FIG. 1. Flow chart of the proposed scheme: (a) encryption process, (b) decryption process.
FIG. 2. Four SPK patterns: (a) LPK, (b) QPK, (c) SPPK, (d) SQPK.
FIG. 3. Original image.
FIG. 4. Encrypted images (intensity) for different types of SPKs in the SPK+RPK scheme: (a) LPK, (b) QPK, (c) SPPK, (d) SQPK.
FIG. 5. The keys and encrypted image (intensity and phase) for different hybrid-key-pattern combinations: (a)~(d) RPK+ RPK, (e)~(h) RPK+SPK, (i)~(l) SPK+RPK, (m)~(p) SPK+ SPK. The 1st column is KEY1, the 2nd column is KEY2, the 3rd column is the intensity of the encrypted image, and the 4th column is the phase of the encrypted image.
FIG. 6. Decrypted images using partial-error keys for different schemes: (a)~(d) RPK+RPK, (e)~(h) RPK+SPK, (i)~(l) SPK+RPK.
FIG. 7. Relationship between CC and percentage correctness of the key for the four schemes.
FIG. 8. Relationship between CC and percentage of key parameters in error for the RPK+SPK and SPK+SPK schemes.
TABLE 1. Quality evaluation of encrypted images
참고문헌
- A. Alfalou and C. Brosseau, "Optical image compression and encryption methods," Adv. Opt. Photon. 1, 590-636 (2009).
- M. S. Millan, "Advanced optical correlation and digital methods for pattern matching-50th anniversary of Vander Lugt matched filter," J. Opt.-UK 14, 103001 (2012) https://doi.org/10.1088/2040-8978/14/10/103001
- W. Chen, B. Javidi, and X. Chen, "Advances in optical security systems," Adv. Opt. Photon. 6, 121-155 (2014)
- S. Liu, C. Guo, and J. T. Sheridan, "A review of optical image encryption techniques," Opt. Laser Technol. 57, 327-342 (2014). https://doi.org/10.1016/j.optlastec.2013.05.023
- B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, X. Peng, A. Stern, Y. Rivenson, A. Alfalou, C. Brosseau, C. Guo, J. T. Sheridan, G. Situ, M. Naruse, T. Matsumoto, I. Juvells, E. Tajahuerce, J. Lancis, W. Chen, X. Chen, P. W. H. Pinkse, A. P. Mosk, and A. Markman, "Roadmap on optical security," J. Opt.-UK 18, 083001 (2016).
- E. Perez-Cabre, M. Cho, and B. Javidi, "Information authentication using photon-counting double-random-phase encrypted images," Opt. Lett. 36, 22-24 (2011). https://doi.org/10.1364/OL.36.000022
- I. Lee and M. Cho, "Optical encryption and information authentication of 3D objects considering wireless channel characteristics," J. Opt. Soc. Korea 17, 494-499 (2013). https://doi.org/10.3807/JOSK.2013.17.6.494
- M. Cho and B. Javidi, "Three-dimensional photon counting double-random-phase encryption," Opt. Lett. 38, 3198-3201 (2013). https://doi.org/10.1364/OL.38.003198
- I. Lee and M. Cho, "Double random phase encryption using orthogonal encoding for multiple-image transmission," J. Opt. Soc. Korea 18, 201-206 (2014). https://doi.org/10.3807/JOSK.2014.18.3.201
- A. Vaish and M. Kumar, "Color image encryption using singular value decomposition in discrete cosine Stockwell transform domain," Opt. Appl. 48, 25-38 (2018).
