【正文】 entium M processor, GHz clock and 512 MB RAM. Three benchmark graylevel images of256 256 pixels of Lenna, Baboon and Airplane were used as host images, as shown in Fig. 3. A black and white (binary)image of Panda was used as the watermark. Several watermark dimensions were used in the simulations, ., 32 32,32 64, 64 64 and 128 64. The results are based on Lenna (host image, 256 256) watermarked with Panda (watermark, 32 32), unless otherwise stated. We have observed that the results of simulations using the other two host images(Baboon and Airplane) were similar to that of Lenna.We pare the embedding and extraction time of the proposed scheme against Schemes 1 and 2. Ten simulation runswere conducted for each scheme to determine the average timing for each scheme and are plotted in Fig. 4. The host imageswere watermarked with Panda image (32 32).From Fig. 4 one can see that the proposed scheme is able to embed and extract the watermark in much less time thanSchemes 1 and 2. On averaging over the three host images, the embedding time for Scheme 1, Scheme 2 and proposedCRTbased scheme were found to be 250, 130 and 40 ms, respectively. The proposed scheme is faster because only simpleCRT calculations are required for embedding, which makes up the bulk of the embedding time. The difference in timingsbetween Schemes 1 and 2 is due to the calculation of ranks of the individual blocks and selection of blocks to embed thewatermark bits. Furthermore, it can also be seen that the time taken to select blocks based on rank is imagedependentthat gives rise to significant differences in timing. However, in our proposed scheme, the embedding time is found to beindependent of the host image. The extraction time in the proposed scheme (as shown in Fig. 4(b)) is also reduced to alarge extent, because only CRT calculations are needed during extraction phase. The average extraction time for Scheme 1,Scheme 2 and proposed scheme was observed to be 190, 90 and 20 ms, respectively. It is also noticed that unlike the twoSVDbased schemes, the extraction time in our proposed scheme does not depend on the host image. Scheme 2 is fasterthan Scheme 1 because of absence of rank calculation and selection of blocks based on rank.The putational advantage of the proposed scheme is derived from the fact that CRT involves only modular operationswhich are putationally e?cient pared to SVD. In the SVDbased Schemes 1 and 2, the basic operations involved inthe embedding phase are given by: (i) given a matrix A, generate the three matrices, U, V and D, (ii) manipulate someelements of U or V matrix, and (iii) obtain the matrix?A through SVD using modified U, V and D. In our proposed scheme,the basic operations in the embedding stage are given by: (i) given an integer Z, using CRT determine the residues R1. Patra et al. / Digital Signal Processing 20 (2020) 442–453 449Fig. 5. Quality of watermarked image in PSNR for different host images.and R2, (ii) check the embedding conditions, and (iii) modify Z until embedding conditions are satisfied. We simulatedthese operations in an Intel Duo P8600based CPU with GHz clock and 4 GB RAM using JAVA programming language.The average putation time for one run of the SVD and CRT based basic operations were found to be 37 ms and 92 ns,respectively. This shows that the CRTbased putations are much faster than SVD putations. The relative timingsshown in Fig. 4 are much higher because they were based on a different PC specification and are meant for pleteembedding and extraction phases.. Quality of watermarked imagesThe quality of the watermarked images used to embed the watermark with respect to the different schemes is investigated here. Fig. 5 shows the quality of the watermarked images based on PSNR for the different host images. In Schemes1 and 2, a strength factor, α = was used for embedding. The performance difference between Schemes 1 and 2 is notsignificant. Note that Scheme 1 utilizes 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 w