High Payload Watermarking using Residue Number System(IJIGSP-V7-N3-1)

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 (/doc/84b03b26ec630b1c59eef8c75fbfc77da2699737.html/)DOI: 10.5815/ijigsp.2021.03.01High Payload Watermarking using Re

2、sidueNumber SystemShubhendu BanerjeeDept. of CSE, Narula Institute of Technology, Kolkata, West Bengal, India,shankushubhendu/doc/84b03b26ec630b1c59eef8c75fbfc77da2699737.htmlSayan Chakraborty, Nilanjan DeyDept. of CSE, Bengal College of Engineering & Technology, Durgapur, West Be

3、ngal, India,Email: sayan.cb/doc/84b03b26ec630b1c59eef8c75fbfc77da2699737.html, neelanjan.dey/doc/84b03b26ec630b1c59eef8c75fbfc77da2699737.htmlArijit Kumar PalCMC Limited, India,arijit1421/doc/84b03b26ec630b1c59eef8c75fbfc77da2699737.html,Ruben

4、 RayDept. of IT, Government College of Engineering and Leather Technology,Kolkata, West Bengal, India,ruben.ray/doc/84b03b26ec630b1c59eef8c75fbfc77da2699737.htmlAbstractInformation hiding or data hiding, also known as watermarking, has become a part and parcel of covert communicat

5、ion and copyright protection. Maximizing watermark payload is a major challenge for watermark researchers. To overcome this 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

6、on the Chinese remainder theorem of modular arithmetic for its operation. The proposed method takes pixel values from three 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 fro

7、m an image, without distorting the original image using the proposed technique. The high peak signal to noise ratio (PSNR) and payload values claims the robustness of the proposed method.Index TermWatermarking, Payload, Residue Number System, Chinese Remainder Theorem, PSNR.I.I NTRODUCTIONHiding any

8、 message within an image, signal or video is known as watermarking 1. To hide the message, an image is used as a cover, which 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

9、 and robustness are two main features of a good watermark 5,6. Robust watermarking 7, 8, 9 means, when an image is less damaged 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 propert

10、y of less degradation of an image is referred to as imperceptibility 13, 14, 15. The secret message is embedded as an invisible 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 infor

11、mation hiding and transform domain (such as the DCT transform domain, the wavelet transform domain, etc.). In spatial domain information hiding, most watermarking 21, 22 methods embed the information directly to the original image. If some valuable information which was required during embedding wat

12、ermark 23, 24 is provided to the user, then it should be non-blind watermarking 25, 26, 27. The properties are the same as 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 w

13、atermark 30, 31 refers to the method that can hide large amount of data. The chief factors influencing payload are size of 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

14、et al. proposed a method of recovering watermark from images after it suffered some type of attacks. Some watermarking methods 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 f

15、or the purpose of image authentication and protection. Two watermarks are embedded using quantization of wavelet coefficients 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,

16、 a study on the RNS (residue number system) application in digital image processing was done and a RNS image coding scheme 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. I

17、n this technique, electronic digital signature embedding using RNS-based designs was used to protect the author rights of 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

18、the other to balance distortion. A series of experiments established the effectiveness of this method. In 2009, Kumari 6 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 m

19、essage is inserted in the image using those gray values. In 2010, Wu 7 et al. presented a paper on fixed point and floating 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

20、 added to the watermarked 11, 12 object for security purpose.Methodology is described in section 2. Section 3 illustrates 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

21、 the same section. Paper concludes in section 6.II. M ETHODOLOGYA. Residue Number System (RNS)The residue number system is 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

22、 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.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

23、it is imperative that all the moduli are co-prime; that is no modulas may have a common factor with any other. The number 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 wh

24、ere 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 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

25、) o represents arithmetic operations i.e. addition, subtraction, multiplication. Now,(A o B)= C (5) This implies,(a1 o b1) 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

26、 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 multiplication.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 in

27、to 3 gray planes (Red, Blue and Green).Step 2. Size of the image is calculated.Step 3. Three binary images (same size of 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.

28、The very first bit is taken from each of thewatermark image and the generated three bits are clubbed and converted into corresponding 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

29、 three numbers generated from step 4 and 6.Step 8. The resultant three numbers are placedrespectively to generate a single 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 isd

30、ivided by 9 such that the quotient is y and the single digit remainder is x .Step 10. y and x is clubbed together (yx ) to 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 1

31、2.The modified blue plane, red plane and green plane is combined to generate the colorwatermarked image.B.Extraction of Watermark 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

32、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 result 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

33、 by taking moduli of 3, 2 and 7for the respective three digits.Step 5.Modulo results for 3, 2 and 7 (mutually prime) is summed 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 fir

34、st pixel value of the blue plane is subtracted from the generated closest value. Step 8.The result is converted into binary 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 TH

