一种新的基于中国剩余数定理的多媒体内容认证水印算法英文-外文文献(编辑修改稿)

一种新的基于中国剩余数定理的多媒体内容认证水印算法英文-外文文献(编辑修改稿)内容摘要：

pectively.The initial steps of the extraction procedure are similar to that of the embedding process up to and including theselection of the coefficients c1and c2.Thevalueofc1− c2determines the value of the extracted watermark bit. A positivedifference indicates that the watermark bit is a ‘1.’ Whereas, a negative difference would imply that a watermark bit ‘0’ isextracted.. Watermarking Scheme 2The embedding procedure of the scheme proposed by Patra et al. [15] is an improved version of Scheme 1. The hostimage is divided into a number of superblocks that is equal to the number of watermark bits. From each superblock,a subblock is selected which is transformed via SVD to embed the watermark. Instead of embedding exclusively in theU matrix, the V matrix is also utilized. A counter is introduced to allow random selection of embedding the watermark bitin either U or V matrix to improve the security and robustness.In addition, the coefficients (c1and c2) are selected randomly from the first column of the U or V matrices using a PRNG.This flexibility gives an edge over the scheme proposed by Chang et al. [14], as malicious tampering cannot be targeted atthe two modified coefficients due to their random selection. However, to minimize the distortion to the watermarked image,the position of c2must be consecutive to c1. Experiments show that the watermarked image quality reduces as the distancebetween the modified coefficients is increased. The modifications of c1and c2are similar to the procedure in Scheme 1. Thereconstruction of the new block, replacement of the block into the image, and extraction procedure are also similar to thatof Scheme 1.This scheme removes the reliance on rank and also improves security by using random selection of coefficients forembedding the watermark bits. The weakness of this scheme is that the robustness of the scheme is inversely proportional. Patra et al. / Digital Signal Processing 20 (2020) 442–453 445to the watermarked image quality. A higher strength factor would increase the watermarked image to be resistant to attacks,but it also means a drop in image quality. On the other hand, too low a strength factor would reduce its robustnessagainst attacks. Moreover, the concept of using a superblock in this case causes a sharp drop in the capacity of embeddedwatermark bits. It may be insufficient for a smallsized watermark to provide evidence of ownership of a document or animage.3. Chinese remainder theorem. The CRTThe CRT can be pactly stated as follows. Let 181。 be a set of r integers given by 181。 ={M1, M2,...,Mr}, such that Miare pairwise relatively prime. Let a set of r simultaneous congruences is given byZ ≡ Ri(modMi), (4)where Riare called residues. The solution for the integer Z can be found asZ ≡parenleftBiggrsummationdisplayi=1RiMMiKiparenrightBigg(modM), (5)where M = M1 M2Mrand Kiare determined fromKiMMi≡ 1 (modMi). (6)Let us take a simple example with r = 2 to illustrate CRT. Let M1= 6, M2= 11, and R1= 4, R2= 8. That is, Z ≡4 (mod6) and Z ≡ 8 (mod11).ComputeM = M1M2= 66. K1and K2are to be determined such that (6) is satisfied. Thatis, (K1666) ≡ 1 (mod6) and (K26611) ≡ 1 (mod11). We can see that for K1= 5 and K2= 2, these two equations are satisfied.Now Z is determined as Z ≡ (4 6665+866112)(mod66) = 52.. The inverse CRTGiven that 181。 ={M1, M2,...,Mr} and M = M1 M2Mr. 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) 442–4。