Image encryption.rar_image_encryption_电子书籍下载-pudn.com

<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/62572ce9bd8c6f2306b96d9f/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62572ce9bd8c6f2306b96d9f/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">Image encryption scheme with bit-level scrambling</div><div class="t m0 x1 h2 y2 ff1 fs0 fc0 sc0 ls0 ws0">and multiplication diffusion</div><div class="t m0 x1 h3 y3 ff2 fs1 fc0 sc0 ls0 ws0">Chun-Lai Li</div><div class="t m1 x2 h4 y4 ff2 fs2 fc0 sc0 ls0 ws0">1</div><div class="t m0 x3 h3 y3 ff3 fs3 fc0 sc0 ls0 ws0">& Yang Zhou</div><div class="t m1 x4 h4 y4 ff2 fs2 fc0 sc0 ls0 ws0">1</div><div class="t m0 x5 h3 y3 ff3 fs3 fc0 sc0 ls0 ws0">& Hong-Min Li</div><div class="t m1 x6 h4 y4 ff2 fs2 fc0 sc0 ls0 ws0">1</div><div class="t m0 x7 h3 y3 ff3 fs3 fc0 sc0 ls0 ws0">& Wei Feng</div><div class="t m1 x8 h4 y4 ff2 fs2 fc0 sc0 ls0 ws0">1</div><div class="t m0 x9 h3 y3 ff3 fs3 fc0 sc0 ls0 ws0">& Jian-Rong Du</div><div class="t m1 xa h4 y4 ff2 fs2 fc0 sc0 ls0 ws0">1</div><div class="t m0 x1 h5 y5 ff4 fs3 fc0 sc0 ls0 ws0">Received: 16 June 2020 /Revised: 14 January 2021 / Accepted: 4 February 2021</div><div class="t m0 x1 h6 y6 ff5 fs3 fc0 sc0 ls0 ws0">#</div><div class="t m0 xb h5 y7 ff4 fs3 fc0 sc0 ls0 ws0">The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature 2021</div><div class="t m0 x1 h7 y8 ff6 fs1 fc0 sc0 ls0 ws0">Abstract</div><div class="t m0 x1 h8 y9 ff7 fs4 fc0 sc0 ls0 ws0">As the most effective method of multimedia security protection, image encryption is</div><div class="t m0 x1 h8 ya ff7 fs4 fc0 sc0 ls0 ws0">widely used in data hiding, security authentication and content protection. However, the</div><div class="t m0 x1 h8 yb ff7 fs4 fc0 sc0 ls0 ws0">security and efficiency are still the key issues of image encryption algorithm. In this</div><div class="t m0 x1 h8 yc ff7 fs4 fc0 sc0 ls0 ws0">paper, a grayscale image encryption scheme based on the architecture of bit-level</div><div class="t m0 x1 h8 yd ff7 fs4 fc0 sc0 ls1 ws0">scrambling and multiplication diffusion is proposed. Firstly, the input image is</div><div class="t m0 x1 h8 ye ff7 fs4 fc0 sc0 ls0 ws0">decomposed into eight bit planes and randomly divided into three parts. Secondly, the</div><div class="t m0 x1 h8 yf ff7 fs4 fc0 sc0 ls0 ws0">scrambling process of each part is respectively realized by using binary tree, flip</div><div class="t m0 x1 h8 y10 ff7 fs4 fc0 sc0 ls0 ws0">scrambling and improved circle index scrambling. Finally, the diffusing operation of</div><div class="t m0 x1 h8 y11 ff7 fs4 fc0 sc0 ls0 ws0">the scrambled components is executed by improving the GF (257) domain multiplication.</div><div class="t m0 x1 h8 y12 ff7 fs4 fc0 sc0 ls0 ws0">The remarkable advantage of the scrambling operation is that it not only effectively</div><div class="t m0 x1 h8 y13 ff7 fs4 fc0 sc0 ls0 ws0">permutes the pixels, but also permutes the bits in each pixel, and consequently it</div><div class="t m0 x1 h8 y14 ff7 fs4 fc0 sc0 ls0 ws0">sufficiently destroys the correlation of adjacent pixels. And the parallel processing of</div><div class="t m0 x1 h8 y15 ff7 fs4 fc0 sc0 ls0 ws0">different scrambling operations will increase the confusion effect and real-time perfor-</div><div class="t m0 x1 h8 y16 ff7 fs4 fc0 sc0 ls0 ws0">mance. Moreover, the key stream for scrambling and diffusion operations is designed and</div><div class="t m0 x1 h8 y17 ff7 fs4 fc0 sc0 ls0 ws0">selected strictly dependent on the plain-image. Therefore, our encryption scheme signif-</div><div class="t m0 x1 h8 y18 ff7 fs4 fc0 sc0 ls0 ws0">icantly improves the security by disturbing known-plaintext and chosen-plaintext attacks.</div><div class="t m0 x1 h8 y19 ff7 fs4 fc0 sc0 ls0 ws0">Simulation experiments and security analyses further verify that the proposed algorithm is</div><div class="t m0 x1 h8 y1a ff7 fs4 fc0 sc0 ls0 ws0">secure and effective to withstand various attacks.