Multiple Information Hiding using Spherical Random Grids

2nd International conference on Innovative Engineering Technologies (ICIET'2015) August 7-8, 2015 Bangkok (Thailand)

Multiple Information Hiding using Spherical Random Grids Sandeep Gurung1, Abhi Agarwal2, and M K Ghose3 

Validation of the end users has given additional concerns to authentication problems especially over the usage of mobile code and agents. The secret sharing scheme is a technique which limits the validity of information not only to single authorized personnel but requires the presence of a group of known users to decode the secret information. One such cryptographic scheme was suggested by Naor and Shamir [1] which encodes secret information into different noisy shares. The decoding process includes superimposing of a minimum number of shares to produce the secret information making use of Human Visual System (HVS). Visual Cryptography is a powerful cryptographic scheme that involves the use of the Secret Sharing Scheme. In a k : n scheme, a digital information is divided into n shares and distributed to the authorized participants. The shares are a random collection of noise and just by looking at a share one cannot make out the content of the share. Decryption in this case in very simple and does not require computer participation. For decryption, the shares are printed on transparencies and superimposed. The decryption requires superimposition of k shares. The hidden information cannot be extracted if there are less than k shares present. The main drawbacks of the visual cryptography scheme are mentioned below: i. It involves pixel expansion and thus the size of the shares gets increased changing the aspect ratio of the decoded secret information. ii. It requires the use of a complex codebook as a reference to generate the cipher text. iii. The number of secret image can be encrypted is restricted to one. The solution to the first drawback is to use Visual Cryptographic techniques that are implemented without the idea of pixel expansion like the size invariant VC technique and random grids [2]. Random grid is a simple probabilistic methodology that utilizes a 2-D array to be filled randomly with transparent and opaque pixels with equal probability of occurrence. It does not involve pixel expansion and thus the size of the shares generated is same as that of the original the secret information. It also omits the use of any codebook and thus helps us solve the second drawback as mentioned before. The amount of information to be embedded can be increased by exploiting the spatial domain which includes various angular rotations of the shares represented in a circular fashion. To increase the security and the carrying capacity of a security system various multilevel schemes have been

Abstract— Security is of vital importance in today‟s world. Our dependence on information and its exponential growth demands that proper security measures are needed to be taken for its safety and security. For ensuring the security of information transmitted over a network many different techniques are used to achieve the prime security goals of authentication, security and integrity. Cryptography is one such technique which converts a readable data or information into an unintelligible form. Visual cryptography (VC) is an example of a k:n Secret Sharing scheme used for encrypting data into noisy shares where procession of a minimum of k share are required to decode the secret information. Decryption can be performed easily by stacking the shares and using the Human Visual System (HVS). The proposed system uses a specialized probabilistic based Visual Cryptography Scheme named as Random Grids. Random Grids are simple and easy to use thus avoiding the problems of pixels expansions and the maintenance of a code book which is used as a reference to generate the random individual shares. To increase the carrying capacity Multiple Information are hidden based on the concept of Geometric Rotations. Finally the spherical representation is used to decrease the distortion of the decoded message.

Keywords— Authentication, Contrast, Multiple Information Hiding, PSNR, Spherical Random Grids, Secret Sharing Scheme, Visual Cryptography I. INTRODUCTION

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HE exponential growth of information and its ever increasing demand has been of great concern today. Computer networks are a powerful tool for data communication. Nowadays almost everything is done over the network, ensuring the security concerns of the information before it is transmitted is therefore of prime importance.

Sandeep Gurung1 is with the Sikkim Manipal Institute of Technology, Majhitar, Sikkim, India 737136. Abhi Agarwal2 is a Final Semester Computer Science student of Sikkim Manipal Institute of Technology, Majhitar, Sikkim, India 737136. Mrinal Kanti Ghosh3 is currently working as the Professor and Dean(Academics) at Sikkim Manipal Institute of Technology, Majhitar, Sikkim, India 737136.

