{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T14:05:49Z","timestamp":1772460349973,"version":"3.50.1"},"reference-count":45,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2026,3,1]],"date-time":"2026-03-01T00:00:00Z","timestamp":1772323200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Scientific and Technological Project of Henan Province","award":["252102210161"],"award-info":[{"award-number":["252102210161"]}]},{"name":"Scientific Research Foundation of Nanyang Normal University","award":["2025STP001"],"award-info":[{"award-number":["2025STP001"]}]},{"name":"Scientific Research Foundation of Nanyang Normal University","award":["2024ZX031"],"award-info":[{"award-number":["2024ZX031"]}]},{"name":"Scientific Research Foundation of Nanyang Normal University","award":["2022PY008"],"award-info":[{"award-number":["2022PY008"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>To achieve high capacity, high speed, and secure image transmission, we propose a multi-image computational ghost imaging (CGI)-based encryption scheme that integrates compressed sensing (CS), block scrambling, and dynamic-salt-driven bidirectional XOR diffusion. First, multiple images are partitioned into 8 \u00d7 8 pixel blocks, and their spatial structure is disrupted through random scrambling. The scrambled composite image then undergoes pixel-level encryption via two-round bidirectional XOR diffusion, using session-unique keys derived from SHA-256-based dynamic salt, eliminating the statistical characteristics of the original images. Subsequently, each pixel block is subjected to both Gaussian CS and Hadamard-based CGI measurements in parallel, achieving dual-mode compressive encryption and enhancing robustness through measurement redundancy. Finally, only the scrambling key, the XOR-diffusion key, and the compressed measurements are stored; the original image information is thus transformed into unrecognizable measurement data. During the decryption process, the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) with a Discrete Cosine Transform (DCT) sparse basis is employed for dual-sparse reconstruction from the compressed measurements, recovering the encrypted composite image. An inverse XOR operation is then applied to remove the pixel-level diffusion, followed by block reordering using the scrambling key to restore the original images. Experimental results demonstrate that the proposed scheme enables efficient and secure multi-image transmission while maintaining high decrypted image quality. Security analysis indicates that the scheme possesses high key sensitivity, effectively resisting chosen-plaintext attacks. Histogram uniformity analysis and cropping attack resistance experiments further confirm its excellent statistical security and robustness.<\/jats:p>","DOI":"10.3390\/info17030239","type":"journal-article","created":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T12:39:56Z","timestamp":1772455196000},"page":"239","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Computational Ghost Imaging Encryption for Multiple Images Based on Compressed Sensing and Block Scrambling"],"prefix":"10.3390","volume":"17","author":[{"given":"Zhipeng","family":"Wang","sequence":"first","affiliation":[{"name":"College of Physics and Electronic Engineering, Nanyang Normal University, Nanyang 473061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiahuan","family":"Yang","sequence":"additional","affiliation":[{"name":"College of Physics and Electronic Engineering, Nanyang Normal University, Nanyang 473061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruizhi","family":"Ge","sequence":"additional","affiliation":[{"name":"College of Physics and Electronic Engineering, Nanyang Normal University, Nanyang 473061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingying","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Physics and Electronic Engineering, Nanyang Normal University, Nanyang 473061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7772-6702","authenticated-orcid":false,"given":"Yi","family":"Qin","sequence":"additional","affiliation":[{"name":"College of Intelligent Manufacturing and Electrical Engineering, Nanyang Normal University, Nanyang 473061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,3,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/j.ins.2020.10.007","article-title":"An efficient approach for encrypting double color images into a visually meaningful cipher image using 2D compressive sensing","volume":"556","author":"Chai","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ins.2022.01.042","article-title":"An image encryption algorithm based on new generalized fusion fractal structure","volume":"592","author":"Ahmad","year":"2022","journal-title":"Inf. Sci."},{"key":"ref_3","first-page":"125153","article-title":"Cryptanalysis and constructing S-box based on chaotic map and backtracking","volume":"376","author":"Liu","year":"2020","journal-title":"Appl. Math. Comput."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"107879","DOI":"10.1016\/j.optlastec.2022.107879","article-title":"Image encryption scheme based on discrete cosine Stockwell transform and DNA-level modulus diffusion","volume":"149","author":"Huang","year":"2022","journal-title":"Opt. Laser Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"116891","DOI":"10.1016\/j.image.2022.116891","article-title":"Hybrid quantum\u2013classical generative adversarial networks for image generation via learning discrete distribution","volume":"110","author":"Zhou","year":"2023","journal-title":"Signal Process. Image Commun."