</div><div class="t m0 x1 h9 y1b ff1 fs1 fc0 sc0 ls0 ws0">Keywords Binary tree</div><div class="t m0 xc ha y1c ff7 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 xd ha y1b ff7 fs1 fc0 sc0 ls0 ws0">Chaos dynamics</div><div class="t m0 xe ha y1c ff7 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 xf ha y1b ff7 fs1 fc0 sc0 ls0 ws0">Multiplication diffusion</div><div class="t m0 x10 ha y1c ff7 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m0 x11 ha y1b ff7 fs1 fc0 sc0 ls0 ws0">Image encryption</div><div class="t m0 x1 h5 y1d ff4 fs3 fc0 sc0 ls0 ws0">Multimedia Tools and Applications</div><div class="t m0 x1 h5 y1e ff4 fs3 fc0 sc0 ls0 ws0">https://doi.org/10.1007/s11042-021-10631-7</div><div class="t m0 x1 hb y1f ff8 fs5 fc0 sc0 ls0 ws0">* Chun-Lai Li</div><div class="t m0 x12 hc y20 ff7 fs5 fc0 sc0 ls2 ws0">lichunlai33@126.com</div><div class="t m2 x1 hd y21 ff7 fs6 fc0 sc0 ls0 ws0">1</div><div class="t m0 x13 hc y22 ff7 fs5 fc0 sc0 ls0 ws0">Key Laboratory of Hunan Province on Information Photonics and Freespace Optical</div><div class="t m0 x13 hc y23 ff7 fs5 fc0 sc0 ls0 ws0">Communications, Hunan Institute of Science and Technology, Yueyang 414006, China</div><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a></div><div class="pi" data-data='{"ctm":[2.037103,0.000000,0.000000,2.037103,0.000000,0.000000]}'></div></div> </body> </html>

<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62572ce9bd8c6f2306b96d9f/bg2.jpg"><div class="t m0 x1 he y24 ff6 fs7 fc0 sc0 ls0 ws0">1 Introduction</div><div class="t m0 x1 ha y25 ff7 fs1 fc0 sc0 ls0 ws0">With the rapid development of communication and multimedia technology, huge number of</div><div class="t m0 x1 ha y26 ff7 fs1 fc0 sc0 ls0 ws0">image and video data are generated, transmitted and stored over the networks. However, it is</div><div class="t m0 x1 ha y27 ff7 fs1 fc0 sc0 ls0 ws0">liable to access, steal and redistribute these data through computer terminal or information</div><div class="t m0 x1 ha y28 ff7 fs1 fc0 sc0 ls0 ws0">channel. Therefore, if there is no technical protection, data leakage, data forgery and other</div><div class="t m0 x1 ha y29 ff7 fs1 fc0 sc0 ls0 ws0">security risks will happen. For example, when an image is stored in a cyberspace without</div><div class="t m0 x1 ha y2a ff7 fs1 fc0 sc0 ls0 ws0">technical protection, confidential information will be exposed. Therefore, how to protect the</div><div class="t m0 x1 ha y2b ff7 fs1 fc0 sc0 ls0 ws0">image from unauthorized access and destruction has attracted more and more attention [16].</div><div class="t m0 x1 ha y2c ff7 fs1 fc0 sc0 ls0 ws0">Encrypting image is an effective approach for image protection, which converts a meaningful</div><div class="t m0 x1 ha y2d ff7 fs1 fc0 sc0 ls0 ws0">image into a noise-like meaningless cipher-image [5, 18, 37], and is widely used in data</div><div class="t m0 x1 ha y2e ff7 fs1 fc0 sc0 ls0 ws0">hiding, security authentication, copyright protection and fragile watermarking [13, 17, 22].</div><div class="t m0 x1 ha y2f ff7 fs1 fc0 sc0 ls0 ws0">Because chaotic system has good pseudo-random, ergodicity, high sensitivity to initial</div><div class="t m0 x1 ha y30 ff7 fs1 fc0 sc0 ls0 ws0">condition and system parameter, chaotic cryptographic technology is recognized as an impor-</div><div class="t m0 x1 ha y31 ff7 fs1 fc0 sc0 ls0 ws0">tant candidate for image encryption [3, 29, 32, 39].</div><div class="t m0 x14 ha y32 ff7 fs1 fc0 sc0 ls0 ws0">Since the first chaotic image encryption scheme was proposed in 1989 [25], many chaos-</div><div class="t m0 x1 ha y33 ff7 fs1 fc0 sc0 ls0 ws0">based image encryption techniques have been proposed [7, 23, 25, 38]. And according to</div><div class="t m0 x1 ha y34 ff7 fs1 fc0 sc0 ls4 ws0">Shannon’s information theory, the cryptographic structure with permutation and diffusion</div><div class="t m0 x1 ha y35 ff7 fs1 fc0 sc0 ls0 ws0">operations is generally adopted [28]. The permutation operation mainly includes two methods:</div><div class="t m0 x1 ha y36 ff7 fs1 fc0 sc0 ls0 ws0">pixel-level-based permutation and bit-level-based permutation. The pixel-level permutation</div><div class="t m0 x1 ha y37 ff7 fs1 fc0 sc0 ls0 ws0">will change the position of the pixel while the value of the pixel keeps invariable. However, the</div><div class="t m0 x1 ha y38 ff7 fs1 fc0 sc0 ls0 ws0">bit-level permutation can not only change the position of the pixel, but also change the value of</div><div class="t m0 x1 ha y39 ff7 fs1 fc0 sc0 ls5 ws0">the pixel [44]. Therefore, the bit-level permutation is considered to be more effective [36]. In</div><div class="t m0 x1 ha y3a ff7 fs1 fc0 sc0 ls0 ws0">the process of diffusion operation, the pixel value would be modified. In addition, the tiny</div><div class="t m0 x1 ha y3b ff7 fs1 fc0 sc0 ls0 ws0">change of any bit in the plain-image will affect the whole cipher-image. The permutation-only</div><div class="t m0 x1 ha y3c ff7 fs1 fc0 sc0 ls0 ws0">encryption is vulnerable to be cracked by known-plaintext attack or chosen-plaintext attack.