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Optical image encryption based on 3D double-phase encoding algorithm in the gyrator transform domain

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Abstract

In this paper, we propose an optical image encryption scheme based on modified 3D double-phase encoding algorithm (3D-DPEA) in the gyrator transform (GT) domain, in which a plaintext is encrypted into two sparse volumetric ciphertexts under the constraints of chaos-generated binary amplitude masks (BAMs). Then, the two volumetric ciphertexts are multiplexed into the corresponding 2D ciphertexts for convenient storage and transmission. First, due to the synergistic adjustment of the two sparse volumetric ciphertexts during the iterative process, the 3D-DPEA would achieve higher recovery quality of the decrypted image with fewer iterations. In addition, because the BAMs are generated by the logistic-tent (LT) chaotic map which is closely related to the rotation angles of GT, and the LT chaotic map has several advantages such as nonlinear, pseudorandom behavior, and high sensitivity of initial conditions, the sensitivity of the secret key could be significantly improved by several orders of magnitude, reaching up to 10−14. As a result, the 3D-DPEA scheme not only eliminates the explicit/linear relationship between the plaintext and the ciphertext but also substantially enhances security. For decryption, the corresponding decrypted image can be achieved by recording an intensity pattern when a coherent beam crosses two sparse volumetric ciphertexts sequentially. Furthermore, BAMs wouldn’t impose an additional burden on the storage and transmission of secret keys. A series of numerical simulations are performed to verify the effectiveness and security of the proposed encryption scheme.

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Data availability

The data that support the findings of this study are openly available in CVG-UGR database at http://decsai.ugr.es/cvg/dbimagenes/, reference number [39].

Abbreviations

3D-DPEA:

3D double-phase encoding algorithm

GT:

Gyrator transform

BAMs:

Binary amplitude masks

LT:

Logistic-tent

DRPE:

Double random phase encoding

FT:

Fourier transform

FrT:

Fresnel transform

KPA:

Known-plaintext attack

CPA:

Chosen-plaintext attack

CCA:

Chosen-ciphertext attack

PTFT:

Phase truncated Fourier transform

APRA:

Amplitude-phase retrieval algorithm

DRPAE:

Double random phase-amplitude encoding

1D:

One-dimension

2D:

Two-dimension

3D:

Three-dimensional

3D-SPEA:

3D single-phase encoding algorithm

RPMs:

Random phase masks

LCT:

Linear canonical transform

SLMs:

Spatial light modulators

CC:

Correlation coefficient

NPCR:

Number of pixels change rate

UACI:

Unified average changing intensity

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Acknowledgements

The authors would like to thank the anonymous reviewers for their great efforts and valuable comments that are greatly helpful to improve the clarity and quality of this manuscript. Special thanks are also due to the instrumental and data analysis from Analytical and Testing Center, Northeastern University. This work was supported by “985 Project” of Northeastern University (No. 985-3-DC-F24), National Natural Science Foundation of China (No. 61202446), and Fundamental Research Funds for the Central Universities (N150404004).

Funding

National Natural Science Foundation of China, 61202446, Jun Lang, Fundamental Research Funds for the Central Universities, N150404004, Jun Lang

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Authors and Affiliations

  1. College of Computer Science and Engineering, Northeastern University, Shenyang, Liaoning Province, 110819, China

    Jun Lang & Fan Zhang

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  1. Jun Lang
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Contributions

Jun Lang: Conceptualization, Methodology, Writing – review & editing. Fan Zhang: Software, Validation, Formal analysis, Writing – original draft.

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Correspondence to Jun Lang.

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Lang, J., Zhang, F. Optical image encryption based on 3D double-phase encoding algorithm in the gyrator transform domain. Multimed Tools Appl 83, 85963–85985 (2024). https://doi.org/10.1007/s11042-024-20176-0

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