35、E P ROPOSED M ETHODLet us consider that the first pixel (gray value) of the cover image is 255 and the first binary bits 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 R

36、esidueNumber System (RNS) Moduli of 3, 2 and 7 respectively is applied on 255 and 5 to generate the following results:255 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

37、. 2, 0, 1 are clubbed together to generate a single decimal number 201 of length three digits.Fig. 1: Watermark embedding 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 di

38、git 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 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 add

39、ed with 3. The generated result (201) is split into 3 single digit numbers (2, 0, 1). i.e.-= 198 + 3= 201Chinese Remainder 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 m

40、od 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. 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 mutual

41、ly 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 16 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

42、 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 (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 = 1

43、7692 + 42 3 = 92+126 = 21892 + 42 4 = 92 + 168 = 260By subtracting 255 from 260, 5 is obtained. The binary representation 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

44、 with the help of watermark 18, 19 image bits of the corresponding positions. During extraction 20, 21, 22 process the recovery 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

45、D ISCUSSIONMATLAB 7.0.1 Software is extensively used for the study of RNS based multiple image embedding technique. Concerned 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

46、watermarked image (f) Baboon watermarked image (g) Pepper watermarked image (h) Zelda watermarked image.(a) (b) (c) (d) (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

47、high correlation valuesobtained from current multiple image hiding technique12, 13, 14. To our knowledge, substantial amount 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

48、16 based technique. Considering thescaling factors (k1, k2, k3=1) the following results areobtained (Table 2). The comparative result clearly showsthe efficacy and robustness of our proposed RNS basedtechnique.Table 1. Statistical analysis of RNS based multiple image watermarking techniqueTable 2. S

49、tatistical analysis of DWT-DCT-SVD based multiple image watermarking techniqueFig. 4 and Fig. 5 and Table 3 illustrate the effect ofcommon attacks (effect of noise, rotation and flip) on thecover image. The obtained results show that RNS basedtechnique is significantly robust and quiet encouraging.T

50、able 1 also shows correlation between watermark andrecovered watermark became 1, which ultimately denotesthat our method is robust. Also, Table 2 shows otherwatermarking techniques results are poor compared toour method as the correlation obtained in thosetechniques are lesser than one. (a)(b)(c)(d)

51、 (e)(f)(g)(h)Fig. 4. (a) Original image (b) 90 ? Rotated Image (c) 180 ? Rotated Image (d) Flipped image (e) Watermarked image (f) Watermarked 90 ? rotatedImage (g) 180 ? Watermarked rotated image (h) Watermarked flipped image Fig. 5. (a) Cover image with 5% Noise, (b) Cover image with 10% Noise, (c

52、) Cover image with 30% Noise, (d) Cover image with 50% Noise, (e) Watermarked image with 5% Noise, (f) Watermarked image with 10% Noise, (g) Watermarked image with 30% Noise, (h) Watermarked image with50% NoiseTable 3. Effect of Rotation, flip and noise.VI. C ONCLUSION In thispresent work, wecan emb

53、ed 3 watermark images in a single image. Hence, the payload in this algorithm is extremely high. The watermarks areembedded in cover image and there was no distortion. Moreover, noise was mixed to establish much better comparison among the cover image and the watermarked image. The obtained values o

54、f correlation and PSNR are very much encouraging regarding the faithfulness of the reconstruction of the image. We have compared RNS technique with DWT-DCT-SVD based multiple image hiding technique. The obtained high PSNR value from our proposed RNS based multiple image embedding technique compared

55、to the previous DWT-DCT-SVD based multiple image watermarking schema establishes the robustness of our proposed method.R EFERENCES1 N.F. Johnson, An Introduction to Watermark Recoveryfrom Images, Proceedings of the SANS Intrusion (a)(b)(c)(d) (e)(f)(g)(h)Detection and Response Conference (IDR99) hel

56、d in SanDiego, CA, February 9-13, 1999.2L. Chun-Shien, and M. L. Hong-Yuan,MultipurposeWatermarking for Image Authentication and Protection,IEEE transactions on image processing, vol. 10, no. 10,October 2001.3W. Wang, M.N.S. Swamy, and M.O. Ahmad, “RNSappli cation for digital image processing, Proce

57、edings.4th IEEE International Workshop on System-on-Chip forReal-Time Applications, 2004.4 E. Castillo, A. Garcia, L. Parrilla, A. Lloris, and U.Meyer-Baese, RNS-based Watermarking for IP Cores,Research in Microelectronics and Electronics 2006,Page(s): 357 - 360 ISBN: 1-4244-0157-7.5S. Weng, Y. Zhao, P. Jeng-Shyang and R. Ni, ReversibleWatermarking Based on Invariability and Adjustment onPixel Pairs, IEEE signal processing letters, vol. 15, 2008.6G. Rosline, N. Kumari, B. VijayaKumar, L. Sumalatha,and V.V. Krishna, Secure and Rob