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"22","DOI":"10.1186\/s13640-018-0402-7","article-title":"Fractional-order 4D hyperchaotic memristive system and application in color image encryption","volume":"2019","author":"Li","year":"2019","journal-title":"EURASIP J. Image Video Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3726","DOI":"10.1109\/TCSI.2024.3407809","article-title":"Multi-image encryption algorithm based on novel spatiotemporal chaotic system and fractal geometry","volume":"71","author":"Huang","year":"2024","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"9558","DOI":"10.1364\/AO.400465","article-title":"Optical single-channel cryptosystem based on the discrete wavelet transform and the chaotic standard map for multi-image","volume":"59","author":"Shen","year":"2020","journal-title":"Appl. Opt."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"15737","DOI":"10.1038\/s41598-021-94748-7","article-title":"A new image encryption scheme based on fractional-order hyperchaotic system and multiple image fusion","volume":"11","author":"Gao","year":"2021","journal-title":"Sci. Rep."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"108071","DOI":"10.1016\/j.optlastec.2022.108071","article-title":"Multiple color image fusion, compression, and encryption using compressive sensing, chaotic-biometric keys, and optical fractional Fourier transform","volume":"151","author":"Abuturab","year":"2022","journal-title":"Opt. Laser Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2827","DOI":"10.1140\/epjs\/s11734-024-01321-0","article-title":"Multi-image encryption combining four-dimensional chaotic systems and multi-layer embedding","volume":"234","author":"Zhou","year":"2025","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"110574","DOI":"10.1016\/j.isci.2024.110574","article-title":"Robust optical multi-image encryption with lossless decryption Recovery Based on phase recombination and vector decomposition","volume":"27","author":"Guo","year":"2024","journal-title":"iScience"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"11411","DOI":"10.1021\/acs.nanolett.4c02153","article-title":"Single-Shot Multispectral Encoding: Advancing Optical Lithography for Encryption and Spectroscopy","volume":"24","author":"Shim","year":"2024","journal-title":"Nano Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"9775","DOI":"10.1038\/s41598-025-92065-x","article-title":"A new multiple image encryption algorithm using hyperchaotic systems, SVD, and modified RC5","volume":"15","author":"Alexan","year":"2025","journal-title":"Sci. Rep."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"106448","DOI":"10.1016\/j.optlaseng.2020.106448","article-title":"A novel chaos based optical cryptosystem for multiple images using DNA-blend and gyrator transform","volume":"138","author":"Chen","year":"2021","journal-title":"Opt. Lasers Eng."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"30597","DOI":"10.1038\/s41598-024-79282-6","article-title":"Multiple image encryption algorithm using channel randomization and multiple chaotic maps","volume":"14","author":"Hosny","year":"2024","journal-title":"Sci. Rep."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.apm.2024.04.012","article-title":"Optical image encryption and authentication scheme with computational ghost imaging","volume":"131","author":"Guo","year":"2024","journal-title":"Appl. Math. Model."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.optcom.2015.09.039","article-title":"Multiple-image encryption based on computational ghost imaging","volume":"359","author":"Wu","year":"2016","journal-title":"Opt. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3917","DOI":"10.1364\/OL.392424","article-title":"Forgery attack on optical encryption based on computational ghost imaging","volume":"45","author":"Yuan","year":"2020","journal-title":"Opt. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/j.optcom.2015.12.013","article-title":"Cryptanalysis and security enhancement of optical cryptography based on computational ghost imaging","volume":"365","author":"Yuan","year":"2016","journal-title":"Opt. Commun."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1109\/TIT.2006.871582","article-title":"Compressed sensing","volume":"52","author":"Donoho","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Eldar, Y.C., and Kutyniok, G. (2012). Compressed Sensing: Theory and Applications, Cambridge University Press.","DOI":"10.1017\/CBO9780511794308"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"065702","DOI":"10.1088\/2040-8986\/ac6597","article-title":"An encryption method based on computational ghost imaging with chaotic mapping and DNA encoding","volume":"24","author":"Yang","year":"2022","journal-title":"J. Opt."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"7676","DOI":"10.1038\/s41598-017-07816-2","article-title":"Information security scheme based on computational temporal ghost imaging","volume":"7","author":"Jiang","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"119557","DOI":"10.1109\/ACCESS.2019.2936119","article-title":"Known-plaintext attack and ciphertext-only attack for encrypted single-pixel imaging","volume":"7","author":"Jiao","year":"2019","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"43860","DOI":"10.1364\/OE.445689","article-title":"Known-plaintext cryptanalysis for a computational-ghost-imaging cryptosystem via the Pix2Pix generative adversarial network","volume":"29","author":"Liu","year":"2021","journal-title":"Opt. Express"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2350190","DOI":"10.1142\/S0218127423501900","article-title":"Chaotic multiple-image encryption algorithm based on block scrambling and dynamic DNA coding","volume":"33","author":"Chen","year":"2023","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"170590","DOI":"10.1016\/j.ijleo.2023.170590","article-title":"Color image encryption algorithm based on Double layer Josephus scramble and laser chaotic system","volume":"275","author":"Wang","year":"2023","journal-title":"Optik"},{"key":"ref_29","first-page":"3900511","article-title":"Multiple-image encryption based on compressive ghost imaging and coordinate sampling","volume":"8","author":"Li","year":"2016","journal-title":"IEEE Photonics J."