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suggested. A hybrid model of visual cryptography and steganography [3] has been suggested to increase the security of such systems. Recursive techniques [4] in Visual Cryptography are also used to increase the number of secret images that can be hidden. However they tend to increase the size of the images as the number of hidden messages increases. The rest of the paper is organized as follows: In Section II a brief overview of Random Grids and the method of generating random grids is discussed. Section III gives a review of the various techniques used for hiding multiple information. Section IV contains the proposed methodology and Section V contains the detailed design strategy used to achieve the goal. The Section VI and VII contain the experimental results and the conclusion of this article respectively. The final Section VIII discusses about the future scope of the methodology discussed here.

Algorithm 1 1: Generate R1 as a random grid // for (each pixel R1[i, j ], 1 ≤ i ≤ w and 1 ≤ j ≤ h ) do // R1[i, j] = random_pixel(0, 1) 2: for (each pixel B[i, j ], 1 ≤ i ≤ w and 1 ≤ j ≤ h ) do 2.1: { if (B[i, j] = 0) R2[i, j] = R1[i, j ] else R2[i, j] = 1 - R1[i, j ] } 3: output (R1,R2)

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(b)

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II. RANDOM GRIDS Random grid was suggested by Kafri and Keren in 1987[2] and consists of 2-D array of pixels for binary image. The pixels can be either completely transparent or completely opaque where the opaque pixels block light and transparent pixels allow light to pass through. This scheme of encrypting the images is similar to the usage of a one-time pad which adds to its security. Random grid method is completely probabilistic where the probability of a pixel being transparent (white) is ½ and is represented as P(white). The probability of a pixel being opaque (black) is also ½ since the number of white pixels is approximately equal to the number of black pixels and is represented by P(black). If „r‟ is a pixel in the random grid R then the probability of a „r‟ being white (transparent) is same as the probability of „r‟ being black (opaque) and so P(r=0)=P(r=1)=1/2 where we consider 1 as a black pixel and 0 as a white pixel. If „r‟ is any pixel in the random grid then light transmission of b denoted as t(b) is 1 if b is white and 0 if b is black. The average light transmission through the random grid is calculated by the equation given below

(e) Fig. 1 Implementation details [3] of Algorithm 1 for encrypting image B: (a) Input image B; (b) Threshold image; (c) and (d) Encrypted Shares using random grids; (e) Final output image with PSNR value 4.0923.

III. MULTIPLE INFORMATION HIDING The problem with most of the visual cryptographic technique is that we are able to encrypt only one secret image. Chen et al [5] extended this concept to encrypting two secret images in which hidden images were obtained by stacking the shares on top of each other and then rotating the grids. For this, the user was required to possess both the random grids (shares) and the angle of rotation in which the grids are to be rotated to obtain the hidden image. The limitation of this scheme is the angle of rotation to obtain the second hidden image. Since the shares are rectangular in shape so the angle of rotation can be 90° , 180° or 270°. Since there are only three available angles and an intruder can easily decrypt the information by using Brute-force technique. H.C. Hsu et al [6] proposed the concept of using circular random grids to eliminate the limitation of random grids and to encrypt multiple images within the same grids with flexible rotations

T(B) = . (1) In equation (1), „w‟ × „h‟ is the image size and b[i,j] is the binary pixel corresponding to cell (i,j). In a random grid, number of black pixels is approximately equal to the number of white pixels so T(B)=1/2 . The algorithm for implementing random grid is taken from [2] that offers the highest contrast value of ½ and is given below. An example of the algorithm implementation is given in the Figure 1. Input: A w × h binary image B where B[i, j] ∈ {0, 1}(white or black), 1 ≤ i ≤ w and 1 ≤ j ≤ h Output: Two shares of random grids R1 and R2 which reveal G when superimposed where Rk[i, j] ∈ B, 1 ≤ i ≤ w and 1 ≤ j ≤ h and k ∈ {1, 2}