</div><div class="t m0 x1 ha y3d ff7 fs1 fc0 sc0 ls0 ws0">Therefore, the chaotic encryption scheme combining permutation and diffusion would have</div><div class="t m0 x1 ha y3e ff7 fs1 fc0 sc0 ls0 ws0">higher security [19, 31, 34].</div><div class="t m0 x14 ha y3f ff7 fs1 fc0 sc0 ls0 ws0">However, many permutation-diffusion-based encryption schemes are found to contain</div><div class="t m0 x1 ha y40 ff7 fs1 fc0 sc0 ls0 ws0">security defects. For example, Wang reported an image encryption method by adopting the</div><div class="t m0 x1 ha y41 ff7 fs1 fc0 sc0 ls0 ws0">simulated annealing algorithm to generate excellent random sequence for the confusion, but</div><div class="t m0 x1 ha y42 ff7 fs1 fc0 sc0 ls0 ws0">some of the plain-image pixels still remain in the original positions after permutation [40].</div><div class="t m0 x1 ha y43 ff7 fs1 fc0 sc0 ls0 ws0">Mirzaei introduced a parallel image encryption scheme based on total shuffling matrix. The</div><div class="t m0 x1 ha y44 ff7 fs1 fc0 sc0 ls0 ws0">encryption process is simple and the key stream is invariable for different plain-images, thus it</div><div class="t m0 x1 ha y45 ff7 fs1 fc0 sc0 ls0 ws0">cannot effectively resist the plaintext attack [26]. Murillo-Escobar proposed a chaotic image</div><div class="t m0 x1 ha y46 ff7 fs1 fc0 sc0 ls0 ws0">encryption algorithm based on the characteristics of total plain-image. This scheme is simple</div><div class="t m0 x1 ha y47 ff7 fs1 fc0 sc0 ls0 ws0">and is difficult to reflect the main features of plain-image only by simple sum and remainder</div><div class="t m0 x1 ha y48 ff7 fs1 fc0 sc0 ls0 ws0">operation [27]. Fu presented a fast scheme for encrypting medical image based on bit-level</div><div class="t m0 x1 ha y49 ff7 fs1 fc0 sc0 ls0 ws0">substitution mechanism. However, the permutation key is independent of the plaintext to</div><div class="t m0 x1 ha y4a ff7 fs1 fc0 sc0 ls0 ws0">weaken the capability of resisting differential cryptanalysis [11]. Sun reported a hyperchaotic</div><div class="t m0 x1 ha y4b ff7 fs1 fc0 sc0 ls0 ws0">image encryption algorithm based on pixel-level scrambling, bit-level scrambling and DNA</div><div class="t m0 x1 ha y4c ff7 fs1 fc0 sc0 ls0 ws0">encoding [35]. The main security issue of this method is that the diffusion stage can be</div><div class="t m0 x1 ha y4d ff7 fs1 fc0 sc0 ls0 ws0">eliminated by simple calculation and the key stream is independent of the plain-images [9]. Ye</div><div class="t m0 x1 ha y4e ff7 fs1 fc0 sc0 ls0 ws0">proposed a chaotic image encryption algorithm based on information entropy [47]. However,</div><div class="t m0 x1 ha y4f ff7 fs1 fc0 sc0 ls0 ws0">when the round number is only one, the equivalent key of each basic operation can be</div><div class="t m0 x1 ha y50 ff7 fs1 fc0 sc0 ls0 ws0">recovered by differential attack [21]. In Ref. [46], a scrambling encryption algorithm was</div><div class="t m0 x1 ha y51 ff7 fs1 fc0 sc0 ls0 ws0">proposed, which scrambles the binary representation of gray-scale image by using the pseudo-</div><div class="t m0 x15 h5 y1d ff4 fs3 fc0 sc0 ls0 ws0">Multimedia Tools and Applications</div><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a></div><div class="pi" data-data='{"ctm":[2.037103,0.000000,0.000000,2.037103,0.000000,0.000000]}'></div></div>

<div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62572ce9bd8c6f2306b96d9f/bg3.jpg"><div class="t m4 x1 ha y24 ff7 fs1 fc0 sc0 ls0 ws0">random sequence generated by the iteration of digital chaotic map. However, it does not act on</div><div class="t m4 x1 ha y52 ff7 fs1 fc0 sc0 ls0 ws0">the M×(8 N) scrambling domain, but only cascades two scrambling algorithms with the</div><div class="t m4 x1 ha y53 ff7 fs1 fc0 sc0 ls0 ws0">scrambling domains of sizes M and 8 N [20].