基于混沌映射和DCT变换的图像加密解密算法(英文)

课程论文学位类型：专业型学科、领域：计算机应用技术研究方向：智能检测和自动控制导师姓名：张凌涛学生姓名：曾照成学号：20141200022入学时间：2014年9月授课教师：车生兵课程名称：高级人工智能基于混沌映射和DCT 变换的图像加密解密算法曾照成1（20141200022）（中南林业科技大学 计算机与信息工程学院 长沙 410004）Image Encryption and Decryption Algorithm Based on Chaotic Mapping and DCT Transform Zeng Zhao Cheng (College of Computer and Information Engineering, Central South University of Forestry and Technology, Changsha 410004, China)Abstract: Image confidential transmission in the protection of private information and trade secrets has wide application space.In this paper, we get the address of the image scrambling transformation code by using the Logistic chaotic map, then the encryption operation for the original color is done through the ranks scrambling, After the feature is extracted by carrier image with the blocked DCT transform, some three-dimensional encrypt images will be directly embedded into it, which are displayed as the carrier image. Extracting the encrypt images has just the inverse process to the embedded one. Finally we made a scrambling again according to the key after extracting the information, which will be a close to the original image, with the Peak Signal to Noise Ratio 27.37.Key words: L ogistic chaotic mapping ; sort transformation; DCT transform; key摘 要： 图像的保密传输在保护私人信息和商业秘密等方面具有广泛的应用空间。

本文利用Logistic 混沌映射得到图像置乱的地址变换码，通过行列置乱直接实现对原始彩色图像的加密操作，再对载体图像利用分块DCT 变换提取特征后直接嵌入三维加密图像信息，嵌入信息后的图像显示为载体图像。