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2nd International conference on Innovative Engineering Technologies (ICIET'2015) August 7-8, 2015 Bangkok (Thailand)

so that the capacity of secret communication is increased. The secrets are revealed by superimposing the two circular random grids and by rotating one of the grids through various angles where as the other grid is kept at a fixed position. Other schemes suggested by Jeanne Chen et al [7] and Chang et al [8] gave new ways of representing images as circular grids. Simple recursive techniques can be implemented to hide number of information as suggested in [9] and the utilization of the bits in such ideas is nearly 100%. The technique simply tried to utilize the Least Significant Bits (LSBs) of images to hide the Most Significant Bits (MSBs) of other secret images. Recursive techniques were also implemented on circular grids to implement a multiple information hiding scheme [10] where the shares of the previous levels were concatenated to create a reference share for embedding the other secret information. The scheme uses a random grid as a guide line to represent the images in a circular fashion for flexible angular rotations (columnar shifts) but however the size of the shares is increased at each iteration.

example of the spherical representation of shares and the decoded image is given in Figure 3.

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Under this section the overall stratagem of approaching the solution is discussed. This section discusses the technique of encryption and decryption of the image with the secret embedded in it. In order to improve the quality of the reconstructed image, the natural (continuous-tone) images must be first converted into half tone images by using the density of the net dots to simulate the original gray of color levels in the target binary representation; also the VC scheme by nature is lossy. The Floyd-Steinberg Error Diffusion [11] technique is used to convert the original colored image to gray scale. To implement this scheme for multiple secret hiding, the binary image for the first secret which is generated by using the concept of thresholding and error diffusion is fed to the Random Generator to generate the first random grid pairs. The secret images are then randomly selected and using the pixel information of the randomly selected secret image and the first share generated by the random grid generator, the second share is constructed. The pixel information of all the secret images is now stored in the two shares generated. The block diagram of the overall procedure as mentioned above is given in Figure 4. Once the two spherical grids have been generated, the secret can be revealed by simply stacking the two spherical grids on each other for the correct angle of rotation (or orientation). The angle shifts that is used for rotating the spherical grids is proportional to the step size governed by (w/m) „w‟ the width of the image by „m‟ where m is the number of secret images that is to be hidden. The approach extends the idea suggested at [5] and transforms the design methodology by representing the information in polar coordinates. The modified approach is given in Algorithm 3. For creating the first random share, the following algorithm is used. Input: A w × h binary image B1 or B2 or … or Bm where Bk[i, j] ∈{0, 1}(white or black), 1 ≤ i ≤ w , 1 ≤ j ≤ h and 1 ≤ k≤m Output: A single share of random grid R1.

Secr et 1 – Share 1

1 Secr et 1 – Share 2

1 Secr et n – Share 1

1 Secr et n – Share 2

1

Fig. 2 Generation of Random Girds [10]

The random grid generator shown above takes „n‟ secret images as the input and using the algorithm 1 generates two random shares for each of the „n‟ secret images gives as input producing a total of 2n shares where „n‟ is any positive integer number. Random grid removes the problem of pixel expansion and does not require maintaining a complex codebook. The aspect ratio of the image is preserved since the size of the secret image and equal to the size of the shares generated. The proposed methodology extends the concept proposed by T.H. Chen[5] and represents the shares in a spherical manner to minimize visual distortion. For the purpose of decryption the shares are represented as spheres and then the participating spheres are stacked together. For decrypting the first hidden image both the shares are simply stacked together. For decrypting other hidden images both the shares are stacked and then keeping one sphere fixed, the other sphere is rotated at various degrees over the fixed one. An http://dx.doi.org/10.15242/IIE.E0815017

(d)

(c)

V. DESIGN STRATEGY

Most of the multiple information hiding techniques uses the traditional visual cryptography schemes and thus needs pixel expansion and requires the construction of a complex codebook. The proposed methodology uses the concept of random grids as suggested by Kafri as a basis for generating the shares. A random grid generator is as shown in Figure 2.