</div><div class="t m4 x14 ha y54 ff7 fs1 fc0 sc0 ls0 ws0">Following the analysis mentioned above, this paper proposes a grayscale image encryption</div><div class="t m4 x1 ha y55 ff7 fs1 fc0 sc0 ls0 ws0">scheme based on plaintext-related mechanism and chaotic system. This scheme involves two</div><div class="t m4 x1 ha y56 ff7 fs1 fc0 sc0 ls0 ws0">main processes of bit-level scrambling and multiplication diffusion (BLSMD). Specifically, the</div><div class="t m4 x1 ha y57 ff7 fs1 fc0 sc0 ls0 ws0">input image is firstly decomposed into 8 bit-planes and randomly divided into three parts. Then,</div><div class="t m4 x1 ha y58 ff7 fs1 fc0 sc0 ls0 ws0">the scrambling process for each part is conducted by using binary tree [12], flip scrambling and</div><div class="t m4 x1 ha y59 ff7 fs1 fc0 sc0 ls0 ws0">improved circle index scrambling [53], respectively. Finally, GF (257) domain multiplication</div><div class="t m4 x1 ha y5a ff7 fs1 fc0 sc0 ls0 ws0">[50] is improved and adopted to realize the diffusion operation of the scrambled image. The</div><div class="t m4 x1 ha y5b ff7 fs1 fc0 sc0 ls0 ws0">main contributions of this paper are as follows: (1) Pixel value is updated before executing</div><div class="t m4 x1 ha y5c ff7 fs1 fc0 sc0 ls0 ws0">scrambling process, which helps to resist chosen-plaintext attack since the attacker can’t choose</div><div class="t m4 x1 ha y5d ff7 fs1 fc0 sc0 ls0 ws0">the special plaintext image at will. (2) The scrambling operation is realized by introducing</div><div class="t m4 x1 ha y5e ff7 fs1 fc0 sc0 ls0 ws0">binary tree and flip scrambling for the first time and by improving circle index scrambling,</div><div class="t m4 x1 ha y5f ff7 fs1 fc0 sc0 ls0 ws0">based on bit-level decomposition and reconstruction. Thus the scrambling operation can</div><div class="t m4 x1 ha y60 ff7 fs1 fc0 sc0 ls0 ws0">efficaciously permute the position of pixels and the bits in each pixel, so as to modify the pixel</div><div class="t m4 x1 ha y61 ff7 fs1 fc0 sc0 ls0 ws0">value at the same time. And the parallel processing of different scrambling operations will</div><div class="t m4 x1 ha y62 ff7 fs1 fc0 sc0 ls0 ws0">increase the confusion effect and real-time performance. (3) The diffusion operation is realized</div><div class="t m4 x1 ha y63 ff7 fs1 fc0 sc0 ls0 ws0">by improving the GF (257) domain multiplication, based on the binary processing of high 4 bits</div><div class="t m4 x1 ha y64 ff7 fs1 fc0 sc0 ls0 ws0">and low 4 bits. (4) The chaotic sequences are generated according to the image information and</div><div class="t m4 x1 ha y65 ff7 fs1 fc0 sc0 ls0 ws0">initial value of dynamical system, and the processes of scrambling and diffusion are dynami-</div><div class="t m4 x1 ha y66 ff7 fs1 fc0 sc0 ls0 ws0">cally executed by selecting the chaotic sequence and SHA256 hash value of plain-image. Thus,</div><div class="t m4 x1 ha y67 ff7 fs1 fc0 sc0 ls0 ws0">even a small change in plaintext will have a significant impact on the encryption result.</div><div class="t m4 x14 ha y68 ff7 fs1 fc0 sc0 ls0 ws0">The rest of the paper is arranged as below. In Section 2, some related knowledge is</div><div class="t m4 x1 ha y69 ff7 fs1 fc0 sc0 ls0 ws0">introduced for encryption algorithm. In Section 3, the detailed encryption process is described.</div><div class="t m4 x1 ha y6a ff7 fs1 fc0 sc0 ls0 ws0">The simulation experiment and security analysis are presented in Section 4.Finally,we</div><div class="t m4 x1 ha y6b ff7 fs1 fc0 sc0 ls0 ws0">conclude this work in Section 5.</div><div class="t m4 x1 he y6c ff6 fs7 fc0 sc0 ls0 ws0">2 The preliminary knowledge</div><div class="t m4 x1 hf y6d ffc fs4 fc0 sc0 ls0 ws0">2.1 2D-LSCM map</div><div class="t m4 x1 ha y6e ff7 fs1 fc0 sc0 ls0 ws0">2D-LSCM is a combination of logistic map and sine map, defined as [15].</div><div class="t m4 x16 h10 y6f ffa fs1 fc0 sc0 ls0 ws0">x</div><div class="t m4 x17 h11 y70 ffa fs8 fc0 sc0 ls0 ws0">iþ1</div><div class="t m4 x18 h12 y71 ffd fs1 fc0 sc0 ls0 ws0">¼ sin π 4γx</div><div class="t m4 x19 h13 y70 ffa fs8 fc0 sc0 ls0 ws0">i</div><div class="t m4 x1a ha y71 ff7 fs1 fc0 sc0 ls0 ws0">1−x</div><div class="t m4 x1b h13 y70 ffa fs8 fc0 sc0 ls0 ws0">i</div><div class="t m4 x1c h12 y71 ffd fs1 fc0 sc0 ls8 ws0">ðÞþ1−γðÞsin πy</div><div class="t m4 x1d h13 y72 ffa fs8 fc0 sc0 ls0 ws0">i</div><div class="t m4 x1e h12 y71 ffd fs1 fc0 sc0 lsb ws0">ðÞðÞðÞ</div><div class="t m4 x16 h10 y73 ffa fs1 fc0 sc0 ls0 ws0">y</div><div class="t m4 x17 h11 y74 ffa fs8 fc0 sc0 ls0 ws0">iþ1</div><div class="t m4 x18 h12 y75 ffd fs1 fc0 sc0 ls0 ws0">¼ sin π 4γy</div><div class="t m4 x19 h13 y74 ffa fs8 fc0 sc0 ls0 ws0">i</div><div class="t m4 x1a ha y75 ff7 fs1 fc0 sc0 ls0 ws0">1−y</div><div class="t m4 x1b h13 y74 ffa fs8 fc0 sc0 ls0 ws0">i</div><div class="t m4 x1c h12 y75 ffd fs1 fc0 sc0 ls8 ws0">ðÞþ1−γðÞsin πx</div><div class="t m4 x1d h11 y76 ffa fs8 fc0 sc0 ls0 ws0">iþ1</div><div class="t m4 x1e h12 y75 ffd fs1 fc0 sc0 lse ws0">ðÞðÞðÞ</div><div class="t m4 xc h14 y77 ff10 fs1 fc0 sc0 ls0 ws0"></div><div