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1、High Payload Watermarking using Residue Number System(IJIGSP-V7-N3-1)I.J. Image, Graphics and Signal Processing, 2021, 3, 1-8Published Online February 2021 in MECS (http:/ 10.5815/ijigsp.2021.03.01High Payload Watermarking using ResidueNumber SystemShubhendu BanerjeeDept. of CSE, Narula Institute of
2、 Technology, Kolkata, West Bengal, India,shankushubhenduhttp:/ Chakraborty, Nilanjan DeyDept. of CSE, Bengal College of Engineering & Technology, Durgapur, West Bengal, India,Email: sayan.cbhttp:/ neelanjan.deyhttp:/ Kumar PalCMC Limited, India,arijit1421http:/ RayDept. of IT, Government College of
3、Engineering and Leather Technology,Kolkata, West Bengal, India,ruben.rayhttp:/ hiding or data hiding, also known as watermarking, has become a part and parcel of covert communication and copyright protection. Maximizing watermark payload is a major challenge for watermark researchers. To overcome th
4、is issue, we have proposed a new color image watermarking technique, using residue number system (RNS). RNS refers to a large integer using a set of smaller integers which relies on the Chinese remainder theorem of modular arithmetic for its operation. The proposed method takes pixel values from thr
5、ee watermark images and embeds them into the main cover image. Experimental results presented in this paper shows that the watermark can be successfully embedded and extracted from an image, without distorting the original image using the proposed technique. The high peak signal to noise ratio (PSNR
6、) and payload values claims the robustness of the proposed method.Index TermWatermarking, Payload, Residue Number System, Chinese Remainder Theorem, PSNR.I.I NTRODUCTIONHiding any message within an image, signal or video is known as watermarking 1. To hide the message, an image is used as a cover, w
7、hich is intended for transfer. Digital watermarking has become an integral part in various applications. Watermarking 2, 3, 4 is mainly used for security purpose. Imperceptibility and robustness are two main features of a good watermark 5,6. Robust watermarking 7, 8, 9 means, when an image is less d
8、amaged after retrieving. If the quality of the watermarked 10, 11, 12 image is seriously affected after embedding, then the watermarked image can be identified easily. The property of less degradation of an image is referred to as imperceptibility 13, 14, 15. The secret message is embedded as an inv
9、isible mark 16,17 and recovered back after the extraction of watermark. The traditional watermarking 18, 19, 20 techniques can be divided into two categories: spatial domain information hiding and transform domain (such as the DCT transform domain, the wavelet transform domain, etc.). In spatial dom
10、ain information hiding, most watermarking 21, 22 methods embed the information directly to the original image. If some valuable information which was required during embedding watermark 23, 24 is provided to the user, then it should be non-blind watermarking 25, 26, 27. The properties are the same a
11、s watermarking scheme. The watermark can be easily embedded 28, 29 and retrieved by the users. Payload means the amount of data which requires to be watermarked. High payload in watermark 30, 31 refers to the method that can hide large amount of data. The chief factors influencing payload are size o
12、f an image or data, the embedding intensity, image roughness, visual sensitivity etc. High payload and better watermark 32, 33 leads to perceptual invisibility.In 1999, Johnson 1 et al. proposed a method of recovering watermark from images after it suffered some type of attacks. Some watermarking me
13、thods which has suffered from attacks such that the hidden secret information cannot be recovered, was included in this work. In 2001, Lu 2 et al. proposed a watermarking scheme for the purpose of image authentication and protection. Two watermarks are embedded using quantization of wavelet coeffici
14、ents of the host image and they are extracted without accessing the original image. In 2004, Wang 3 et al. proposed an RNS application for digital image processing. In this paper, a study on the RNS (residue number system) application in digital image processing was done and a RNS image coding schem
15、e that offers high-speed and low-power VLSI implementation for secure image processing was proposed.In 2006, Castillo, 4 et al . proposed an RNS-based watermarking for IP cores. In this technique, electronic digital signature embedding using RNS-based designs was used to protect the author rights of
16、 IP cores. In 2008, Zhao 5 et al . proposed a reversible watermarking scheme. In this paper, a pair of pixel is considered and a certain value is added to one and subtracted from the other to balance distortion. A series of experiments established the effectiveness of this method. In 2009, Kumari 6
17、et al . proposed a watermarking technique for gray level images. The watermark is inserted using LSB. The gray value of the image does not change successively and later a secret message is inserted in the image using those gray values. In 2010, Wu 7 et al. presented a paper on fixed point and floati
18、ng point data. In this paper, watermarked image 8, 9, 10 is exploited to get the actual recovery of the original value with the smallest error and then a pseudorandom sequence was added to the watermarked 11, 12 object for security purpose.Methodology is described in section 2. Section 3 illustrates
19、 the proposed method. Proposed method is further explained in detail in section 4. Simulation results is shown in section 5 and also analysis of those obtained results are done in the same section. Paper concludes in section 6.II. M ETHODOLOGYA. Residue Number System (RNS)The residue number system i
20、s a non-weighted number system that has a certain advantage over the weighted number systems. RNS arithmetic is basically carry free and in the case of multiplication the need for partial products is eliminated.In RNS representation of a number takes the form of N tuple of X that is X=x 1, x 2, x 3.
