Graceful Labeling of Assignable Information Hiding in Image

INTRODUCTION

The hackers also grew up to counter these safety measures. Rupert Murdoch, Julian Assange to name a few. Hence, Emphasis given on a powerful algorithm. Conventional steganography involves the concept of one image per user, where only one user can embed the information within an image. The proposed work here has gone up a level where up to five users can use a single colour image to embed and transmit their data. Each user has been assigned a pixel to embed ones data and after embedding, one has to go to other pixel for embedding which will be determined by the Graceful Labeling methodology and the order of user index will be all combinations of five users i.e., 1, 2, 3, 4, 5; 3, 1, 4, 2, 5 and so on. This introduces the randomization in the order of embedding. Randomization in the selection of planes is done by using a slightly altered PIT. The strength of the whole system is enhanced further by the RSA public crypto system and AES. Each user first has to encrypt his data by using AES and then RSA will be employed. This Randomized multi-user steganography amplify the strength of the system and thus making attack nohow. Finally the quality of the proposed system is justified using the parameters MSE and PSNR.

A decade back, Information technology was just a branch of study. But now it’s become the way of life with so many developments and new technology added in it. In the world of internet, people have reached such great heights that anything is just but surely possible. The communication sector taking IT and its developments as a platform has also made renovations in itself. The Stone Age communication was replaced by paper and then to the mobiles, then was the computer laptops and presently we are in the TAB’s era.

This all innovations exhibit major platform is the Internet and again the base being the Information technology. With so many advantages of IT, there are again equivalent or rather more number of disadvantages and one of the major being security. The security of data in this mode of communication is almost nothing. A deeper insight into it, leads to a conclusion that the inventor of the technology is itself the creator the security issues.

So to tackle such crisis of security, lot of new methods and algorithms of encryption for the data have been formulated and were collectively called “Cryptography”. The then efficient means of security for the data was widely accepted. But over time, as this method leaves out traces of data modification, the search started again.

Then into the race was steganography, with much vibrant and safer algorithms to just tackle any security in any domain. May it be audio, video, or images. Every form of communication has just the place for steganography as its principles are simple but with lot of security. The concept of steganography deals simply with a cover image, which hides (Karzenbeisser and Perircolas, 2000; Provos and Honeyman, 2003) the secret information in it. The cover being a very common image has a lot of pixel modification being done to it with many randomizations in the bits.

The changed image is now again retrieved back to its original form, but still keeping the bits just in place. This piece of technology has reached ever dreaming heights of security (Marvel et al., 1999) and the end still to be discovered.

The color image steganography (Petitcolas et al., 1999) is a most widely used technique used in the field of information hiding. The steganographic techniques used keeps the existence of the data secret. LSB substitution (Thien and Lin, 2003; Chan and Cheng, 2004; Yang, 2008) is a simple technique in spatial domain steganography .It involves the substitution of least significant bits of the image pixels, by the secret data in binary format.

RSA is an effective algorithm for public-key cryptosystem (Rivest et al., 1978). This is the first cryptoscheme cognized to be worthy for signing as well as encryption and was one of the first groovy advances of public-key cryptoprotocol. A involves key generation, encryption and decryption. The secret data is encrypted (Karzenbeisser and Perircolas, 2000) with a public-key which is known to all. It can only be decrypted by a private key.

The planes in which the data is embedded can be controlled by a technique called the Pixel indicator (Gutub et al., 2008; Gutub, 2010; Amirtharajan and Balaguru, 2009; Amirtharajan et al., 2010a, b, c, 2011, 2012). The pixel indicator technique assigns one of the three planes as the indicator channel and based on the last two bits of the indicator channel the embedding is done in the other two planes. The embedding order in the planes can be changed for increasing the complexity of the algorithm. In this proposed study, the conventional pixel indicator has been changed. If the LSB is 0 the embedding is done in the blue plane and if the LSB is 1 the embedding is done in the green plane.

Sometimes the same image can be used by the different users for embedding their data (Padmaa et al., 2011).

Graphs considered in this paper are simple, tree, finite and undirected. In general G (V, E) denotes the graph G with vertex set V (G) and edge set E (G), such that |V (G)| = p , |E (G)| = q. A labeling of the vertices of G with the numbers from 0 to q is an injective map f: V→{0, 1,..., q}. Let G: E →{1, 2, …, q} be a bijective. Then a graph G is graceful (Rosa, 1967) introduced as a β-valuation), if there exists a labeling of its vertices and edges with the condition for all u, v εV (G) with u vεE (G) such that g (u v) = | f (u)-f (v)|.

Fig. 1:	A Random Tree in which its branches are non decreasing order

The same type of analysis by Golomb (1972) is called Graceful labeling. An extensive survey of contributions to graceful labeling of variety of graphs is made (Gallian, 2011).The structure of the graceful labeling is shown in the Fig. 1.

Let P_n(s₁-s₂-…-s_n) be basic path of T_S(n) tree. The vertices of the path P_n are also termed as supporting vertices of T_S(n) tree. In T_S(n) at each s_i, a star S_i hangs with i branches having centre c_i with one of the branch vertices of S_i is merged with s_i. The special tree with hanging stars whose branches satisfy the condition |E (S₁)| = |E (S₂)| = …= |E (S_n)| (non-decreasing number of branches in the hanging stars).