class="t m4 x1f h12 y78 ffd fs1 fc0 sc0 ls0 ws0">ð1Þ</div><div class="t m4 x1 ha y79 ff7 fs1 fc0 sc0 ls0 ws0">where x</div><div class="t m4 x20 h13 y7a ffa fs8 fc0 sc0 ls0 ws0">i</div><div class="t m4 x21 ha y7b ff7 fs1 fc0 sc0 ls6 ws0">and y</div><div class="t m4 x22 h13 y7a ffa fs8 fc0 sc0 ls0 ws0">i</div><div class="t m4 x23 ha y7b ff7 fs1 fc0 sc0 ls0 ws0">are the system states generated by the i-th iteration; γ∈[0, 1] is the control</div><div class="t m4 x1 ha y7c ff7 fs1 fc0 sc0 ls0 ws0">parameter. Compared with many one-dimensional (1D) maps and improved hybrid maps, 2D-</div><div class="t m4 x1 ha y7d ff7 fs1 fc0 sc0 ls0 ws0">LSCM has better chaotic performance. Specifically, it has a wider chaotic range of γ∈(0, 1)</div><div class="t m4 x1 ha y7e ff7 fs1 fc0 sc0 ls0 ws0">and is hyper-chaotic in the range of γ∈(0, 0.34)∪(0.67, 1). When the representation precision</div><div class="t m4 x1 ha y7f ff7 fs1 fc0 sc0 ls0 ws0">reaches 10</div><div class="t m4 x24 h15 y80 fff fs8 fc0 sc0 ls0 ws0">−8</div><div class="t m4 x2 ha y81 ff7 fs1 fc0 sc0 ls0 ws0">, the average cycle length of 2D-LSCM is as high as 4,455,734, which can fully</div><div class="t m4 x1 ha y82 ff7 fs1 fc0 sc0 ls0 ws0">meet the requirement of image encryption. Furthermore, the state output of 2D-LSCM is also</div><div class="t m4 x1 ha y83 ff7 fs1 fc0 sc0 ls0 ws0">very uniform in the whole phase space and has excellent randomness.</div><div class="t m4 x14 ha y84 ff7 fs1 fc0 sc0 ls0 ws0">Before encrypting the plain-image sized M × N, we will iterate 2D-LSCM by respectively</div><div class="t m4 x1 ha y85 ff7 fs1 fc0 sc0 ls0 ws0">adopting two different set of the initial values and control parameter x</div><div class="t m4 x25 h15 y86 ff7 fs8 fc0 sc0 ls0 ws0">1</div><div class="t m4 x25 h15 y87 ff7 fs8 fc0 sc0 ls0 ws0">0</div><div class="t m4 x26 ha y88 ff7 fs1 fc0 sc0 ls0 ws0">,y</div><div class="t m4 x27 h15 y86 ff7 fs8 fc0 sc0 ls0 ws0">1</div><div class="t m4 x27 h15 y87 ff7 fs8 fc0 sc0 ls0 ws0">0</div><div class="t m4 x28 ha y88 ff7 fs1 fc0 sc0 ls0 ws0">, γ</div><div class="t m4 x29 h15 y89 ff7 fs8 fc0 sc0 ls0 ws0">1</div><div class="t m4 x2a ha y88 ff7 fs1 fc0 sc0 ls6 ws0">and x</div><div class="t m4 x2b h15 y86 ff7 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m4 x2b h15 y87 ff7 fs8 fc0 sc0 ls0 ws0">0</div><div class="t m4 x2c ha y88 ff7 fs1 fc0 sc0 ls0 ws0">,y</div><div class="t m4 x2d h15 y86 ff7 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m4 x2d h15 y87 ff7 fs8 fc0 sc0 ls0 ws0">0</div><div class="t m4 x2e ha y88 ff7 fs1 fc0 sc0 ls0 ws0">, γ</div><div class="t m4 x2f h15 y89 ff7 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m4 x30 ha y88 ff7 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m4 x1 h5 y1d ff4 fs3 fc0 sc0 ls0 ws0">Multimedia Tools and Applications</div><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a></div><div class="pi" data-data='{"ctm":[2.037103,0.000000,0.000000,2.037103,0.000000,0.000000]}'></div></div>

<div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62572ce9bd8c6f2306b96d9f/bg4.jpg"><div class="t m4 x1 ha y8a ff7 fs1 fc0 sc0 ls0 ws0">Specifically, the set of initial values x</div><div class="t m4 x31 h15 y8b ff7 fs8 fc0 sc0 ls0 ws0">1</div><div class="t m4 x31 h15 y8c ff7 fs8 fc0 sc0 ls0 ws0">0</div><div class="t m4 x32 ha y8a ff7 fs1 fc0 sc0 ls0 ws0">,y</div><div class="t m4 x33 h15 y8b ff7 fs8 fc0 sc0 ls0 ws0">1</div><div class="t m4 x33 h15 y8c ff7 fs8 fc0 sc0 ls0 ws0">0</div><div class="t m4 x19 ha y8a ff7 fs1 fc0 sc0 ls6 ws0">and system parameter γ</div><div class="t m4 x34 h15 y8d ff7 fs8 fc0 sc0 ls0 ws0">1</div><div class="t m4 x35 ha y8a ff7 fs1 fc0 sc0 ls11 ws0">isadoptedtogeneratethe</div><div class="t m4 x1 ha y8e ff7 fs1 fc0 sc0 ls0 ws0">chaotic sequencex</div><div class="t m4 x36 h15 y8f ff7 fs8 fc0 sc0 ls0 ws0">1</div><div class="t m4 x36 h13 y90 ffa fs8 fc0 sc0 ls0 ws0">i</div><div class="t m4 x37 ha y91 ff7 fs1 fc0 sc0 ls6 ws0">and y</div><div class="t m4 x16 h15 y8f ff7 fs8 fc0 sc0 ls0 ws0">1</div><div class="t m4 x16 h13 y90 ffa fs8 fc0 sc0 ls0 ws0">i</div><div class="t m4 x38 ha y91 ff7 fs1 fc0 sc0 ls0 ws0">with the length of M × N, by discarding the transition states. And we</div><div class="t m4 x1 ha y92 ff7 fs1 fc0 sc0 ls0 ws0">obtain the integer sequence K</div><div class="t m4 x39 h15 y93 ff7 fs8 fc0 sc0 ls0 ws0">1</div><div class="t m4 x3a ha y94 ff7 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m4 x3b h10 y95 ffa fs1 fc0 