21、x n . Here x i =X modulo m i , which is the i-th residue digit and m i is the i-th modulas and all m i are mutually prime numbers. Note that for maximum representation efficiency it is imperative that all the moduli are co-prime; that is no modulas may have a common factor with any other. The number
22、 of distinct values that can be represented, is called Dynamic range, M, whereNi i=0M=m and XFor signed RNS any integer in (-M/2, M/2), has a unique RNS. N tuple representation where x i =(X modulo m i ) if X 0, and (M-|X|) mod m i otherwise.Suppose there are two numbers A and B and after performing
23、 arithmetic operations a result is obtained which is denoted by C. Now(A) modulo (m1|m2|m3)=(a1|a2|a3) (2) (B) modulo (m1|m2|m3)=(b1|b2|b3) (3) (C) modulo (m1|m2|m3)=(c1|c2|c3) (4) o represents arithmetic operations i.e. addition, subtraction, multiplication. Now,(A o B)= C (5) This implies,(a1 o b1
24、) modulo m1|(a2 o b2) modulo m2|(a3 o b3) modulo m3) = (C) modulo (m1|m2|m3) = (c1|c2|c3)For example, suppose, A=7, B=3 , m 1=2 ,m 2=3 ,m 3=5; 7(1|1|2) + 3(1|0|3)=10(2 modulo 2| 1 modulo 3| 5 1,X 2,.,X L ) (6)1,Y 2,.,Y L ) (7) Z = X o Y (8) Here, o can represent addition, subtraction or multiplicati
25、on.1,Z 2,.,Z L ) (9) =( (X 1 Y 1)mod p 1 , (X 2 Y 2)mod p 2 , . (X L Y L ) mod p L )III. P ROPOSED M ETHODA. Embedding Watermark within an image Step 1.Color image is converted into 3 gray planes (Red, Blue and Green).Step 2. Size of the image is calculated.Step 3. Three binary images (same size of
26、the colorimage) are taken as a watermark.Step 4. Residue number system (RNS) moduli of 3, 2and 7 respectively is applied on the first pixel value of the blue plane (gray).Step 5. The very first bit is taken from each of thewatermark image and the generated three bits are clubbed and converted into c
27、orresponding decimal number.Step 6. RNS mod of 3, 2 and 7 respectively isapplied on the generated decimal number.Step 7. RNS addition is performed between the moduliresults of the three numbers generated from step 4 and 6.Step 8. The resultant three numbers are placedrespectively to generate a singl
28、e decimal number (Z) of length three (from the left the first digit or first & second both digits can be zero) for using the Step 9.Step 9. The above produced decimal number Z isdivided by 9 such that the quotient is y and the single digit remainder is x .Step 10. y and x is clubbed together (yx ) t
29、o give thewatermarked pixel.Step 11. Step 4 to 10 is applied for all the pixels of theblue plane of the color image and 3 watermark images to generate the watermarked image.Step 12.The modified blue plane, red plane and green plane is combined to generate the colorwatermarked image.B.Extraction of W
30、atermark from Watermarked image Step 1.Color watermarked image is again decomposed into three planes.Step 2.The very first decimal number (yx) where x is single digit of the blue plane is expressed as theeqn. yx =9*y+x.Step 3.The resultant of 9*y+x is separated into three individual digits (if the r
31、esult is two digits then1st digit is zero and if the result is one digit thenboth 1st and 2nd digits are zero).Step 4.Chinese remainder theorem is applied to get back the original by taking moduli of 3, 2 and 7for the respective three digits.Step 5.Modulo results for 3, 2 and 7 (mutually prime) is s
32、ummed up.Step 6.The L.C.M. of 3, 2 and 7 i.e., 42 is added or subtracted from the generated sum repeatedly tofind out the closest value of the first blue planepixel.Step 7.The first pixel value of the blue plane is subtracted from the generated closest value. Step 8.The result is converted into bina
33、ry number system i.e. three watermark bits. Step 9.Step 2 to 8 is applied for all pixels of the whole watermarked image to retrieve the threewatermark images.IV.E XPLANATION OF THE P ROPOSED M ETHODLet us consider that the first pixel (gray value) of the cover image is 255 and the first binary bits
34、of the three watermarks 8, 9, 10 are 1, 0, 1 respectively as shown in the Fig. 1. The corresponding decimal number of 3 binary bits is 5. In the watermark embedding process, the ResidueNumber System (RNS) Moduli of 3, 2 and 7 respectively is applied on 255 and 5 to generate the following results:255