n Secr et Images

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Fig. 3 (a) Secret image; (b) Spherical share 1; (c) Spherical share 2; (d) Spherical image formed by overlapping (b) and (c); (e) Image obtained by unfolding (d)

IV. PROPOSED METHODOLOGY

Random Grid Generator

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2nd International conference on Innovative Engineering Technologies (ICIET'2015) August 7-8, 2015 Bangkok (Thailand)

Here, is the maximum possible pixel value of the image. When the pixels are represented using 8 bits per sample, this is 255. For Binary image it is 1. The PSNR comparison of the three secret images is given in Figure 6, 7 and 8. In these experiment three secret images of size 420 by 420 is taken as input. Then using random grid generator, a random grid is generated which is then converted to a sphere. After this, a recursive procedure is carried out and the three secret images are randomly selected recursively. In each iteration depending on the (i,j) pixel of the secret image selected, the (i,j) pixel of the second spherical share is generated using algorithm 3 discussed above.

Algorithm 2 1: Generate R1 as a random grid // for (each pixel R1[i, j ], 1 ≤ i ≤ w and 1 ≤ j ≤ h ) do // R1[i, j] = random_pixel(0, 1) 2: output (R1) For creating the second share, the algorithm is given below. Input: m w × h binary image B1, B2 …, Bm where Bk[i, j] ∈ {0, 1}(white or black), 1 ≤ i ≤ w, 1 ≤ j ≤ h and 1 ≤ k ≤ m Output: A single share of random grid R2. Algorithm 3 1: Generate R1 as a random grid // for (each pixel R1[i, j ], 1 ≤ i ≤ w and 1 ≤ j ≤ h ) do //k=floor(rand(1)*m+1) // jnew =( r1*sinθ1 +r*sinθ) mod w //if Bk[i,j]=0 then // R2[i,j]=R1[i, jnew] //else // R2[i,j]=1-R1[i, jnew] 2: output (R2) r = x (1+tan2θ)1/2 , x = (k-1) ,y = x*tanθ and tanθ=h/m The columnar shifts depending on the secret information chosen is specified by jnew = jold + ((k-1)*h/m) mod w……. (i) The expression can be mapped to a line equation as: y = mx + c ………. (ii) By comparing the two equations we get the following deduction; y = jnew , the slope m = h/w, the value of x is equal to (k-1) and the y intercept is taken as c = jnew as it remains a constant on a given pixel being chosen. Now on converting the information to the polar form the radius r and the angle θ are represented as; r = x (1+tan2θ)1/2 , x = (k-1) ,y = x*tanθ and tanθ=h/m. Thus the value of r and θ is reduced to r = (k-1)(1+h2/m2)1/2 and θ = tan-1(h/m). The (i,j) coordinates can be computed as (r*cosθ,r*sinθ). Similarly the value of jold can be remodeled as jold = r1*sinθ1 where r1 = (iold2 + jold2)1/2 and θ1=tan-1(jold/iold) VI. SIMULATION AND EXPERIMENT

The two generated spherical shares R1 and R2 are then stacked to reveal the first secret image. To decrypt more secret images one spherical share is kept fixed and the other spherical share is then rotated with different angles and in different directions. In this case R1 is kept fixed and R2 is first rotated with 140 pixels to reveal the second secret image. To reveal the third secret image, R1 is kept fixed and R2 is rotated with 280 pixels.