sc0 ls0 ws0">K</div><div class="t m4 x3c h15 y96 ff7 fs8 fc0 sc0 ls0 ws0">1</div><div class="t m4 x39 h12 y97 ffa fs1 fc0 sc0 ls0 ws0">iðÞ¼floor x</div><div class="t m4 x3d h15 y98 ff7 fs8 fc0 sc0 ls0 ws0">1</div><div class="t m4 x3d h13 y99 ffa fs8 fc0 sc0 ls0 ws0">i</div><div class="t m4 x3e h12 y97 ffd fs1 fc0 sc0 ls0 ws0">þ y</div><div class="t m4 x3f h15 y98 ff7 fs8 fc0 sc0 ls0 ws0">1</div><div class="t m4 x3f h13 y99 ffa fs8 fc0 sc0 ls0 ws0">i</div><div class="t m4 x40 h14 y9a ff10 fs1 fc0 sc0 ls13 ws0"></div><div class="t m4 x41 h12 y9b ffd fs1 fc0 sc0 ls0 ws0"> 10</div><div class="t m4 x42 h15 y98 ff7 fs8 fc0 sc0 ls14 ws0">14</div><div class="t m4 x43 h14 y9a ff10 fs1 fc0 sc0 ls15 ws0"></div><div class="t m4 x44 h12 y9b ff7 fs1 fc0 sc0 ls0 ws0">mod256 ð2Þ</div><div class="t m4 x1 ha y9c ff7 fs1 fc0 sc0 ls0 ws0">Similarly, the chaotic sequence x</div><div class="t m4 x45 h15 y9d ff7 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m4 x45 h13 y9e ffa fs8 fc0 sc0 ls0 ws0">i</div><div class="t m4 x46 ha y9f ff7 fs1 fc0 sc0 ls6 ws0">and y</div><div class="t m4 x47 h15 y9d ff7 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m4 x47 h13 y9e ffa fs8 fc0 sc0 ls0 ws0">i</div><div class="t m4 x48 ha y9f ff7 fs1 fc0 sc0 ls16 ws0">with the length of M × N are generated based on the</div><div class="t m4 x1 ha ya0 ff7 fs1 fc0 sc0 ls0 ws0">set of initial values x</div><div class="t m4 x49 h15 ya1 ff7 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m4 x49 h15 ya2 ff7 fs8 fc0 sc0 ls0 ws0">0</div><div class="t m4 x4a ha ya3 ff7 fs1 fc0 sc0 ls0 ws0">,y</div><div class="t m4 xd h15 ya1 ff7 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m4 xd h15 ya2 ff7 fs8 fc0 sc0 ls0 ws0">0</div><div class="t m4 x4b ha ya3 ff7 fs1 fc0 sc0 ls6 ws0">and system parameter γ</div><div class="t m4 x7 h15 ya4 ff7 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m4 x4c ha ya3 ff7 fs1 fc0 sc0 ls0 ws0">, by discarding the transition states. And we</div><div class="t m4 x1 ha ya5 ff7 fs1 fc0 sc0 ls0 ws0">obtain the integer sequence K</div><div class="t m4 x39 h15 ya6 ff7 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m4 x3a ha ya7 ff7 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m4 x3b h10 ya8 ffa fs1 fc0 sc0 ls0 ws0">K</div><div class="t m4 x3c h15 ya9 ff7 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m4 x39 h12 yaa ffa fs1 fc0 sc0 ls0 ws0">iðÞ¼floor x</div><div class="t m4 x3d h15 yab ff7 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m4 x3d h13 yac ffa fs8 fc0 sc0 ls0 ws0">i</div><div class="t m4 x3e h12 yaa ffd fs1 fc0 sc0 ls0 ws0">þ y</div><div class="t m4 x3f h15 yab ff7 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m4 x3f h13 yac ffa fs8 fc0 sc0 ls0 ws0">i</div><div class="t m4 x40 h14 yad ff10 fs1 fc0 sc0 ls13 ws0"></div><div class="t m4 x41 h12 yae ffd fs1 fc0 sc0 ls0 ws0"> 10</div><div class="t m4 x42 h15 yab ff7 fs8 fc0 sc0 ls14 ws0">14</div><div class="t m4 x43 h14 yad ff10 fs1 fc0 sc0 ls15 ws0"></div><div class="t m4 x44 h12 yae ff7 fs1 fc0 sc0 ls0 ws0">mod256 ð3Þ</div><div class="t m4 x1 ha yaf ff7 fs1 fc0 sc0 ls0 ws0">Further, we have the integer sequences K</div><div class="t m4 x48 h15 yb0 ff7 fs8 fc0 sc0 ls0 ws0">3</div><div class="t m4 x3d ha yb1 ff7 fs1 fc0 sc0 ls6 ws0">and K</div><div class="t m4 x4d h15 yb0 ff7 fs8 fc0 sc0 ls0 ws0">4</div><div class="t m4 x4e ha yb1 ff7 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m4 x4f h10 yb2 ffa fs1 fc0 sc0 ls0 ws0">K</div><div class="t m4 x50 h15 yb3 ff7 fs8 fc0 sc0 ls0 ws0">3</div><div class="t m4 x51 h12 yb4 ffd fs1 fc0 sc0 ls0 ws0">¼ K</div><div class="t m4 x52 h15 yb3 ff7 fs8 fc0 sc0 ls0 ws0">1</div><div class="t m4 x53 h10 yb4 fff fs1 fc0 sc0 ls0 ws0">⊕circshift K</div><div class="t m4 x54 h15 yb3 ff7 fs8 fc0 sc0 ls0 ws0">1</div><div class="t m4 x55 h12 yb4 ff11 fs1 fc0 sc0 ls0 ws0">; SðÞðÞ ð4Þ</div><div class="t m4 x4f h10 yb5 ffa fs1 fc0 sc0 ls0 ws0">K</div><div class="t m4 x50 h15 yb6 ff7 fs8 fc0 sc0 ls0 ws0">4</div><div class="t m4 x51 h12 yb7 ffd fs1 fc0 sc0 ls0 ws0">¼ K</div><div class="t m4 x52 h15 yb6 ff7 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m4 x53 h10 yb7 fff fs1 fc0 sc0 ls0 ws0">⊕circshift K</div><div class="t m4 x54 h15 yb6 ff7 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m4 x55 h16 yb7 ff11 fs1 fc0 sc0 ls0 ws0">; S</div><div class="t m4 x56 h12 yb8 ffd fs1 fc0 sc0 ls17 ws0">ðÞðÞ</div><div class="t m4 x1f h12 yb7 ffd fs1 fc0 sc0 ls0 ws0">ð5Þ</div><div class="t