【正文】 can be found asZ ≡parenleftBiggrsummationdisplayi=1RiMMiKiparenrightBigg(modM), (5)where M = M1 2020 Elsevier Inc. All rights reserved.1. IntroductionToday’s information driven economy is dominated by the tremendous growth of the Inter and explosion of daytodaydata processing with huge amount of multimedia data. Easy availability of contentediting software, mobile and pactdigital devices and the Inter, make the digital lifestyle of mon man quite different from that of few years ago. Digitalmultimedia contents, ., text, image, video and audio, can be easily altered, stored or transmitted to any point of the globeinstantly. However, multimedia digital content owners are skeptical of putting their content on the Inter due to lack ofintellectual property protection available to them. In order to address this situation, digital watermarking is indeed one ofthe solutions to protect the ownership of these contents. In digital watermarking techniques, some digital signature thatis unique to the owner or copyright information is embedded into the host multimedia content. The signature embeddedremains invisible and imperceptible and cannot be removed easily even under certain manipulations, ., addition of noise,pression, tampering and scaling operations. Only the authorized recipient of the digital content can extract the watermark from the watermarked content with the knowledge of some key information. In this way security, content integrityand intellectual protection can be provided to the owner. In this direction, starting from mid1990, several researchers havereported many watermarking techniques in spatial and transform domains [1–3].Some important properties of an effective watermarking scheme are [1–3]: (i) imperceptibility: there should not be anynoticeable difference between a watermarked content and the original, (ii) robustness: the embedded watermark should beable to withstand to some extent of content manipulation. Any attempt to destroy a watermark should also void the watermarked content and (iii) trustworthiness: no other watermark other than the embedded watermark should be extracted*Corresponding author.Email addresses: (. Patra), (A. Karthik), (C. Bornand).10512020/$ – see front matter 169。666Mr. The objective of the inverse CRT is to represent any integer Z,{0 Z lessorequalslant M ?1} by a set of integers Z ={R1, R2,...,Rr}.TheRiare obtained from the following congruences:Z ≡ Ri(modMi). (7)Let us take the previous example in which M1= 6 and M2= 11. Therefore, M = M1M2= 66. Let the given integer beZ = 52. Using (7), 52 ≡ R1(mod6) and 52 ≡ R2(mod11).Thus,wegetR1= 4 and R2= 8. Therefore, Z can be representedas Z ={4,8}. For detailed discussions on CRT, one can refer to any textbook on number theory or cryptography [22,23].4. Proposed CRTbased watermarking schemeThe embedding and extraction procedure of the proposed scheme is based on CRT technique. This scheme attemptsto provide improved security and minimal distortion to the host image. In addition, it needs minimal information duringextraction phase and provides robustness to some severe attacks.. Embedding procedureThe process begins by dividing the host image into equalsized blocks based on the number of watermark bits to beembedded. For example, to embed a 32 32 binary watermark (black and white) into a 256 256 host image, the hostimage is divided into 1024 blocks each of size 88. Therefore, there would be one watermark bit embedded in each block.After dividing the host image into blocks, consider one block at a time to embed the watermark bits. The pixel intensity ofthe host image is represented by 8bits. Therefore, the pixel intensity ranges from 0 to 255 (0 and 255 represent pure blackand pure white, respectively). The embedding procedure is given by the following steps:Step 1. Select the pixel (with intensity X), to be embedded in a block, using a PRNG.Step 2. Convert the decimal value of X, which ranges from 0–255, into a binary form.Step 3. Consider the 6 least significant bits (LSBs) of X and convert it into a decimal value Z. The range of Z is 0–63.Step 4. Consider the 2 most significant bits (MSBs) of X and convert it into a decimal value Y, which can take the values0, 64, 128 and 192.Step 5. Select the pairwise coprime numbers as M1= 6, M2= 11.Step 6. Find R1and R2for Z by applying the inverse CRT using (7).446 . Patra et al. / Digital Signal Processing 20 (2020) 442–453Step 7. To embed bit ‘1,’ the required condition is given byR1greaterorequalslant R2. (8)If (8) is not satisfied, then Z is modified using the modification procedure, as explained below, until it is satisfied.Step 8. To embed bit ‘0,’ the required condition is:R1 R2. (9)If (9) is not satisfied, then Z is modified using the modification procedure, as explained below, until it is satisfied.Step 9. After deciding on the values R1and R2, using CRT (5) bine them with M1and M2to get Zprime.Step 10. Combine the value of Y with Zprimeto get Xprime, the new watermarked pixel value.Step 11. Reconstruct the block with the new watermarked pixel value Xprime.Step 12. Repeat Steps 1–11 for all the blocks until all the watermark bits are embedded.There were some considerations to be made for embedding a watermark bit. Firstly, we are using only the 6 LSBs and notthe full 8 bits, because we do not want to modify the pixel values to a large extent, which can cause some visual distortion.Our focus in this scheme is to keep distortion minimal. Secondly, we have selected the pairwise coprime numbers M1and M2, as 6 and 11, respectively. According to CRT, the product of the pairwise coprime numbers should be greater thanthe possible range of numbers under cons