{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:50:57Z","timestamp":1760241057622,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2019,11,19]],"date-time":"2019-11-19T00:00:00Z","timestamp":1574121600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Image hash is an alternative to cryptographic hash functions for checking integrity of digital images. Compared to cryptographic hash functions, an image hash or a Perceptual Hash Function (PHF) is resilient to content preserving distortions and sensitive to malicious tampering. In this paper, a robust and secure image hashing technique using a Gaussian pyramid is proposed. A Gaussian pyramid decomposes an image into different resolution levels which can be utilized to obtain robust and compact hash features. These stable features have been utilized in the proposed work to construct a secure and robust image hash. The proposed scheme uses Laplacian of Gaussian (LOG) and disk filters to filter the low-resolution Gaussian decomposed image. The filtered images are then subtracted and their difference is used as a hash. To make the hash secure, a key is introduced before feature extraction, thus making the entire feature space random. The proposed hashing scheme has been evaluated through a number of experiments involving cases of non-malicious distortions and malicious tampering. Experimental results reveal that the proposed hashing scheme is robust against non-malicious distortions and is sensitive to detect minute malicious tampering. Moreover, False Positive Probability (FPP) and False Negative Probability (FNP) results demonstrate the effectiveness of the proposed scheme when compared to state-of-the-art image hashing algorithms proposed in the literature.<\/jats:p>","DOI":"10.3390\/e21111132","type":"journal-article","created":{"date-parts":[[2019,11,19]],"date-time":"2019-11-19T11:30:17Z","timestamp":1574163017000},"page":"1132","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["A Secure and Robust Image Hashing Scheme Using Gaussian Pyramids"],"prefix":"10.3390","volume":"21","author":[{"given":"Iram","family":"Bashir","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, HITEC University Taxila, Punjab 47080, Pakistan"}]},{"given":"Fawad","family":"Ahmed","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, HITEC University Taxila, Punjab 47080, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6289-8248","authenticated-orcid":false,"given":"Jawad","family":"Ahmad","sequence":"additional","affiliation":[{"name":"School of Computing, Edinburgh Napier University, Edinburgh EH10 5DT, UK"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2133-0757","authenticated-orcid":false,"given":"Wadii","family":"Boulila","sequence":"additional","affiliation":[{"name":"College of Computer Science and Engineering, Taibah University, Al-Madinah P.O. Box 344, Saudi Arabia"},{"name":"RIADI Laboratory, University of Manouba, Manouba 2010, Tunisia"}]},{"given":"Nouf","family":"Alharbi","sequence":"additional","affiliation":[{"name":"College of Computer Science and Engineering, Taibah University, Al-Madinah P.O. Box 344, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Sajjad, M., Haq, I.U., Lloret, J., Ding, W., and Muhammad, K. (2019). Robust image hashing based efficient authentication for smart industrial environment. IEEE Trans. Ind. Inform.","DOI":"10.1109\/TII.2019.2921652"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"21999","DOI":"10.1007\/s11042-019-7513-8","article-title":"Geometrically robust video hashing based on ST-PCT for video copy detection","volume":"78","author":"Tang","year":"2019","journal-title":"Multimed. Tools Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"5969","DOI":"10.1007\/s11042-018-6373-y","article-title":"An audio encryption based on synchronization of robust BAM FCNNs with time delays","volume":"78","author":"Kalpana","year":"2019","journal-title":"Multimed. Tools Appl."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Gentry, E., McIntyre, R., Soltys, M., and Lyu, F. (2019, January 14\u201315). SEAKER: A tool for fast digital forensic triage. Proceedings of the Future of Information and Communication Conference, San Francisco, CA, USA.","DOI":"10.1007\/978-3-030-12385-7_87"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"5305","DOI":"10.1007\/s11042-018-5732-z","article-title":"Image authentication and tamper localization based on relative difference between DCT coefficient and its estimated value","volume":"78","author":"Ding","year":"2019","journal-title":"Multimed. Tools Appl."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"\u017divic, N. (2015). Robust Image Authentication in the Presence of Noise, Springer.","DOI":"10.1007\/978-3-319-13156-6"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1456","DOI":"10.1016\/j.sigpro.2009.05.024","article-title":"A secure and robust hash-based scheme for image authentication","volume":"90","author":"Ahmed","year":"2010","journal-title":"Signal Process."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"532","DOI":"10.1109\/TCOM.1983.1095851","article-title":"The Laplacian pyramid as a compact image code","volume":"31","author":"Burt","year":"1983","journal-title":"IEEE Trans. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1023\/B:VISI.0000029664.99615.94","article-title":"Distinctive image features from scale-invariant keypoints","volume":"60","author":"Lowe","year":"2004","journal-title":"Int. J. Comput. Vis."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1109\/TIFS.2006.873601","article-title":"Robust and secure image hashing","volume":"1","author":"Swaminathan","year":"2006","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.dsp.2015.03.006","article-title":"Robust hashing for image authentication using quaternion discrete Fourier transform and log-polar transform","volume":"41","author":"Ouyang","year":"2015","journal-title":"Digit. Signal Process."