m4 x1 h12 yb9 ff7 fs1 fc0 sc0 ls0 ws0">where S ¼ mod floor ∑</div><div class="t m4 x4b h15 yba ff7 fs8 fc0 sc0 ls14 ws0">16</div><div class="t m4 x16 h11 ybb ffa fs8 fc0 sc0 ls0 ws0">i¼1</div><div class="t m4 x3c h10 ybc ffa fs1 fc0 sc0 ls0 ws0">K</div><div class="t m4 x39 h15 ybd ff7 fs8 fc0 sc0 ls0 ws0">1</div><div class="t m4 x57 h12 ybc ffa fs1 fc0 sc0 ls0 ws0">iðÞþ ∑</div><div class="t m4 x58 h15 yba ff7 fs8 fc0 sc0 ls0 ws0">32</div><div class="t m4 x59 h11 ybb ffa fs8 fc0 sc0 ls0 ws0">i¼17</div><div class="t m4 x33 h10 ybc ffa fs1 fc0 sc0 ls0 ws0">K</div><div class="t m4 x53 h15 ybd ff7 fs8 fc0 sc0 ls0 ws0">2</div><div class="t m4 x5a h12 ybc ffa fs1 fc0 sc0 ls0 ws0">iðÞ</div><div class="t m4 x5b h14 ybe ff10 fs1 fc0 sc0 ls1a ws0"></div><div class="t m4 x5c h16 ybc ff11 fs1 fc0 sc0 ls0 ws0">; 8</div><div class="t m4 x5d h14 ybe ff10 fs1 fc0 sc0 ls1b ws0"></div><div class="t m4 x5e ha ybc ff7 fs1 fc0 sc0 ls0 ws0">.</div><div class="t m4 x1 hf ybf ffc fs4 fc0 sc0 ls0 ws0">2.2 Binary tree</div><div class="t m4 x1 ha yc0 ff7 fs1 fc0 sc0 ls0 ws0">As a tree structure, binary tree is frequently used to implement binary search tree, binary heap,</div><div class="t m4 x1 ha yc1 ff7 fs1 fc0 sc0 ls1c ws0">image mosaic, public auditing and morphological character analysis for its fast search capa-</div><div class="t m4 x1 ha yc2 ff7 fs1 fc0 sc0 ls0 ws0">bility [1, 12, 51]. In this paper, binary tree is introduced into the scrambling operation of image</div><div class="t m4 x1 ha yc3 ff7 fs1 fc0 sc0 ls0 ws0">encryption for the first time.</div><div class="t m4 x14 ha yc4 ff7 fs1 fc0 sc0 ls1d ws0">In general, each node of binary tree has at most two sub-trees called left sub-tree and right</div><div class="t m4 x1 ha yc5 ff7 fs1 fc0 sc0 ls0 ws0">sub-tree respectively. For a full binary tree, its depth and nodes are h and L</div><div class="t m4 x29 h13 yc6 ffa fs8 fc0 sc0 ls0 ws0">B</div><div class="t m4 x5f ha yc7 ff7 fs1 fc0 sc0 ls1e ws0">=2</div><div class="t m4 x60 h13 yc8 ffa fs8 fc0 sc0 ls0 ws0">h</div><div class="t m4 x61 ha yc7 ff7 fs1 fc0 sc0 ls0 ws0">-1, so the</div><div class="t m4 x1 ha yc9 ff7 fs1 fc0 sc0 ls0 ws0">number of nodes on each layer is the maximum [12]. The basic operation of binary tree is</div><div class="t m4 x1 ha yca ff7 fs1 fc0 sc0 ls0 ws0">traversal [1]. Because the structure of binary tree is nonlinear, traversal is essentially to</div><div class="t m4 x1 ha ycb ff7 fs1 fc0 sc0 ls0 ws0">transform each node of binary tree into a linear sequence in a certain rule and order. Let D,</div><div class="t m4 x1 ha ycc ffa fs1 fc0 sc0 ls0 ws0">L and R represent the root node, left sub-tree and right sub-tree respectively, then there are</div><div class="t m4 x1 ha ycd ff7 fs1 fc0 sc0 ls0 ws0">three traversal forms: preorder traversal (DLR, DRL), inorder traversal (LDR, RDL) and</div><div class="t m4 x1 ha yce ff7 fs1 fc0 sc0 ls0 ws0">postorder traversal (LRD, RLD) [51].</div><div class="t m4 x14 ha ycf ff7 fs1 fc0 sc0 ls0 ws0">As an illustrated example, we consider a four-layer full binary tree with 2</div><div class="t m4 x62 h15 yd0 ff7 fs8 fc0 sc0 ls0 ws0">4</div><div class="t m4 x63 ha yd1 ff9 fs1 fc0 sc0 ls0 ws0">–1 = 15 leaf</div><div class="t m4 x1 ha yd2 ff7 fs1 fc0 sc0 ls0 ws0">nodes, as described by Fig. 1a. We first execute the preorder traversal of DLR for the primitive</div><div class="t m4 x1 ha yd3 ff7 fs1 fc0 sc0 ls0 ws0">binary tree. Five access sequences {1}, {2,4,8,9}, {5,10,11}, {3,6,12,13} and {7,14,15} are</div><div class="t m4 x1 ha yd4 ff7 fs1 fc0 sc0 ls0 ws0">successively acquired, based on the access path of root node, left sub-tree and right sub-tree.</div><div class="t m4 x1 ha yd5 ff7 fs1 fc0 sc0 ls0 ws0">Thus, the disordered sequence of the binary tree is {1,2,4,8,9,5,10,11,3,6,12, 13,7,14,15}, as</div><div class="t m4 x1 ha yd6 ff7 fs1 fc0 sc0 ls0 ws0">shown in Fig. 1b. When we access the primitive binary tree in inorder traversal of LDR, we</div><div class="t m4 x1 ha yd7 ff7 fs1 fc0 sc0 ls1d ws0">will successively obtain the access sequences {8,4,9}, {2} {10,5,11}, {1}, {12,6,13}, {3},</div><div class="t m4 x1 ha yd8 ff7 fs1 fc0 sc0 ls0 ws0">{14,7,15} based on the access path of left sub-tree, root node and right sub-tree. And the</div><div class="t m4 x1 ha yd9 ff7 fs1 fc0 sc0 ls0 ws0">disordered binary tree is {8,4,9,2,10,5,11,1,12,6,13,14,7,15}, as shown in Fig. 1c.Similarly,</div><div class="t m4 x1 ha yda ff7 fs1 fc0 sc0 ls0 ws0">we will successively obtain the access sequences {8,9,4}, {10, 11, 5}, {2}, {12,13,6},</div><div class="t m4 x1 ha ydb ff7 fs1 fc0 sc0 ls0 ws0">{14,15,7}, {3}, {1} when carrying out the postorder traversal of LRD, and the disordered</div><div class="t m4 x1 ha ydc ff7 fs1 fc0 sc0 ls0 ws0">sequence is {8,9,4,10,11,5,2,12,13,6,14,15,7,3,1}, as shown in Fig. 1d.