- Z. Shao, Y. Shang, Q. Tong, H. Ding, X. Zhao, and X. Fu, "Multiple color image encryption and authentication based on phase retrieval and partial decryption in quaternion gyrator domain," Multimedia Tools Appl. 77, 25821-25840 (2018). https://doi.org/10.1007/s11042-018-5818-7
- X. Li, X. Meng, X. Yang, Y. Wang, Y. Yin, X. Peng, W. He, G. Dong, and H. Chen, "Multiple-image encryption via lifting wavelet transform and XOR operation based on compressive ghost imaging scheme," Opt. Laser Eng. 102, 106-111 (2018). https://doi.org/10.1016/j.optlaseng.2017.10.023
- H. Xu, W. Xu, S. Wang, and S. Wu, "Phase-only asymmetric optical cryptosystem based on random modulus decomposition," J. Mod. Opt. 65, 1245-1252 (2018). https://doi.org/10.1080/09500340.2018.1431314
- K. Ravi, B. Basanta, and K. N. Naveen, "Nonlinear QR code based optical image encryption using spiral phase transform, equal modulus decomposition and singular value decomposition," J. Opt.-UK 20, 015701 (2018). https://doi.org/10.1088/2040-8986/aa9943
- J. F. Barrera, R. Henao, and R. Torroba, "Optical encryption method using toroidal zone plates," Opt. Commun. 248, 35-40 (2005). https://doi.org/10.1016/j.optcom.2004.11.086
- Y. Xiong, A. He, and C. Quan, "Security analysis of a double-image encryption technique based on an asymmetric algorithm," J. Opt. Soc. Am. A 35, 320-326 (2018). https://doi.org/10.1364/JOSAA.35.000320
- M. Liao, W. He, D. Lu, and X. Peng, "Ciphertext-only attack on optical cryptosystem with spatially incoherent illumination: from the view of imaging through scattering medium," Sci. Rep. 7, 41789 (2017). https://doi.org/10.1038/srep41789
- T. Li, Z. Miao, and Y. Shi, "Ciphertext-only attack on phase-shifting interferometery-based encryption," IEEE Photon. J. 9, 1-8 (2017).
- W. Qin and X. Peng, "Asymmetric cryptosystem based on phase-truncated Fourier transforms," Opt. Lett. 35, 118-120 (2010). https://doi.org/10.1364/OL.35.000118
- M. Khurana and H. Singh, "An asymmetric image encryption based on phase truncated hybrid transform," 3D Res. 8 (2017).
- S. K. Gil, "Asymmetric public key cryptography by using logic-based optical processing," J. Opt. Soc. Korea 20, 55-63 (2016). https://doi.org/10.3807/JOSK.2016.20.1.055
- H. Yu, J. Chang, X. Liu, C. Wu, Y. He, and Y. Zhang, "Novel asymmetric cryptosystem based on distorted wavefront beam illumination and double-random phase encoding," Opt. Express 25, 8860 (2017). https://doi.org/10.1364/OE.25.008860
- H. Chen, C. Tanougast, Z. Liu, and L. Sieler, "Asymmetric optical cryptosystem for color image based on equal modulus decomposition in gyrator transform domains," Opt. Lasers Eng. 93, 1-8 (2017).
- L. Yao, C. Yuan, J. Qiang, S. Feng, and S. Nie, "Asymmetric color image encryption based on singular value decomposition," Opt. Lasers Eng. 89, 80-87 (2017). https://doi.org/10.1016/j.optlaseng.2016.06.007
- X. Li, M. Zhao, Y. Xing, L. Li, S. T. Kim, X. Zhou, and Q. H. Wang, "Optical encryption via monospectral integral imaging," Opt. Express 25, 31516-31527 (2017). https://doi.org/10.1364/OE.25.031516
- T. Zhao, Y. Jiang, and C. Liu, "Demonstration and a practical scheme of the optical asymmetric cryptosystem," Optik 138, 509-515 (2017). https://doi.org/10.1016/j.ijleo.2017.03.013
- L. Ma and W. Jin, "Symmetric and asymmetric hybrid cryptosystem based on compressive sensing and computer generated holography," Opt. Commun. 407, 51-56 (2018). https://doi.org/10.1016/j.optcom.2017.08.047
- M. Tebaldi, W. D. Furlan, R. Torroba, and N. Bolognini, "Optical-data storage-readout technique based on fractal encrypting masks," Opt. Lett. 34, 316 (2009). https://doi.org/10.1364/OL.34.000316
- W. Zamrani, E. Ahouzi, A. Lizana, J. Campos, and M. J. Yzuel, "Optical image encryption technique based on deterministic phase masks," Opt. Eng. 55, 103108 (2016). https://doi.org/10.1117/1.OE.55.10.103108
- J. F. Barrera, R. Henao, and R. Torroba, "Optical encryption method using toroidal zone plates," Opt. Commun. 248, 35-40 (2005). https://doi.org/10.1016/j.optcom.2004.11.086
- J. F. Barrera, R. Henao, and R. Torroba, "Fault tolerances using toroidal zone plate encryption," Opt. Commun. 256, 489-494 (2005). https://doi.org/10.1016/j.optcom.2005.06.077
- S. K. Rajput and N. K. Nishchal, "Asymmetric color cryptosystem using polarization selective diffractive optical element and structured phase mask," Appl. Opt. 51, 5377-5386 (2012). https://doi.org/10.1364/AO.51.005377
- C. Lin and X. Shen, "Design of reconfigurable and structured spiral phase mask for optical security system," Opt. Commun. 370, 127-134 (2016). https://doi.org/10.1016/j.optcom.2016.03.021
- C. Lin, X. Shen, and M. Lei, "Generation of plaintextindependent private key based on conditional decomposition strategy," Opt. Lasers Eng. 86, 303-308 (2016). https://doi.org/10.1016/j.optlaseng.2016.06.023
- H. Singh, "Nonlinear optical double image encryption using random-optical vortex in fractional Hartley transform domain," Opt. Appl. 47, 557-578 (2017).
