[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-37255-en":3,"doc-seo-37255-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},37255,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1782698725881665579",8,"Research & Report","Chaos-Based Symmetric Image Encryption Scheme with Bit-Level Permutation","Recent years have seen a wide range of chaos-based digital image encryption algorithms, many treating a pixel as the smallest atomic element and applying permutations and diffusions at the pixel level. A bit-level permutation can both relocate pixel positions and change their values. This work proposes a symmetric image cryptosystem using the Arnold cat map for bit-level permutation and the logistic map for diffusion, with simulations showing improved security and high efficiency.","| A chaos-based symmetric image encryption scheme using a bit-level permutation\u003Cbr>Zhi-liang Zhu a, Wei Zhang c, ⇑, Kwok-wo Wongb, Hai Yu a\u003Cbr>a Software College, Northeastern University, No. 11, Lane 3, WenHua Road, Shenyang, Liaoning, China\u003Cbr>b Department of Electronic Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong\u003Cbr>c College of Information Science and Engineering, Northeastern University, No. 11, Lane 3, WenHua Road, Shenyang, Liaoning, China |  |\n| --- | --- |\n| a r t i c l e i n f o | a b s t r a c t\u003Cbr>In recent years, a variety of chaos-based digital image encryption algorithms have been suggested. Most of these algorithms implement permutations and diffusions at the pixel level by considering the pixel as the smallest (atomic) element of an image. In fact, a permutation at the bit level not only changes the position of the pixel but also alters its value. Here we propose an image cryptosystem employing the Arnold cat map for bit-level permutation and the logistic map for diffusion. Simulations have been carried out and analyzed in detail, demonstrating the superior security and high efficiency of our cryptosystem.\u003Cbr>Crown Copyright 􀀂 2010 Published by Elsevier Inc. All rights reserved. |\n| Article history:\u003Cbr>Received 9 July 2009\u003Cbr>Received in revised form 4 November 2010 Accepted 8 November 2010 |  |\n| Keywords:\u003Cbr>Bit-level permutation\u003Cbr>Chaos\u003Cbr>Cryptography\u003Cbr>Image encryption |  |\n\n1. Introduction  \nInformation security plays a significant role in all fields, especially those related to confidential business or military affairs. This topic is not new and can be traced back to Shannon’s classic paper [18]. In recent years, this has attracted increasing research attention [2–11,19,23]. Due to some interesting intrinsic features such as ergodicity, sensitivity to initial conditions and system parameters, the use of chaotic systems for data encryption has been studied extensively [3,6–10,15–17,20–22,24,26]. Chaos-based algorithms have shown exceptionally superior properties in aspects such as security and complexity [3].  \nThe existing chaos-based image cryptosystems can be classified into two categories. In the first category, a pixel is considered as the smallest element, and a digital image is considered as a collection of pixels. However, in the second class, a pixel can be further divided into a number of bits, on which bit-level operations are performed. For example, a pixel in a grey-scale image usually consists of 8 bits, but these bits carry different amount of information. In [22], Xiang et al. proposed a selective image encryption algorithm that only encrypts the four higher bits of each pixel and leaves the lower four bits unchanged. This algorithm has a reduced execution time because it only encrypts half of the bits.  \nIn [25], a typical bit-level cipher called Bit Recirculation Image Encryption (BRIE) was suggested. Its two-dimensional version, Two-Dimension Circulation Encryption Algorithm (TDCEA), was studied in [4]. In TDCEA, eight consecutive pixels are treated as a group and the corresponding 64 bits form a matrix M of size 8 􀀂 8. There are two kinds of bit rotation operating on M. They are defined as follows:  \n1. In the horizontal direction, Xpi;r denotes the cyclic shift of the ith row of the matrix to the left (when p = 1) or the right (when p = 0) by r bits.  \n⇑ Corresponding author. Tel.: +86 13998228657.  \nE-mail [address: wei.zhang2010@gmail.com](address: wei.zhang2010@gmail.com) (W. Zhang).  \n0020-0255/$ -see front matter Crown Copyright 􀀂 2010 Published by Elsevier Inc. All rights reserved.  \ndoi:10.1016/j.ins.2010.11.009  \n1172 Z.-l. Zhu et al. /Information Sciences 181 (2011) 1171–1186  \n2. In the vertical direction, Yqj;s denotes the cyclic shift of the jth column of the matrix upwards (when q = 1) or downwards (when q = 0) by s bits.  \nThe coefficientsp, q, r, and s ofthe two rotation operations are governed by a logistic map. These operations are","cbCaimbnG21pS0rj","https://ap.wps.com/l/cbCaimbnG21pS0rj","pdf",2598367,4,1,16,"English","en",105,"# Introduction\n## Pixel-level vs bit-level encryption\n## Bit rotation and related prior schemes","[{\"question\":\"Why does bit-level permutation provide stronger protection than pixel-level permutation?\",\"answer\":\"Bit-level permutation not only changes where pixel bits go but also alters their values. This increases the effect compared with treating pixels as atomic elements.\"},{\"question\":\"What chaotic systems are used in the proposed cryptosystem?\",\"answer\":\"The Arnold cat map performs the bit-level permutation, while the logistic map drives diffusion to modify bit values across the image.\"},{\"question\":\"What security weakness exists in permutation-only bit-level ciphers like BRIE and TDCEA?\",\"answer\":\"Because they rely on cyclic bit shifting without changing element values, they are insecure under known/chosen-plaintext attacks, as noted by subsequent cryptanalysis.\"}]",1783026038,40,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"chaos-based-symmetric-image-encryption-scheme-with-bit-level-permutation","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":20},"https://docshare.wps.com/document/chaos-based-symmetric-image-encryption-scheme-with-bit-level-permutation/37255/",{"url":52,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-09","2026-07-02",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why does bit-level permutation provide stronger protection than pixel-level permutation?","Question",{"text":75,"@type":76},"Bit-level permutation not only changes where pixel bits go but also alters their values. This increases the effect compared with treating pixels as atomic elements.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What chaotic systems are used in the proposed cryptosystem?",{"text":80,"@type":76},"The Arnold cat map performs the bit-level permutation, while the logistic map drives diffusion to modify bit values across the image.",{"name":82,"@type":73,"acceptedAnswer":83},"What security weakness exists in permutation-only bit-level ciphers like BRIE and TDCEA?",{"text":84,"@type":76},"Because they rely on cyclic bit shifting without changing element values, they are insecure under known/chosen-plaintext attacks, as noted by subsequent cryptanalysis.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,119,122,127,130,134],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":29,"slug":118},7,"Healthcare","healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":125,"slug":126},9,"Religion & Spirituality",20,"religion-spirituality",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":128,"show_sort_weight":125,"slug":129},"World Cup","world-cup",{"id":131,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":131,"slug":133},10,"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]