A. PSNR comparison This section evaluates the PSNR (Peak Signal to Noise Ratio) value of the input image and the secret image that is revealed at the end using the formula:

The PSNR is defined as:

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B. Contrast The average light transmission on the (black/white) area is given as T[area(white/black) ]. In case of the original random grid algorithm T[area(white/black) ] = 1/2. The first secret is created by using the original algorithm. If G1 and G2 are two grids then the overlapping of the grids produce T[(G1+G2)area(white)] = ½*1/2 = ¼. Similarly the value of T[(G1+G2)area(black)]= 1-1/4 = ¾. 29

2nd International conference on Innovative Engineering Technologies (ICIET'2015) August 7-8, 2015 Bangkok (Thailand)

Let Ti denote the area taken by the first secret and Tj denote the area taken by the rest of the secret information, then the average light transmission of the final overlapped shares would give the following information. T[area(white)] = 1/3 * Ti [area(white)] + 2/3 * Tj [area(white)] = 1/3*1/2+2/3*1/4 = 1/3 T[area(black)] = 1/3 * Ti [area(black)] + 2/3*Tj [area(black)] = 1/3*0 +2/3*1/4= 1/6 The contrast α is calculated as follows: α(contrast) = T[area(white)] – T[area(black)] (1 + T[area(black)]) Thus the contrast calculated for the given example is equal to α = (1/3 – 1/6)/(1+1/6) = 1/7 = 0.1428. The contrast can be generalized as α = 2/(5*m-1) where m is the number of secret information.

get the original image using the decryption scheme mentioned in [13]. There are also many techniques that can be used for RGB images one of which is stated above. XI. ACKNOWLEDGEMENT The corresponding author deeply acknowledges the guidance and inspiration by his Ph.D. guide Prof. (Dr.) M K Ghose, Dean Academics, Sikkim Manipal Institute of Technology, Sikkim, India. The author also deeply acknowledges the contribution of Arindam Parmar, B.Tech student of Computer Science and Engineering Department, Sikkim Manipal Institute of Technology, Sikkim for his contribution towards the work.

C. Security On possessing a single share it would not be possible to derive the secret information. The security constraints are preserved as the contrast for a single share is always equal to zero(0) as the average light transmission of the white and the black area are the same. VII. CONCLUSION This paper has successfully been able to suggest the following ideas for a given set of secrets keeping in view the constraint on the dimension chosen for the secret images. 1. Generation of spherical random grids which correspond to the rectangular grids generated. 2. Recursively use of the idea can be used to hide more information. 3. The shares in isolation leak no information about the information contained in it. 4. Both confidentiality and authentication can be achieved by this method of encryption. 5. The spherical representation minimizes visual distortion as all the pixels are uniformly distributed. However the paper can be modified to work on colored images. VIII.

FUTURE SCOPE

The project can be extended further to incorporate the following: i> Encryption of gray scale and colored images rather than just binary images. ii> Hiding of multiple secret images within the two shares since the shares are spherical in shape so many secret images can be hidden along the three axes (x, y, z) because of the symmetric property of the shares along the axes. For RGB images, the cipher can be obtained using the scheme discussed in [13] and then follow the same steps discussed above to generate the spherical shares. The cipher obtained by stacking the spherical shares can then be used to http://dx.doi.org/10.15242/IIE.E0815017

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2nd International conference on Innovative Engineering Technologies (ICIET'2015) August 7-8, 2015 Bangkok (Thailand) M.K.Ghose obtained his Ph.D. from Dibrugarh University, Assam, India in 1981. He is currently working as the Professor and Dean (Academics) at Sikkim Manipal Institute of Technology, Mazitar, Sikkim, India. Dr. Ghose also served in the Indian Space Research Organization (ISRO) – during 1981 to 1994 at Vikram Sarabhai Space Centre, ISRO, Trivandrum in the areas of Mission simulation and Quality & Reliability Analysis of ISRO Launch vehicles and Satellite systems and during 1995 to 2006 at Regional Remote Sensing Service Centre, ISRO, IIT Campus, Kharagpur(WB), India in the areas of RS & GIS techniques for the natural resources management. Dr Ghose has conducted a number of Seminars, Workshop and Training programmes and published around 95 technical papers in various national and international journals in addition to presentation/ publication of 125 research papers in international/ national conferences. He has supervised PhD dissertations in areas like Data Mining, Information Security, Geoinformatics and Robotics. He is a Life Member of Indian Association for Productivity, Quality & Reliability, Kolkata, National Institute of Quality & Reliability, Trivandrum, Society for R & D Managers of India. Trivandrum and Indian Remote Sensing Society, IIRS, Dehradun.

