Abstract
On the basis of fractional wavelet transform, we propose a new method called cascaded fractional wavelet transform to encrypt images. It has the virtues of fractional Fourier transform and wavelet transform. Fractional orders, standard focal lengths and scaling factors are its keys. Multistage fractional Fourier transforms can add the keys easily and strengthen information security. This method can also realize partial encryption just as wavelet transform and fractional wavelet transform. Optical realization of encryption and decryption is proposed. Computer simulations confirmed its possibility.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Chen, L.F., Zhao, D.M., 2005. Optical image encryption based on fractional wavelet transform. Opt. Commun., 254(4–6):361–367. [doi:10.1016/j.optcom.2005.05.052]
Cheng, H., Li, X.B., 2000. Partial encryption of compressed images and videos. IEEE Trans. Signal Process., 48(8):2439–2451. [doi:10.1109/78.852023]
Dang, P.P., Chau, P.M., 2000. Image encryption for secure Internet multimedia applications. IEEE Trans. Consum. Electr., 46(3):395–403. [doi:10.1109/30.883383]
Hennelly, B., Sheridan, J.T., 2003. Optical image encryption by random shifting in fractional Fourier domains. Opt. Lett., 28(4):269–271.
Javidi, B., Nomura, T., 2000. Securing information by use of digital holography. Opt. Lett., 25(1):28–30.
Liu, S.T., Wu, J., Li, C.F., 1995. Cascading the multiple stages of optical fractional Fourier transforms under different variable scales. Opt. Lett., 20(12):1415–1417.
Lohmann, A.W., 1993. Image rotation, Wigner rotation, and the fractional Fourier transform. J. Opt. Soc. Am. A, 10(10):2181–2186.
Lohmann, A.W., Mendlovic, D., Zalevsky, Z., 1998. Fractional transformations in optics. Prog. Opt., 38:263–342.
Mendlovic, D., Konforti, N., 1993. Optical realization of the wavelet transform for two-dimensional objects. Appl. Opt., 32(32):6542–6546.
Mendlovic, D., Ozaktas, H.M., 1993. Fractional Fourier transforms and their optical implementation: I. J. Opt. Soc. Am. A, 10(9):1875–1881.
Mendlovic, D., Zalevsky, Z., Mas, D., Garcia, J., Ferreira, C., 1997. Fractional wavelet transform. Appl. Opt., 36(20):4801–4806.
Naulleau, P., 2001. A coherence encoding method for optical switching, encryption, and arithmetic. Opt. Commun., 189(1–3):55–61. [doi:10.1016/S0030-4018(01)00991-9]
Nishchal, N.K., Joseph, J., Singh, K., 2004. Securing information using fractional Fourier transform in digital holography. Opt. Commun., 235(4–6):253–259. [doi:10.1016/j.optcom.2004.02.052]
Tajahuerce, E., Lancis, J., Javidi, B., Andrés, P., 2001. Optical security and encryption with totally incoherent light. Opt. Lett., 26(10):678–680.
Unnikrishnan, G., Joseph, J., Singh, K., 2000a. Optical encryption by double-random phase encoding in the fractional Fourier domain. Opt. Lett., 25(12):887–889.
Unnikrishnan, G., Pohit, M., Singh, K., 2000b. A polarization encoded optical encryption system using ferroelectric spatial light modulator. Opt. Commun., 185(1–3):25–31. [doi:10.1016/S0030-4018(00)00977-9]
Author information
Authors and Affiliations
Corresponding author
Additional information
Project (No. 10276034) supported by the National Natural Science Foundation of China
Rights and permissions
About this article
Cite this article
Bao, Lh., Chen, Lf. & Zhao, Dm. Optical encryption with cascaded fractional wavelet transforms. J. Zhejiang Univ. - Sci. A 7, 1431–1435 (2006). https://doi.org/10.1631/jzus.2006.A1431
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/jzus.2006.A1431