Let T_S(n) be a tree with n stars T₁, T₂, ..., T_n be stars with |v(s_i)| = i for i = 1, 2, 3,..., n. Free leaves of each of the stars S_i are denoted by u_im for i = 1, 2 ,…, n.

Let T₁, T₂, …, T_n be the central values of the stars S₁, S₂, S₃, …, S_n respectively. It can be verified that|V(T_s(n))| = |V(S₁)|+|V(S₂) |+…+|V(S_n)|and |E(T_s(n))| = |E(S₁)|+|E(S₂) |+ …+ |E(S_n)| +(n-1).

Let |E(S_i)| = q_i for i = 1, 2, …, n and Q= q₁+q₂+…+q_n+(n-1). Labeling of vertices in general denoted by l(v):

•	l (s1) = 0; l (c1) = Q; l (c2) = q1 and l (s2) = Q-q1
•	l(c2j +1) = Q- (), j = 1
•	l(c2j) = , j = 1.
•	l(s2j) = Q - (), j = 1.
•	l(s2j+1) = , j = 1

Let the users in growing ith star of T_S(i) at s_i be u_i1, u_i2, …, u_in.

Let the users in S₁ are labeled with values 1 to q₁-1. Then for i = 1, the labeling of users in odd stars of S_2i+1 based on its supporting vertex s_2i+1 as follows:

The labeling of users in even stars S_2i based on its supporting vertex s_2i as follows.

The labeling of S_i’s in which s_2i+1, i≥1 are increasing order and s_2i, i = 2 are decreasing order in relation with q.

PROPOSED ALGORITHM

In the conventional Image Steganography (Amirtharajan et al., 2010a-c, 2011, 2012; Janakiraman et al., 2012; Thanikaiselvan et al., 2011) algorithms mostly one user will use one image for his covert communication. In many of the Stego (Karzenbeisser and Perircolas, 2000) applications size of the secret data will be less than that of the size of the carrier (Cover Image). This is equivalent to the wastage of bandwidth in a good communication Padmaa et al. (2011) proposed a method, where in embedding of two user’s data in the same image with high non linearity which is essential for security.

In this proposed study, a novel method for multi-user embedding is proposed as shown in Fig. 2 and implementation is done for 5 users and has been tabulated.

Secret data of all the users will be first encrypted by using AES and then RSA will be employed which escalates the complexity. A graceful graph (Janakiraman and Sathiamoorthy, 2011) has been used for fixing the randomized order of embedding. Priority in the order of embedding among the five users will be changed during every cycle. This precedence is provided by taking all 120 combinations (5!) which introduces more randomness (Lu et al., 2009; Amirtharajan and Rayappan, 2012a, b; Bandyopadhyay et al., 2008; Schneier, 2007) in the order of embedding.

Complexity has reached to next level by slightly modified PI technique where LSB of the Red Channel will indicate the embedding in the other two channels. This scheme can be effectively employed in Banks, Office, Universities, etc., where resource sharing by multiple users are involved.

Embedding algorithm:

Fig. 2:	Flowchart of the proposed methodology

Recovery algorithm:

ERROR METRICS

Parameters that are helpful in estimating the standard of the Stego (Sutaone and Khandare, 2008) object are MSE and PSNR. The Mean Square Error is calculated by using the equation:

where, X_{i, j} is Stego value and Y_i,j is the cover object.

The PSNR is calculated using the Eq.:

where, I_max is the intensity value of each pixel, which is equal to 255 for 8-bit gray scale images.

Higher the value of PSNR betters the image quality. Here in implementation Tree, Football, Lena and baboon (256x256) color digital images has been taken as cover images and tested for full embedding capacity. The effectiveness of the Stego process proposed has been studied by calculating MSE and PSNR for all the four digital images in RGB planes and displayed in Table 1.

Table 1:	Results obtained through number of bits embedded on the respective images

Fig. 3:	Sample images taken as cover images

Fig. 4:	Images after processing of stego

Fig. 5(a-f):	k=1 bit embedding users (a) Red plane of cover, (b) Red plane of stego, (c) Green plane of cover, (d) Green plane of stego, (e) Blue plane of cover and (f) Blue plane of stego

Fig. 6(a-f):	k=2 bit embedding for all users, (a) Red plane of cover, (b) Red plane of stego, (c) Green plane of cover, (d) green plane of stego, (e) Blue plane of cover and (f) Blue plane of stego

Fig. 7(a-f):	k=3 bit embedding for all users, (a) Red plane of cover, (b) Red plane of stego, (c) Green plane of cover, (d) green plane of stego, (e) Blue plane of cover and (f) Blue plane of stego

Fig. 8(a-f):	k=4 bit embedding for all users, (a) Red plane of cover, (b) Red plane of stego, (c) Green plane of cover, (d) green plane of stego, (e) Blue plane of cover and (f) Blue plane of stego

Figure 3 represents the cover images and Fig. 4 represents the stego image after processing. The following are the histograms that are obtained for k = 1, 2, 3 and 4 bit embedding in Lena image are given in Fig. 5, 6, 7 and 8, respectively.