlation distribution of adjacent pixels. (a) Lena's plaintext image; (b) Lena's ciphertext image
    Results of chosen-plaintext attack. (a) Fake plaintext images; (b) decrypted results of Fig.3(a)
    Fig. 6. Results of chosen-plaintext attack. (a) Fake plaintext images; (b) decrypted results of Fig.3(a)
    Decrypted results using a slightly deviated key. (a) a; (b) b; (c) c; (d) x'0
    Fig. 7. Decrypted results using a slightly deviated key. (a) a; (b) b; (c) c; (d) x'0
    Decrypted results when the intensity of Gaussian noise is 1. (a) Proposed algorithm; (b) algorithm in Ref.[16]; (c) algorithm in Ref.[17]
    Fig. 8. Decrypted results when the intensity of Gaussian noise is 1. (a) Proposed algorithm; (b) algorithm in Ref.[16]; (c) algorithm in Ref.[17]
    Average PSNR and CC under Gaussian noise attack. (a) PSNR; (b) CC
    Fig. 9. Average PSNR and CC under Gaussian noise attack. (a) PSNR; (b) CC
    Decrypted images under cropping attack(η=20%). (a) Proposed algorithm; (b) algorithm in Ref.[16]; (c) algorithm in Ref.[17]
    Fig. 10. Decrypted images under cropping attack(η=20%). (a) Proposed algorithm; (b) algorithm in Ref.[16]; (c) algorithm in Ref.[17]
    Average PSNR and CC under cropping attack. (a) PSNR; (b) CC
    Fig. 11. Average PSNR and CC under cropping attack. (a) PSNR; (b) CC
    ImageProposed algorithmAlgorithm in Ref. [16]Algorithm in Ref. [17]
    1D-DFT2D-DFT
    2×22×33×22×22×33×2
    Lena300.4656291.7590287.9488298.4824289.0684295.0256262.7863302.4648
    Elephant291.8283294.5651303.3073293.4864300.8966299.7538272.0697304.3388
    Grnpeace315.7956293.4830286.2010311.1888291.8217296.4422253.9804308.4498
    Peppers296.8666290.3514283.4614296.7653292.6517282.7151259.1771303.3361
    Butterfly304.7186296.1617294.6717301.7734298.5181298.4478243.4396304.2931
    Mean/standard deviation301.9349/ 9.0810293.2640/ 2.2850291.1180/ 7.9695300.3393/ 6.7630294.5913/ 4.9273294.4769/ 6.8212258.2906/ 10.6065304.5765/ 2.2988
    Table 1. PSNR of correctly decryption
    ImageHorizontalVerticalDiagonal
    Lena in Fig.20.94690.90880.8829
    Elephant in Fig.20.96450.95190.9319
    Grnpeace in Fig.20.71270.79330.7001
    Peppers in Fig.20.94690.94070.9289
    Butterfly in Fig.20.87760.89300.8386
    Lena in Fig.3(a)0.01560.1012-0.0047
    Elephant in Fig.3(a)0.04400.0564-0.0013
    Grnpeace in Fig.3(a)0.0377-0.01190.0042
    Peppers in Fig.3(a)0.04490.0018-0.0010
    Butterfly in Fig.3(a)-0.04190.01650.0238
    Table 2. Correlation coefficients of plaintext and ciphertext images
    Xue Wang, Zhuhong Shao, Yunfei Wang, Yuanyuan Shang. Color Image Encryption Based on Symmetry of Fourier Transform and R-MRSVD[J]. Laser & Optoelectronics Progress, 2021, 58(4): 0410021
    Download Citation