Optical asymmetric JTC cryptosystem based on binary phase modulation and image superposition–subtraction operation

Yijie Liu; Xueju Shen; Bing Zhou; Jie Liu; Jianjun Cai; Xun Liu; Yue Cheng

doi:10.1364/AO.466386

Applied Optics
Vol. 61,
Issue 29,
pp. 8711-8729
(2022)
•https://doi.org/10.1364/AO.466386

Optical asymmetric JTC cryptosystem based on binary phase modulation and image superposition–subtraction operation

Yijie Liu, Xueju Shen, Bing Zhou, Jie Liu, Jianjun Cai, Xun Liu, and Yue Cheng

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Yijie Liu, Xueju Shen, Bing Zhou, Jie Liu, Jianjun Cai, Xun Liu, and Yue Cheng, "Optical asymmetric JTC cryptosystem based on binary phase modulation and image superposition–subtraction operation," Appl. Opt. 61, 8711-8729 (2022)

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Table of Contents Category
- Imaging Systems, Image Processing, and Displays
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About this Article
History
- Original Manuscript: June 10, 2022
- Revised Manuscript: September 15, 2022
- Manuscript Accepted: September 16, 2022
- Published: October 3, 2022

Abstract

The joint transform correlator (JTC) cryptosystem is a simple and practical optical cryptosystem. But its identical key in both encryption and decryption brings security risks in the key distribution and management. To overcome these drawbacks, we first create a trapdoor one-way function based on image superposition and subtraction operation. Then combined with the one-way binary phase modulation, an optical asymmetric JTC cryptosystem is proposed in this paper. These two kinds of trapdoor one-way functions are not only effective and implementable, but also can greatly enhance the ability of our proposal to resist various attacks. In addition, we select the structured spiral phase mask (SSPM) controlled by its structural parameters as the key mask of the JTC cryptosystem to facilitate the key transmission. When the structural parameters of the SSPM are protected by the RSA algorithm during encryption and decryption, not only the security of the proposed cryptosystem can be enhanced, but also the key distribution and management will be improved. This also makes our proposal conform more closely to the basic agreement of the public key cryptosystem. Simulation analysis and initial experimental results verified the correctness and feasibility of our proposal.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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CC Values	Baboon	QR Code	Cipher Image
Horizontal	0.9813	0.8999	0.0010
Vertical	0.9774	0.9502	$9.0832 \times 10^{- 4}$
Diagonal	0.9671	0.9475	−0.0011

Decryption Condition	Result	NMSE	SSIM	Retrieve “Baboon”?
All keys correct	Fig. 12(f)	0.0109	0.9862	Yes
$σ = 0.05$	Fig. 15(a)	0.9055	0.0013	No
30% wrong in $P (u, v)$	Fig. 15(b)	0.4695	0.4719	No
One $c_{k}$ incorrect	Fig. 15(c)	0.3246	0.6273	Yes
One other parameter wrong	Fig. 15(d)	0.5391	0.3919	No
Arbitrary two parameters wrong	Fig. 15(e)	0.7579	0.1565	No
$Δ θ = - {0.7}^{\circ}$	Fig. 15(f)	0.4138	0.5355	No

Attack Type	Strength	Result	NMSE	SSIM	Retrieve “Baboon”?
Noise	$K = 30$	Fig. 20(a)	0.2108	0.7498	Yes
	$K = 90$	Fig. 20(b)	0.3893	0.5604	Yes
Occlusion	14.15% cropped	Fig. 22(d)	0.1532	0.8224	Yes
	25% cropped	Fig. 22(e)	0.2202	0.7478	Yes
	50% cropped	Fig. 22(f)	0.3098	0.6475	Yes

Measures		Ref. [60]	Ref. [61]	Ref. [62]	Our Proposal
CC values of adjacent pixels in the cipher image	horizontal	0.0011	−0.0026	0.3233	0.0010
	vertical	0.0018	0.0034	0.2267	$9.0832 \times 10^{- 4}$
	diagonal	0.0016	0.0058	0.4043	−0.0011
Key space		$10^{144}$	$10^{177}$	$10^{78991}$	$10^{277579}$
Resistance to CPA		Yes	Yes	Yes	Yes

Decryption Condition	Result	NMSE	SSIM	Retrieve “Baboon”?
Only cipher image	Fig. 27(a)	0.9062	0.0076	No
Only private image key	Fig. 27(b)	0.9329	0.0069	No
$σ = 0.04$	Fig. 27(c)	0.9112	0.0075	No
One $c_{k}$ incorrect	Fig. 27(d)	0.6586	0.2593	No
$Δ θ = {0.5}^{\circ}$	Fig. 27(e)	0.5228	0.4057	No

Abstract

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