</div><div class="t m4 x14 ha ydd ff7 fs1 fc0 sc0 ls0 ws0">The binary tree-based scrambling operation for the 4 × 4 image with 16 pixel values can be</div><div class="t m4 x1 ha yde ff7 fs1 fc0 sc0 ls0 ws0">executed by a four-layer full binary tree. However, one of pixel y of 4 × 4 image should be</div><div class="t m4 x15 h5 y1d ff4 fs3 fc0 sc0 ls0 ws0">Multimedia Tools and Applications</div><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a></div><div class="pi" data-data='{"ctm":[2.037103,0.000000,0.000000,2.037103,0.000000,0.000000]}'></div></div>

<div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/62572ce9bd8c6f2306b96d9f/bg5.jpg"><div class="t m4 x1 ha ydf ff7 fs1 fc0 sc0 ls0 ws0">extracted before scrambling operation since the node number of four-layer full binary tree is</div><div class="t m4 x1 ha ye0 ff7 fs1 fc0 sc0 ls0 ws0">15. And accordingly, we should add the pixel value y to the result of the scrambling matrix</div><div class="t m4 x1 ha ye1 ff7 fs1 fc0 sc0 ls0 ws0">when the scrambling operation is completed, as shown in Figs. 1e-h.</div><div class="t m4 x1 hf ye2 ffc fs4 fc0 sc0 ls0 ws0">2.3 Flip scrambling</div><div class="t m4 x1 ha ye3 ff7 fs1 fc0 sc0 ls0 ws0">In this section, we propose a new scrambling technology, named as flip scrambling, to execute</div><div class="t m4 x1 ha ye4 ff7 fs1 fc0 sc0 ls0 ws0">the operation of image confusion. As depicted in Fig. 2, the flip scrambling consists of four</div><div class="t m4 x1 ha ye5 ff7 fs1 fc0 sc0 ls0 ws0">steps: (1) transform image matrix into a one-dimensional sequence; (2) perform the reverse</div><div class="t m4 x64 h17 ye6 ff12 fs9 fc2 sc0 ls0 ws0">(a) (b) (c) (d)</div><div class="t m4 x64 h17 ye7 ff12 fs9 fc2 sc0 ls0 ws0">(e) (f) (g) (h)</div><div class="t m4 x1 h5 ye8 ff1 fs3 fc0 sc0 ls21 ws0">Fig. 1 Example of binary tree scrambling: a Four-layer full binary tree; b disordered result by preorder traversal;</div><div class="t m4 x1 h18 ye9 ffb fs3 fc0 sc0 ls0 ws0">c disordered result by inorder traversal; d disordered result by postorder traversal; e restored matrix of original</div><div class="t m4 x1 h18 yea ff7 fs3 fc0 sc0 ls23 ws0">image; f restored matrix of preorder scrambling-based sequence; g restored matrix of inorder scrambling-based</div><div class="t m4 x1 h18 yeb ff7 fs3 fc0 sc0 ls24 ws0">sequence; h restored matrix of postorder scrambling-based sequence</div><div class="t m5 x33 h19 yec ff13 fsa fc2 sc0 ls0 ws0">1 2 3 4</div><div class="t m5 x33 h19 yed ff13 fsa fc2 sc0 ls0 ws0">5 6 7 8</div><div class="t m5 x33 h19 yee ff13 fsa fc2 sc0 ls0 ws0">9</div><div class="t m5 x65 h19 yef ff13 fsa fc2 sc0 ls0 ws0">1 2 3 4 5 6 7 8 9</div><div class="t m5 x66 h19 yf0 ff13 fsa fc2 sc0 ls25 ws0">16 15 14 13 12 11 10</div><div class="t m5 xe h19 yf1 ff13 fsa fc2 sc0 ls0 ws0">9</div><div class="t m5 x67 h19 yf2 ff13 fsa fc2 sc0 ls0 ws0">8 7 6 5</div><div class="t m5 x67 h19 yf3 ff13 fsa fc2 sc0 ls0 ws0">4 3 2 1</div><div class="t m5 x1a h19 yee ff13 fsa fc2 sc0 ls26 ws0">10 11 12</div><div class="t m5 x43 h19 yf4 ff13 fsa fc2 sc0 ls25 ws0">13 14 15 16</div><div class="t m5 x68 h19 yef ff13 fsa fc2 sc0 ls27 ws0">10 11 12 13 14 15 16</div><div class="t m5 x69 h19 yf0 ff13 fsa fc2 sc0 ls0 ws0">9 8 7 6 5 4 3 2 1</div><div class="t m5 x6a h19 yf5 ff13 fsa fc2 sc0 ls25 ws0">16 15 14 13</div><div class="t m5 x6a h19 yf1 ff13 fsa fc2 sc0 ls25 ws0">12 11 10 1</div><div class="t m5 x41 h19 yf2 ff13 fsa fc2 sc0 ls25 ws0">15 11 7 3</div><div class="t m5 x6b h19 yf3 ff13 fsa fc2 sc0 ls0 ws0">2 6 10 14</div><div class="t m5 x41 h19 yf5 ff13 fsa fc2 sc0 ls25 ws0">16 12 8 4</div><div class="t m5 x41 h19 yf1 ff13 fsa fc2 sc0 ls25 ws0">13 9 5</div><div class="t m0 x1 h5 yf6 ff1 fs3 fc0 sc0 ls21 ws0">Fig. 2 Example of flip scrambling</div><div class="t m0 x1 h5 y1d ff4 fs3 fc0 sc0 ls0 ws0">Multimedia Tools and Applications</div><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a><a class="l" rel='nofollow' onclick='return false;'><div class="d m3"></div></a></div><div class="pi" data-data='{"ctm":[2.037103,0.000000,0.000000,2.037103,0.000000,0.000000]}'></div></div>