- R. Kumar and B. Bhaduri, "Optical image encryption in Fresnel domain using spiral phase transform," J. Opt.-UK 19, 095701 (2017). https://doi.org/10.1088/2040-8986/aa7cb1
- M. R. Abuturab, "Securing multiple information using chaotic spiral phase encoding with simultaneous interference and superposition methods," Opt. Lasers Eng. 98, 1-16 (2017). https://doi.org/10.1016/j.optlaseng.2017.05.001
- Q. Chen, X. Shen, S. Dou, C. Lin, and L. Wang, "Topological charge number multiplexing for JTC multiple-image encryption," Opt. Commun. 412, 155-160 (2018). https://doi.org/10.1016/j.optcom.2017.12.015
- K. Ravi, B. Basanta, and K. N. Naveen, "Nonlinear QR code based optical image encryption using spiral phase transform, equal modulus decomposition and singular value decomposition," J. Opt.-UK 20, 015701 (2018). https://doi.org/10.1088/2040-8986/aa9943
- M. Rafiq Abuturab, "Asymmetric multiple information cryptosystem based on chaotic spiral phase mask and random spectrum decomposition," Opt. Laser Technol. 98, 298-308 (2018). https://doi.org/10.1016/j.optlastec.2017.08.010
- M. R. Abuturab, "Color image security system using double random-structured phase encoding in gyrator transform domain," Appl. Opt. 51, 3006-3016 (2012). https://doi.org/10.1364/AO.51.003006
- M. R. Abuturab, "Color information security system using discrete cosine transform in gyrator transform domain radial- Hilbert phase encoding," Opt. Lasers Eng. 50, 1209-1216 (2012). https://doi.org/10.1016/j.optlaseng.2012.03.020
- H. Singh, A. K. Yadav, S. Vashisth, and K. Singh, "Fully phase image encryption using double random-structured phase masks in gyrator domain," Appl. Opt. 53, 6472 (2014). https://doi.org/10.1364/AO.53.006472
- A. K. Yadav, S. Vashisth, H. Singh, and K. Singh, "A phase-image watermarking scheme in gyrator domain using devil's vortex Fresnel lens as a phase mask," Opt. Commun. 344, 172-180 (2015). https://doi.org/10.1016/j.optcom.2015.01.019
- S. Liansheng, Z. Bei, N. Xiaojuan, and T. Ailing, "Optical multiple-image encryption based on the chaotic structured phase masks under the illumination of a vortex beam in the gyrator domain," Opt. Express 24, 499-515 (2016). https://doi.org/10.1364/OE.24.000499
- P. Singh, A. K. Yadav, and K. Singh, "Phase image encryption in the fractional Hartley domain using Arnold transform and singular value decomposition," Opt. Lasers Eng. 91, 187-195 (2017). https://doi.org/10.1016/j.optlaseng.2016.11.022
- H. Singh, "Cryptosystem for securing image encryption using structured phase masks in fresnel wavelet transform domain," 3D Res. 7 (2016).
- H. Singh, "Devil's vortex Fresnel lens phase masks on an asymmetric cryptosystem based on phase-truncation in gyrator wavelet transform domain," Opt. Lasers Eng. 81, 125-139 (2016). https://doi.org/10.1016/j.optlaseng.2016.01.014
- H. Singh, A. K. Yadav, S. Vashisth, and K. Singh, "Double phase-image encryption using gyrator transforms, and structured phase mask in the frequency plane," Opt. Lasers Eng. 67, 145-156 (2015). https://doi.org/10.1016/j.optlaseng.2014.10.011