【正文】 es the rank property of the block matrices by giving preference to higher ranked blocksduring the embedding procedure. However, it does not seem to have a clear advantage in quality of the watermarked imagewhen pared to Scheme 2. It can be seen that our proposed scheme is superior in terms of PSNR than the other twoschemes for different host images. The PSNR of the watermarked image in the CRTbased scheme is about 60 dB, whereasin Schemes 1 and 2 it remains between 30 to 40 dB.In order to have a visual inspection, we magnified the Lenna image that was watermarked using the three schemes. Themagnified images along with the original image are shown in Fig. 6. One can notice by close visual inspection that theresemblance of images between the original (top left) and the watermarked with the proposed scheme (bottom right) ishigher than that with the other two schemes. This provides the evidence that least distortion occurs to the host image thatis watermarked with the CRTbased scheme.. Robustness against attacksIn this section, we pare the proposed scheme against Schemes 1 and 2 in their ability to withstand different typesof attacks. The watermarked image was subjected to different attacks, such as, addition of noise and tampering, beforeextracting the watermark. The quality of the extracted watermark is determined by their TAF value (10). A lower TAF valuewould indicate that the extracted watermark is more similar to the original watermark.Several image manipulation techniques were used to distort the watermarked images. These techniques are: (i) Croppingof a block size of 3232 at the upper left corner of the image, (ii) tampering 25% of the pixels with a strength factor of 25,(iii) adding noise to the entire watermarked image with a 20% distortion rate, (iv) JPEG pression with a value of ,and (v) brightening the watermarked image to 140%.Fig. 7 shows the TAF of the extracted wate。6611 be a set of r integers given by 181。. This fact provides additional security in this scheme. Since CRT is based on simultaneous congruencesand modular arithmetic, it is putationally e?cient. In addition, at the time of extraction of watermark, only a fewinformation are needed. We have shown that the proposed technique introduces minimal distortion to the original hostimage, during embedding process and it can withstand the noise attack quite well. We have pared performance of theproposed scheme with the two recently reported SVDbased schemes, and shown its superior performance by conductingdifferent attacks to the watermarked image. In this paper, we have also proposed a method to increase the watermarkingcapacity.The rest of the paper is as follows. We briefly introduce the two existing SVDbased schemes in Section 2. The mathematics of CRT is introduced in Section 3. Next, the CRTbased watermarking scheme is explained in Section 4. The experimentalresults and performance parison with SVDbased techniques have been included in Section 5. Finally, conclusions anddiscussions on this study have been made in Section 6.2. Existing SVDbased watermarking schemesIn this section, we briefly discuss the two recently reported SVDbased watermarking schemes and their weaknesses.Chang et al. [14] proposed an elegant SVDbased watermarking scheme, but it has some weaknesses. Patra et al. [15] havereported an improved SVDbased scheme that has overe the weaknesses of Chang et al.’s scheme.. Watermarking Scheme 1Let A be a matrix of size M N representing an image. The elements of A will have values between 0 and 255, for 8bitrepresentation of the pixels. Using singular value deposition the matrix A can be deposed into three matrices asfollows:A = UDVT=???u11u12... u1Mu21u22... u2M... ... ... ...uM1uM2... uMM??????λ100... 00 λ20 ... 0... ... ... ... ...000... λM??????ν11ν21... νN1ν12ν22... νN2... ... ... ...ν1Nν2N... νNN???, (1)where U (M M) and V (N N) represent the orthogonal matrices of A, and D (M N) (same dimension as A)representsa diagonal matrix. The eigenvectors of AATmake up the columns of U and the eigenvectors of ATA are the columnsof V. The diagonal elements of D represent square root of eigenvalues of either ATA or AAT, and these are arranged indescending order, ., λ1λ2λ3 Digital Signal Processing 20 (2020) 442–453Contents lists available at ScienceDirectDigital Signal ProcessingA novel CRTbased watermarking technique for authenticationof multimedia contentsJagdish C. Patraa,?,a, Cedric BornandbaSchool of Computer Engineering, Nanyang Technological University, Nanyang Avenue, SingaporebHEIGVD, University of Applied Sciences, YverdonlesBains, Switzerlandarticle info abstractArticle history:Available online 28 July 2020Keywords:Digital watermarkingChinese remainder theoremSingular value depositionDigital watermarking techniques have been proposed as a solution to the problem ofcopyright protection of multimedia data. In this paper, we propose a novel Chineseremainder theorem (CRT)based technique for digital watermarking. The use of CRTfor this purpose provides additional security along with resistance to some familiarattacks. We have shown that this technique is quite resilient to addition of the noise.We have pared performance of the proposed technique with recently reported twosingular value deposition (SVD)based watermarking techniques and shown its superiorperformance in terms of tampering assessment function (TAF), putational e?ciencyand peak signal to noise ratio (PSNR). For example, the embedding time of the proposedCRTbased scheme is 6 and 3 times faster than the SVDbased Schemes 1 and 2,respectively. This technique can also be applied to document, audio and video c