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3878","DOI":"10.1049\/ipr2.13214","article-title":"Multi-image encryption and authentication using computational ghost imaging and singular value decomposition","volume":"18","author":"Huang","year":"2024","journal-title":"IET Image Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"107316","DOI":"10.1016\/j.optlastec.2021.107316","article-title":"An image encryption algorithm based on hyperchaotic system and DNA coding","volume":"143","author":"Wang","year":"2021","journal-title":"Opt. Laser Technol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"5075","DOI":"10.1016\/j.ijleo.2014.06.054","article-title":"Novel hybrid image compression\u2013encryption algorithm based on compressive sensing","volume":"125","author":"Zhou","year":"2014","journal-title":"Optik"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1640","DOI":"10.1137\/140970537","article-title":"An improved fast iterative shrinkage thresholding algorithm for image deblurring","volume":"8","author":"Ahmad","year":"2015","journal-title":"SIAM J. Imaging Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1007\/s11071-021-07192-7","article-title":"A fast and efficient multiple images encryption based on single-channel encryption and chaotic system","volume":"108","author":"Gao","year":"2022","journal-title":"Nonlinear Dyn."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2250186","DOI":"10.1142\/S0218127422501863","article-title":"A chaotic image encryption scheme based on genetic central dogma and KMP method","volume":"32","author":"Sha","year":"2022","journal-title":"Int. J. Bifurc. Chaos"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"112133","DOI":"10.1016\/j.chaos.2022.112133","article-title":"Design and DSP implementation of a fractional-order detuned laser hyperchaotic circuit with applications in image encryption","volume":"159","author":"Li","year":"2022","journal-title":"Chaos Solitons Fractals"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"107373","DOI":"10.1016\/j.sigpro.2019.107373","article-title":"Characteristic analysis of the fractional-order hyperchaotic complex system and its image encryption application","volume":"169","author":"Yang","year":"2020","journal-title":"Signal Process."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1063","DOI":"10.1016\/j.ins.2020.09.032","article-title":"Cross-plane colour image encryption using a two-dimensional logistic tent modular map","volume":"546","author":"Hua","year":"2021","journal-title":"Inf. Sci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2243","DOI":"10.1007\/s11277-020-07680-w","article-title":"Image encryption using dynamic S-box substitution in the wavelet domain","volume":"115","author":"Shafique","year":"2020","journal-title":"Wirel. Pers. Commun."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"107484","DOI":"10.1016\/j.sigpro.2020.107484","article-title":"A novel image encryption scheme based on conservative hyperchaotic system and closed-loop diffusion between blocks","volume":"171","author":"Zhou","year":"2020","journal-title":"Signal Process."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/j.optlaseng.2019.03.006","article-title":"An optical image compression and encryption scheme based on compressive sensing and RSA algorithm","volume":"121","author":"Gong","year":"2019","journal-title":"Opt. Lasers Eng."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"7800116","DOI":"10.1109\/JPHOT.2021.3076480","article-title":"Multi-image encryption based on compressed sensing and deep learning in optical gyrator domain","volume":"13","author":"Ni","year":"2021","journal-title":"IEEE Photonics J."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"106162","DOI":"10.1016\/j.asoc.2020.106162","article-title":"A novel image encryption scheme using both pixel level and bit level permutation with chaotic map","volume":"90","author":"Shahna","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"42227","DOI":"10.1109\/ACCESS.2018.2858839","article-title":"An efficient chaotic image cryptosystem based on simultaneous permutation and diffusion operations","volume":"6","author":"Diab","year":"2018","journal-title":"IEEE Access"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Jiang, M., and Yang, H. (2023). Image Encryption Algorithm Using Multi-Level Permutation and Improved Logistic\u2013Chebyshev Coupled Map. Information, 14.","DOI":"10.3390\/info14080456"}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/17\/3\/239\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T13:12:54Z","timestamp":1772457174000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/17\/3\/239"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,1]]},"references-count":45,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2026,3]]}},"alternative-id":["info17030239"],"URL":"https:\/\/doi.org\/10.3390\/info17030239","relation":{},"ISSN":["2078-2489"],"issn-type":[{"value":"2078-2489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,1]]}}}