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Asymmetric Cryptosystem Using Affine Transform in Fourier Domain

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Advanced Computational and Communication Paradigms

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 706))

Abstract

An improved image encryption scheme that uses affine transform and asymmetric keys in Fourier transform domain has been proposed. The scheme is validated for grayscale images through numerical simulation using MATLAB 7.14. In the proposed scheme, the decryption keys are different from the encryption keys and are obtained by phase truncation Fourier transform method. The performance of the scheme is evaluated in terms of the metrics such as correlation coefficient, mean-squared error, and peak signal-to-noise ratio. We have carried out the sensitivity analysis relative to the affine transform parameter, which serves as an additional security feature. The robustness of the scheme is demonstrated by showing its resistance against noise and occlusion attacks. Since this is the first study that uses affine transform in the phase-truncated Fourier transform based asymmetric cryptosystem, it provides a new scheme for image encryption with enhanced security.

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References

  1. Stallings, W.: Cryptography and Network Security: Principles and Practices. Pearson/Prentice Hall (2006)

    Google Scholar 

  2. Refregier, P., Javidi, B.: Optical image encryption based on input plane and Fourier plane random encoding. Opt. Lett. 20, 767–769 (1995)

    Article  Google Scholar 

  3. Situ, G., Zhang, J.: Double random-phase encoding in the Fresnel domain. Opt. Lett. 29, 1584–1586 (2004)

    Article  Google Scholar 

  4. Unnikrishnan, G., Singh, K.: Double random fractional Fourier-domain encoding for optical security. Opt. Eng. 39, 2853–2859 (2000)

    Article  Google Scholar 

  5. Singh, P., Yadav, A.K., Singh, K., Saini, I.: Optical image encryption in the fractional Hartley domain, using Arnold transform and singular value decomposition. AIP Conf. Proc. 1802, 020017 (2017)

    Article  Google Scholar 

  6. Singh, P., Yadav, A.K., Singh, K.: Phase image encryption in the fractional Hartley domain using Arnold transform and singular value decomposition. Opt. Lasers Eng. 91, 187–195 (2017)

    Article  Google Scholar 

  7. Carnicer, A., Montes-Usategui, M., Arcos, S., Juvells, I.: Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys. Opt. Lett. 30, 1644–1646 (2005)

    Article  Google Scholar 

  8. Peng, X., Zhang, P., Wei, H., Yu, B.: Known-plaintext attack on optical encryption based on double random phase keys. Opt. Lett. 31, 1044–1046 (2006)

    Article  Google Scholar 

  9. Qin, W., Peng, X.: Asymmetric cryptosystem based on phase-truncated Fourier transforms. Opt. Lett. 35, 118–120 (2010)

    Article  Google Scholar 

  10. Sui, L., Lu, H., Ning, X., Wang, Y.: Asymmetric double-image encryption method by using iterative phase retrieval algorithm in fractional Fourier transform domain. Opt. Eng. 53, 026108 (2014)

    Article  Google Scholar 

  11. Liu, H., Kadir, A.: Asymmetric color image encryption scheme using 2D discrete-time map. Signal Process. 113, 104–112 (2015)

    Article  Google Scholar 

  12. Wang, Y., Quan, C., Tay, C.J.: Asymmetric optical image encryption based on an improved amplitude–phase retrieval algorithm. Opt. Lasers Eng. 78, 8–16 (2016)

    Article  Google Scholar 

  13. Chen, H., Tanougast, C., Liu, Z., Sieler, L.: Asymmetric optical cryptosystem for color image based on equal modulus decomposition in gyrator transform domains. Opt. Lasers Eng. 93, 1–8 (2017)

    Article  Google Scholar 

  14. Nag, A., Singh, J.P., Khan, S., Ghosh, S., Biswas, S., Sarkar, D., Sarkar, P.P.: Image encryption using affine transform and XOR operation. In: 2011 International Conference on Signal Processing, Communication, Computing and Networking Technologies, pp. 309–312 (2011)

    Google Scholar 

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Correspondence to Phool Singh .

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Anjana, S., Saini, I., Singh, P., Yadav, A.K. (2018). Asymmetric Cryptosystem Using Affine Transform in Fourier Domain. In: Bhattacharyya, S., Chaki, N., Konar, D., Chakraborty, U., Singh, C. (eds) Advanced Computational and Communication Paradigms. Advances in Intelligent Systems and Computing, vol 706. Springer, Singapore. https://doi.org/10.1007/978-981-10-8237-5_4

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  • DOI: https://doi.org/10.1007/978-981-10-8237-5_4

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-8236-8

  • Online ISBN: 978-981-10-8237-5

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