Single-lens Fourier-transform-based optical color image encryption using dual two-dimensional chaotic maps and the Fresnel transform

Yonggang Su; Chen Tang; Biyuan Li; Xia Chen; Wenjun Xu; Yuanxue Cai

doi:10.1364/AO.56.000498

Applied Optics
Vol. 56,
Issue 3,
pp. 498-505
(2017)
•https://doi.org/10.1364/AO.56.000498

Single-lens Fourier-transform-based optical color image encryption using dual two-dimensional chaotic maps and the Fresnel transform

Yonggang Su, Chen Tang, Biyuan Li, Xia Chen, Wenjun Xu, and Yuanxue Cai

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Yonggang Su, Chen Tang, Biyuan Li, Xia Chen, Wenjun Xu, and Yuanxue Cai, "Single-lens Fourier-transform-based optical color image encryption using dual two-dimensional chaotic maps and the Fresnel transform," Appl. Opt. 56, 498-505 (2017)

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Abstract

We propose an optical color image encryption system based on the single-lens Fourier transform, the Fresnel transform, and the chaotic random phase masks (CRPMs). The proposed encryption system contains only one optical lens, which makes it more efficient and concise to implement. The introduction of the Fresnel transform makes the first phase mask of the proposed system also act as the main secret key when the input image is a non-negative amplitude-only map. The two CRPMs generated by dual two-dimensional chaotic maps can provide more security to the proposed system. In the proposed system, the key management is more convenient and the transmission volume is reduced greatly. In addition, the secret keys can be updated conveniently in each encryption process to invalidate the chosen plaintext attack and the known plaintext attack. Numerical simulation results have demonstrated the feasibility and security of the proposed encryption system.

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Image	CC	SSIM
Fig. 3(a)	0.0080	0.0042
Fig. 3(b)	0.0097	0.0049
Fig. 3(c)	0.0109	0.0061
Fig. 3(d)	0.0096	0.0052
Fig. 3(e)	0.0155	0.0090
Fig. 3(f)	0.0113	0.0075
Fig. 3(g)	0.0108	0.0067
Fig. 3(h)	0.0125	0.0085
Fig. 3(i)	0.0070	0.0063
Fig. 3(j)	0.0107	0.0082
Fig. 3(k)	−0.0211	0.0138
Fig. 3(l)	0.0312	0.0224

Method	Image	CC	SSIM
DLFT [Figs. 4(a-1)–4(a-4)]	Fig. 4(a-1)	0.5396	0.1395
	Fig. 4(a-2)	0.5358	0.1378
	Fig. 4(a-3)	0.5391	0.1393
	Fig. 4(a-4)	0.5386	0.1390
DLFT-FrT [Figs. 4(b-1)–4(b-4)]	Fig. 4(b-1)	0.0080	0.0042
	Fig. 4(b-2)	0.0097	0.0049
	Fig. 4(b-3)	0.0109	0.0061
	Fig. 4(b-4)	0.0096	0.0052

Image	Horizontal	Vertical	Diagonal
Original image	0.9636	0.9636	0.9218
Encrypted image by Ref. [29]	0.0163	0.0215	0.0283
Encrypted image by SLFT-FrT-LM	0.0546	−0.0442	0.0522
Encrypted image by DLFT-FrT	0.0107	0.0029	0.0068
Encrypted image by Proposed system	−0.0034	0.0035	−0.0018

Method	Image	CC	SSIM
Ref. [29] [Figs. 6(a-1)–6(a-3)]	Fig. 6(a-1)	0.3301	0.1387
	Fig. 6(a-2)	0.2067	0.0085
	Fig. 6(a-3)	0.0986	0.0482
DLFT-FrT [Figs. 6(b-1)–6(b-3)]	Fig. 6(b-1)	0.8593	0.3218
	Fig. 6(b-2)	0.7176	0.2274
	Fig. 6(b-3)	0.5152	0.1291
Proposed [Figs. 6(c-1)–6(c-3)]	Fig. 6(c-1)	0.8432	0.3081
	Fig. 6(c-2)	0.7013	0.2192
	Fig. 6(c-3)	0.5032	0.1242

Method	Image	CC	SSIM
Ref. [29] [Figs. 7(a-1)–7(a-3)]	Fig. 7(a-1)	0.6981	0.3460
	Fig. 7(a-2)	0.2492	0.0995
	Fig. 7(a-3)	0.0942	0.0390
DLFT-FrT [Figs. 7(b-1)–7(b-3)]	Fig. 7(b-1)	0.9859	0.8236
	Fig. 7(b-2)	0.7644	0.3616
	Fig. 7(b-3)	0.5090	0.1949
Proposed [Figs. 7(c-1)–7(c-3)]	Fig. 7(c-1)	0.9862	0.8220
	Fig. 7(c-2)	0.7605	0.3649
	Fig. 7(c-3)	0.4998	0.1961

Method	Ref. [30]	Ref. [31]	Ref. [32]	Proposed
Space	$10^{50}$	$10^{87}$	$10^{58}$	$10^{150}$

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Applied Optics