提取加密图像信息的过程是嵌入过程的逆过程，提取信息后再根据密钥进行反置乱，即可恢复出接近原始图像的还原图像，该图像与原始图像的峰值信噪比为27.37。

关键词：Logistic 映射；排序变换；DCT 变换；密钥1 IntroductionWith the continuous development of information network technology, it can be convenient for people to pass every digital information (such as music, video, film and television) to all over the world, and secrecy transmission in fields like private information protection and commercial privacy is widely applied. Secrecy transmission includes first encryption with the objective information, and then transmission after concealing, aiming at improving the security during the whole transmission process, meanwhile, the receiver could get exactly the original information with a key after extracting the encryption information. Information hiding technology takes use of the insensitivity of humans’ sense organs, considers the fact that multi -media digital signals have much redundance, it conceals the private information into a carrier, making it uneasy to be noticed, in the mean time, it should not affect the effect of the carrier so as to hide the information we want to transmit. In order to improve the transmission security, we tend to encrypt the hidden information.2 chaotic encryption algorithm based on the Logistic mappingLogistic map is a kind of power system which is very simple but widely researched, its definition is as follows:)1(1k k k x x x -=+μIn the equation, 40<<μ is named branch parameter, )1,0(0∈x , when 4..3.5699456.<<μ, By the initial conditions under the action of Logistic mapping sequence are generated by the cycle, convergence and is sensitive to the initial value of chaotic sequence. 1 作者简介： 曾照成（1990-），男，湖南邵阳人，在读硕士研究生，主要研究领域为智能检测与自动控制.For size to encrypt color image, this paper use Logistic mapping to iteration length and width of the two respectively, and chaotic sequence, and the two sequences are ascending order, in ascending sequence of elements in the original position in the sequence index sequence as the address of the image scrambling transformation code, and then to the ranks of image scrambling, so as to realize the original image encryption operation. After the test, the model has high security, when the key has a faint difference, will make the chaotic sequence has great changes, thus unable to decode the original image information. The same initial value and different parameter values for the encryption key. Because the image data can be represented by R, G , B three primary colors of three contains eight matrix representation of binary elements, so the matrix operation can greatly simplify the implementation of the algorithm.Fig.1 original image Fig.2 encrypt imageCryptographic operations after encryption image is shown in figure 2, the image is embedded into the carrier image in the image, and for the encrypted image, only three encryption key. That is to say, as long as you know the three keys can be fully restored to the original image, the algorithm of three keys respectively are 58.3,57.3,78.0210===μμx .3 Encryption image hiding algorithm based on DCT transform DCT (discrete cosine transform) is a kind of real number domain image orthogonal transformation. By DCT transformation image space can be the information on the transformation to the frequency domain, it is a good use of the characteristics of human visual system, on the premise of keep the image quality, a better implementation of image compression. The 2-d DCT transform formula is as follows:]2)12(cos[]2)12(cos[),()()(),(1010N q q M p m n m f q a p a q p F M m N n ππ++=∑∑-=-= 1,,1,0;1,,1,0-⋅⋅⋅=-⋅⋅⋅=N q M p , , The DCT transformation formula is as follows:∑∑-=-=++=1010]2)12(cos[]2)12(cos[),()()(),(M p N q N q n M p m q p F q a p a n m f ππ m=0,1,...,M-1; n=0,1,...,N-1，In the above two formulas, a(p) and a(q) are defined as follows:⎪⎩⎪⎨⎧-===⎪⎩⎪⎨⎧-===1,...,2,1,20,1)(,1,...,2,1,20,1)(N q N q N q a M p M p M p a This paper mainly using DCT transform for image feature extraction, which can use the encrypted image data to replace the image of the data on the characteristics of a information, in order to realize the purpose of data hiding. For the carrier image, firstly the carrier image sub-block is divided into several nonoverlapping pixels (often is the subblock pixel size, sub-block image boundary position may be, do not need to supplement for), for each sub-block DCT transform, in order to get the frequency of the coefficient matrix, for example, the matrix with coordinates (0, 0) corresponding to the value of the largest, known as DC DC coefficient, the remaining 63 mostly close to zero frequency coefficient of plus or minus floating point Numbers, all call communication coefficient of AC, DC coefficient of DC represents apiece of the average brightness, the greater the value the more representative image brightness; And the high frequency part of AC AC component coefficient can reflect the image texture complexity, high frequency AC power small region corresponding to the image smoothing, larger value represents the complex texture area, most of the image.Fig.3 carrier image before the hiding informationFig.4 carrier image after the hiding informationEncryption sub-block image data and image data sub-block size difference, the greater the modified information is less, the better the embedded, but these methods tend to amplify the carrier image, also will appear different degrees of Mosaic effect, but also wastes a lot of can embed information of characteristics of the data bits. Based on this, the paper gives a kind of information embedding method. First change the size of the image, that of the encrypted image size,then according to the sub-block size of carrier image, and encryption image segmentation at the same time, For each sub-block image DCT transform, then each coefficient until the first two decimal places, and retain only the secret image data processing at the same time,Each element is not greater than 0.01 form the solid type decimals, added to the carrierfor block DCT coefficient matrix on the corresponding element, embed the encrypted image data. And then to the embedded data after DCT transformation, hides the encrypted information carrier image. Figure 5, figure 6 show the information carrier of before and after the embedded images.Fig.5 carrier image before the hiding informationFig.6 carrier image after the hiding informationVisible by the method of embedding the image resulting from the encrypted message with the original image slightly difference on colour, no Mosaic effect, visual effect is much better.Due to encrypt the image and the image sub-block size is consistent, in the process of implementation is simpler than the previous algorithm. In the process of the simulation running time is less than the previous algorithm.The former method takes 17.033543 s, the algorithm takes 4.457294 s.4 extraction and decryption of encryption image information Encryption image to hide information extraction process and the embedding process, on the other hand, by the carrier of the embedded hidden information by corresponding sub-block picture of DCT coefficient matrix, the matrix element is hidden by the fractional portion of a coded messages, reduction treatment after extraction of the information is converted into RGB image data, the data is encrypted image data of the hidden information. Decryption operation is to encrypt the inverse operation, through the key, can easily get the address of the data encryption transform code, and then to the scrambling of the encrypted data, you can get after reduction of the image. Figure 7 and figure 8 shows the original image and the image after reduction.Fig.7 original image Fig.8 reduction image5. Measurement algorithm based on pixel effect This is a method of quantitative test results with it is not dependent on the subjective evaluation. It allows between different methods are compared, and a fair amount of Distortion in the most used in visual information processing or quality metrics are belong to Difference measure method (Difference Distortion Measures).Now most used in the field of image video coding compression distortion quantity of metrics is SNR Signal to Noise the wire Peak signal-to-noise Ratio (SNR) and Peak Signal to Noise the wire (PSNR).They are usually in dB dB, peak signal to noise ratio of the image to a certain extent, reflects the changes of the image before and after data processing, the response is a statistical average image data change, the higher the value of the peak signal to noise ratio, the better. Peak signal to noise ratio PSNR are defined as follows:)(log 1010PMSE PSNR ⨯-=PMSE represents the peak mean square error of the image,[]2311123),(),(1An m g n m f MN PMSE K N n M m k k ⨯-=∑∑∑=== ),(n m f k means the original image in pixels (m, n) the first k elements on the color component values, ),(n m g k is after restore image in pixels (m, n) the first k elements on the color component values. A is the maximum value of ),(n m g k (k=1,2,3, m=1,2,...,M, n=1,2,...,N). 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