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"711","DOI":"10.1109\/TKDE.2013.45","article-title":"Robust perceptual image hashing based on ring partition and NMF","volume":"26","author":"Tang","year":"2014","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1109\/TMM.2015.2432672","article-title":"Secure and robust two-phase image authentication","volume":"17","author":"Tabatabaei","year":"2015","journal-title":"IEEE Trans. Multimed."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"376","DOI":"10.1109\/TIFS.2007.902670","article-title":"Robust and secure image hashing via non-negative matrix factorizations","volume":"2","author":"Monga","year":"2007","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.dsp.2015.05.002","article-title":"Robust image hashing with embedding vector variance of LLE","volume":"43","author":"Tang","year":"2015","journal-title":"Digital Signal Processing"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Xiang, S., Kim, H.J., and Huang, J. (2007, January 20\u201321). Histogram-based image hashing scheme robust against geometric deformations. Proceedings of the 9th Workshop on Multimedia & Security, Dallas, TX, USA.","DOI":"10.1145\/1288869.1288886"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Abbas, S.Q., Ahmed, F., \u017divi\u0107, N., and Ur-Rehman, O. (2016, January 18\u201320). Perceptual image hashing using SVD based Noise Resistant Local Binary Pattern. Proceedings of the 2016 8th International Congress on Ultra Modern Telecommunications and Control Systems and Workshops (ICUMT), Lisbon, Portugal.","DOI":"10.1109\/ICUMT.2016.7765393"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.neucom.2018.04.057","article-title":"Image hashing with color vector angle","volume":"308","author":"Tang","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"738","DOI":"10.1109\/PIC.2010.5687938","article-title":"Perceptual image hash for tampering detection using Zernike moments","volume":"Volume 2","author":"Zhao","year":"2010","journal-title":"Proceedings of the 2010 IEEE International Conference on Progress in Informatics and Computing (PIC)"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1109\/CMC.2010.233","article-title":"A Self-Synchronized Image Hash Algorithm","volume":"Volume 1","author":"Wu","year":"2010","journal-title":"Proceedings of the 2010 International Conference on Communications and Mobile Computing (CMC)"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"25409","DOI":"10.1007\/s11042-018-5799-6","article-title":"Image authentication based on robust image hashing with geometric correction","volume":"77","author":"Karsh","year":"2018","journal-title":"Multimed. Tools Appl."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1109\/MINES.2009.142","article-title":"Detection of image region duplication forgery using model with circle block","volume":"Volume 1","author":"Wang","year":"2009","journal-title":"Proceedings of the International Conference on Multimedia Information Networking and Security (MINES\u201909)"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"741","DOI":"10.1109\/ICDAR.2017.126","article-title":"A perceptual image hashing algorithm for hybrid document security","volume":"Volume 1","author":"Eskenazi","year":"2017","journal-title":"Proceedings of the 2017 14th IAPR International Conference on Document Analysis and Recognition (ICDAR)"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"981","DOI":"10.1109\/TIP.2009.2038637","article-title":"Perceptual image hashing based on virtual watermark detection","volume":"19","author":"Khelifi","year":"2010","journal-title":"IEEE Trans. Image Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"4031","DOI":"10.7498\/aps.54.4031","article-title":"Pseudo-random number generator based on TD-ERCS chaos and its statistic characteristics analysis","volume":"54","author":"Sheng","year":"2005","journal-title":"Acta Phys. Sin."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"13951","DOI":"10.1007\/s11042-015-2973-y","article-title":"A secure image encryption scheme based on chaotic maps and affine transformation","volume":"75","author":"Ahmad","year":"2016","journal-title":"Multimed. Tools Appl."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"5429","DOI":"10.1007\/s11042-014-1861-1","article-title":"Efficient image encryption with block shuffling and chaotic map","volume":"74","author":"Tang","year":"2015","journal-title":"Multimed. Tools Appl."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3452","DOI":"10.1109\/TIP.2006.881948","article-title":"Perceptual image hashing via feature points: Performance evaluation and tradeoffs","volume":"15","author":"Monga","year":"2006","journal-title":"IEEE Trans. Image Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1016\/S0923-5965(02)00130-3","article-title":"Content-based image copy detection","volume":"18","author":"Kim","year":"2003","journal-title":"Signal Process. Image Commun."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"37211","DOI":"10.1109\/ACCESS.2019.2896661","article-title":"Keyed Hash Function Using Hyper Chaotic System with Time-Varying Parameters Perturbation","volume":"7","author":"Liu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Todorova, M., Stoyanov, B., Szczypiorski, K., and Kordov, K. (2018). SHAH: hash function based on irregularly decimated chaotic map. arXiv.","DOI":"10.24425\/123546"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/11\/1132\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:35:46Z","timestamp":1760189746000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/21\/11\/1132"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,19]]},"references-count":31,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2019,11]]}},"alternative-id":["e21111132"],"URL":"https:\/\/doi.org\/10.3390\/e21111132","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2019,11,19]]}}}