REFERENCES [1] Naor, M., and Shamir, A. (1995), Visual cryptography, in „„Advances in

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Cryptology Eurocrypt ‟94‟‟ (A. De Santis, d.), Lecture Notes in Computer Science, Vol. 950, pp. 1 12, Springer-Verlag, Berlin. http://dx.doi.org/10.1007/bfb0053419 Kafri, O., Keren, E., “Encryption of pictures and shapes by Random Grids.” Optics, Letters, 1987, 377–379. http://dx.doi.org/10.1364/OL.12.000377 Sandeep Gurung, Pratarshi Saha and Kunal Krishanu, “Hybridization of DCT based Steganography and Random Grids” , International Journal of Network Security & Its Applications , Volume 5, Issue 5, ISSN : 0974 9330[Online]; 0975- 2307 [Print] , AIRCC Publications May 2013. Meenakshi Gnanaguruparan , Subhash Kak , “Recursive Hiding Of Secrets In Visual Cryptography” in Cryptologia, Volume XXVI ,Issue 1(2002). T.H. Chen, K.H. Tsao, K.C. Wei, ”Multiple-image encryption by rotating random grids”, Proceedings of the 8th International Conference on Intelligent System Design and Applications (2008). http://dx.doi.org/10.1109/isda.2008.141 H.C. Hsu, J. Chen, T.S Chen, Y.H. Lin, “Special type of circular visual cryptography for multiple secret hiding”, The Imaging Science Journal 55(3)(2007) 175-179. http://dx.doi.org/10.1179/174313107X176289 Jeanne Chen, Tung-Shou Chen, Hwa-Ching Hsu, Hsiao- Wen Chen, “New visual cryptography system based on circular shadow image and fixed angle segmentation”, Journal of Electronic Image(413), 033018 (JulSep 2005). Hsien-Chu Wu, Chin–Chen Chang, “Sharing visual multi- secrets using circle shares”, Computer Standards and Interfaces 28 (2005) 123-135. http://dx.doi.org/10.1016/j.csi.2004.12.006 Lekhika Chhetri, Sandeep Gurung, ”Recursive information hiding in threshold visual cryptography scheme”, International Journal of Emerging Technology and Advanced Engineering, Vol. 3, Issue 5 (May 2013). Sandeep Gurung, G. Ojha, M.K. Ghose, “Multiple Image Encryption using Random Circular Grids and Recursive Image Hiding”, Vol 86 No 10, 2013. Floyd, R. W. and L. Steinberg. “An adaptive algorithm for spatial 21greyscale", Proc. SID, vol. 17/2, pp. 75-77. 1976”. Saman Salehi, M.A. Balafar. “Visual multi secret sharing by cylindrical random grid”, Journal of Information Security and Applications 19 (2014) 245-255. http://dx.doi.org/10.1016/j.jisa.2014.05.003 Quist-Aphetsi Kester, “Image encryption based on the RGB pixel transposition and shuffling”, I. J. Computer Network and Information Security, 2013, 7, 43-5 http://dx.doi.org/10.5815/ijcnis.2013.07.05 Sandeep Gurung1 received his M. Tech degree in Computer Science and Engineering from the Sikkim Manipal University in 2009 and is currently pursuing his Ph.D. degree in Computer Science and Engineering. He is an Assistant Professor in the Department of Computer Science at Sikkim Manipal Institute of Technology, Mazitar, Sikkim, India. His research interests include Computer Networks, Cryptography & Network Security, Distributed Systems and Soft Computing.

Abhi Agarwal is a Final Semester Computer Science student of Sikkim Manipal Institute of Technology currently doing internship at Dell International Services and will be graduated in June 2015. My subjects of Interests are Network Security, Design and Analysis of Algorithms, Formal Languages and Automation and Machine Learning.

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