Abstract
A single-channel color image encryption algorithm is proposed by combining fractional Hartley transform (FRHT) with vector operation. The original color image is decomposed into RGB components and the G and B components are encrypted into two phase-only masks θ G and θ B with vector operation, respectively. The R, θ G and θ B are transformed by FRHT and vector operation twice to obtain amplitude, random phase and decryption phase key. The new amplitude combined with the random phase is transformed by FRHT once more and then the result is scrambled by the chaotic scrambling to strengthen the security of the algorithm. The private phase key is dependent on the original image, which makes the proposed encryption algorithm more secure than the linear color image encryption algorithm based on the double random phase encoding in FRHT. Simulation results demonstrate the security and effectiveness of the proposed algorithm.
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References
Chen W, Chen XD (2011) Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain. Opt Commun 284:3913–3917
Chen LF, Zhao DM (2009) Color image encoding in dual fractional Fourier-wavelet domain with random phases. Opt Commun 282:3433–3438
Deng XP, Zhao DM (2012) Single-channel color image encryption based on asymmetric cryptosystem. Opt Laser Technol 44:136–140
Guo Q, Liu ZJ, Liu ST (2010) Color image encryption by using Arnold and discrete fractional random transforms in IHS space. Opt Laser Eng 48:800–805
Hwang HE, Han P (2006) Fast algorithm of phase mask for image encryption in Fresnel domain. J Opt Soc Am A 23:1870–1874
Jimenez C, Torres C, Mattos L (2011) Fractional Hartley transform applied to optical image encryption. J Phys. doi:10.1088/1742-6596/274/1/012041
Joshi M, Shakher C, Singh K (2007) Color image encryption and decryption using fractional Fourier transform. Opt Commun 279:35–42
LI XX, Zhao DM (2008) Optical Image encryption with simplified fractional Hartley transform. Chinese Phys Lett 25:2477–2480
Li XX, Zhao DM (2010) Optical color image encryption with redefined fractional Hartley transform. Optik 121:673–67
Liu ZJ, Da JM, Sun XG, Liu ST (2010) Color image encryption by using the rotation of color vector in Hartley transform domains. Opt Laser Eng 48:800–805
Madhusudan J, Chandra S, Kehar S (2008) Color image encryption and decryption for twin images in fractional Fourier domain. Opt Commun 281:5713–15720
Pei SC, Ding JJ (2002) Fractional cosine, sine, and Hartley transforms. IEEE Trans Signal Process 50:1661–1680
Refregier P, Javidi B (1995) Optical image encryption based on input plane and Fourier plane random encoding. Opt Lett 20:767–769
Situ G, Zhang J (2004) Double random-phase encoding in the Fresnel domain. Opt Lett 29:1584–1586
Tao R, Xin Y, Wang Y (2007) Double image encryption based on random phase encoding in fractional Fourier domain. Opt Express 15:16067–16079
Unnikrishnan G, Joseph J, Singh K (2000) Optical encryption by double-random phase encoding in the fractional Fourier domain. Opt Lett 25:887–889
Wang XG, Zhao DM (2011) Image encoding based on coherent superposition and basic vector operations. Opt Commun 284:945–951
Zhao DM, Li XX, Chen LF (2008) Optical image encryption with redefined fractional Hartley transform. Opt Commun 281:5326–5329
Zhou NR, Wang YX, Gong LH (2011) Novel optical image encryption scheme based on fractional Mellin transform. Opt Commun 284:3234–3242
Zhou NR, Wang YX, Gong LH, Chen XB, Yang YX (2012) Novel color image encryption algorithm based on the reality preserving fractional Mellin transform. Opt Laser Technol 44:2270–2281
Zhou NR, Wang YX, Gong LH, He H, Wu JH (2011) Novel single-channel color image encryption algorithm based on chaos and fractional Fourier transform. Opt Commun 284:2789–2796
Acknowledgments
The work is supported by the National Natural Science Foundation of China (Grant Nos. 61262084 and 61141007), the Foundation for Young Scientists of Jiangxi Province (Jinggang Star) (Grant No. 20122BCB23002), and the Opening Project of Key Laboratory of Image Processing and Pattern Recognition (Nanchang Hangkong University), Jiangxi Province (Grant No. TX201204002).
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Liu, Y., Du, J., Fan, J. et al. Single-channel color image encryption algorithm based on fractional Hartley transform and vector operation. Multimed Tools Appl 74, 3171–3182 (2015). https://doi.org/10.1007/s11042-013-1778-0
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DOI: https://doi.org/10.1007/s11042-013-1778-0