35、 mod 3 = 0 5 mod 3 = 2255 mod 2 = 1 5 mod 2 = 1255 mod 7 = 3 5 mod 7 = 5The result of RNS addition will be as follows:(0+ 2) mod 3, (1+1) mod 2, (3+5) mod 7. which returns 2, 0, 1. 2, 0, 1 are clubbed together to generate a single decimal number 201 of length three digits.Fig. 1: Watermark embedding
36、 and extraction process.If the generated single decimal number is 2 digit or single digit number e.g. 21 or 1 then we have to add an extra single 0 or two zeros in front of the digit to make it a number whose length is three e.g. 21 or 1 will consider as 021 and 001. 201 is divided by 9 to generate
37、the quotient 22 and the remainder 3. Then 22 and 3 are clubbed together (223) results, the watermarked pixel. As an extraction 12, 13, 14 mechanism, 22 and 9 is multiplied and added with 3. The generated result (201) is split into 3 single digit numbers (2, 0, 1). i.e.-= 198 + 3= 201Chinese Remainde
38、r Theorem is applied by taking 2 for moduli 3, 0 for moduli 2, 1 for moduli 7.2 for mod 30 for mod 21 for mod 7For mod 3: 2 and 7 are mutually prime. So the L.C.M. is 14 (2 7)14 mod 3 = 2, so we will consider 14 for feather processing.For mod 2: 3 and 7 which were also mutually prime. So the L.C.M.
39、is 21 (37).21 mod 2 = 1 0Hence, 21 will not be considered as a value.21 2 =4242 mod 2 = 0.Thus, 42 will be considered for feather processing. Finally,For mod 7: 2 and 3 are mutually prime and the L.C.M. of 2 and 3 is 6 (2x3).6 mod7 = 6 1. Again 6 2 =12 mod 7 = 5 16 3 =18 mod7 = 4 16 4 =24 mod7 = 3 1
40、6 5 =30 mod7 = 2 16 6 =36 mod7 = 1Hence, 36 will be considered for feather processing. By adding up the three results (14+42+36) the obtained result becomes 92.Obviously 92 can be taken as a solution of the respective moduli of 3, 2, 7. In our case, we will try to find out the nearest value of 255 (
41、selected gray value for watermarking) by repeatedly adding (in other case by subtracting also) the L.C.M. of 3, 2, 7 i.e. 42.The nearest value is 260.92+42 = 13492+42 2= 92+84 = 17692 + 42 3 = 92+126 = 21892 + 42 4 = 92 + 168 = 260By subtracting 255 from 260, 5 is obtained. The binary representation
42、 of 5 is 101. Therefore the very first bit for each of the recovered watermark 15, 16, 17 image is 1, 0 and 1 respectively. The whole process is repeated for all other gray values with the help of watermark 18, 19 image bits of the corresponding positions. During extraction 20, 21, 22 process the re
43、covery of watermark 23,24,25 requires the original gray value of the cover image blue plane. Hence, this proposed watermarking 26, 27, 28 is non-blind and lossless.V.R ESULTS AND D ISCUSSIONMATLAB 7.0.1 Software is extensively used for the study of RNS based multiple image embedding technique. Conce
44、rned results are shown in Fig. 2 and Fig. 3.(a) (b) (c)(d)(e)(f)(g) (h)Fig. 2. (a) Lena cover image, (b) Baboon cover image, (c) Pepper cover image (d) Zelda cover image (e) Lena watermarked image (f) Baboon watermarked image (g) Pepper watermarked image (h) Zelda watermarked image.(a) (b) (c) (d) (
45、e) (f)Fig. 3: (A) Watermark I, (B) Watermark II, (C) Watermark III, (D) Recovered Watermark I, (E) Recovered Watermark II, (F) Recovered WatermarkIIITable 1 reports high PSNR and high correlation valuesobtained from current multiple image hiding technique12, 13, 14. To our knowledge, substantial amo
46、unt ofwork has not been done in the domain of multiple imageembedding. In 2013, Dey et al. proposed a method ofmultiple hospital logo embedding in retinal images usingDWT-DCT-SVD 16 based technique. Considering thescaling factors (k1, k2, k3=1) the following results areobtained (Table 2). The compar
47、ative result clearly showsthe efficacy and robustness of our proposed RNS basedtechnique.Table 1. Statistical analysis of RNS based multiple image watermarking techniqueTable 2. Statistical analysis of DWT-DCT-SVD based multiple image watermarking techniqueFig. 4 and Fig. 5 and Table 3 illustrate the effect ofcommon