Encryption Algorithm Using Advance Technique

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Encryption Algorithm Using Advance Technique

Ishwar Lal Paliwal Mahesh Kumar Porwal

MTech Scholar (Digital Communication) Associate professor (ECE) ishwarpaliwal1339@gmail.com porwal5@yahoo.com

Shrinathji Institute of Engineering & Technology Nathdwara (Rajasthan)

Abstract The encrypted image is difficult in compare to the encryption of the text because of the high capacity. Recent methods are difficult to handle the image encryption. Recently, the use of chaotic signals for secure data transmission has shown significant growth in developing chaotic encryption algorithm.In a recent articlet he application of the BrahmaguptaBhaskara (BB) equation for encryption is reported . However, a number of chaos-based algorithms are proved to be insecure in the literature. It is also shown in the literature that the BB equation based algorithm can be broken by a low complexity known as plaintext attack. Hence, in this paper, we are using pixel shuffling and then we make a new secure cryptosystem based on the BB equation and chaos is proposed for image encryption.

Keywords:Image Pixel Shuffling, BB equation, Chaos Cryptosystem, Image encryption.


    In 21st century, due to the fast development in digital

    Pixel shuffling, BB equation and chaos, a new cryptosystem is proposed for image encryption.


    In this Paper Pixel shuffling play very important role. Pixel of image is shuffling from low intensity to high intensity in every row. , first all pixels of row 1 are arranged according to their value of intensity .Then row 2,row 3,etc.At the end we get the new shuffled image.

    So,the further steps of the algorithm is done with this shuffled image



    The Brahmagupta-Bhaskara equation can be written as

    image processing and network communication , the

    (f 2+1)p

    = (y2)

    p ..(1)

    demand for real-time secure transmission of digital images over the networks is getting more and more importance. To meet this challenge, many encryption schemes for image encryption have been proposed. Some traditional encryption algorithms have also been proposed such as DES, Line Map etc; but these algorithms are not suitable for practical image encryption due to the intrinsic features of images such as bulk data capacity and high correlation among pixels. Among them,

    The chaos based image encryption schemes show some exceptionally desirable properties in many aspects regarding speed, security, computational efficiency and practicability.

    Security is the major concern while transmitting signals. So we use pixel shuffling and then we do the encryption of the image. To protect the valuable information in many applications like medical imaging, military image database, communication and confidential video conferencing, there is a need to secure the images by the use of encryption. In such a case, to avoid information leakage to both active and passive attackers, encryption of the military images is very important. By the way, most of the chaos-based algorithms are proved to be insecure. A cryptosystem based on Brahmagupta Bhaskara (BB) equation is proposed in.

    The cryptosystem was proposed to improve and avoid the known plaintext attacks reported in. However, it is shown that the two cryptosystems proposed are vulnerable to known plaintext attacks. Hence, in this paper, based on the

    Here , p stands for modulo operation by p on the argument values of the expressions.

    For obtaining a valid quadratic residues solution of the BB,

    Equation (1) can be written as

    (f(x2)p)p +1 =(y2)p (2)

    Equation (2) can be rewritten as

    (fqx+1)p = (qy)p …(3)

    where qx and qy are the quadratic residues solution of the BB equation.

    To solve the BB equation, find a possible pair (x,y) so that Equation (1) is satisfied for given f and p.

    Once x and y are found, then qx and qy are computed as qx=(x2)p , qy=(y2)p .(4)

    Given qx and qy corresponding to any root of the BB

    equation (fx2 + 1) p = (y2)p, it is always possible to compute uniquely the corresponding value of f, only with the knowledge of p, using the following relation:

    f =(q x )1 (q y 1)mod( p ) …..(5)

    The f corresponds to the clear text or plaintext in a block that is being encrypted and p corresponds to the primary secret key used in the encryption of the plaintext in a block.


    Sensitive dependence is one of the desired feature of the cryptographic algorithm. As, if the initial conditions that are use to encrypt any data are change even by a small amount,

    one bit for instance, then the encrypted text will change widely . This is one of the fundamental principles of the chaotic functions which is given by the following equation-

    Xc(i+1)=Xc(i)(1-Xc(i)) …….(6)

    When Âµ = 3.9, the logistic map exhibits chaotic behavior, and hence the property of sensitive dependency.


The block diagram of the proposed algorithm for encryption is shown in Figure 1. In this , for a given primary key p, the root pair of

the BB equation corresponding to each pixel of the image is found. Then, according to a binary sequence generated from a chaotic system, a mod oper ation is performed on

the root pair of the BB equation corresponding to each pixel and then each root is XORed or XNORed bit-by- bit to one of the two predetermined keys, key1 and key2.

Let f denote an image of size M Ã— N pixels and f(i, j), 0 i M 1, 0 j N 1 be the gray level of f at position (i, j). The encryption algorithm for the proposed f cryptosystem is as follows.







Figure 1: Block diagram of the proposed Algorithm.


The proposed algorithm for encryption is as follows. Step 1:Choose p, key1 and key2 and set l = 0.

Step 2: Choose the initial point Xc (0) and generate the chaotic sequence Xc (0), Xc (1), Xc (2), , Xc (MN/16 1) using Equation (4) and then create b (0), b (1), b (2), , b (2MN 1) from Xc (0), Xc (1), Xc (2) ,,

Xc (MN/16 1) by the generating scheme such that b(32i + 0)b(32i + 1) …………………. b(32i + 29)b(32i + 30)b(32i +

31)………… is the binary representation of Xc (i) for i = 0, 1, 2, (MN/16 1).

Step 3: For i = 0 to M 1

For j = 0 to N 1, obtain Qx(i, j) and Qy(i, j) from the solution of BB equation.

Figure 2: Original image

Figure 3: Shuffled image

Figure 4: Encrypted Qx of the Shuffled image

Figure 5: Encrypted Qy of the Shuffled image


In this paper , a secure algorithm based on Brahmagupta Bhaskara equation is design for image encryption. From the result, it is concluded that the proposed algorithm is effective for secure image encryption.


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  1. G Alvarez ,L H Encinas, and J M Masque, Known-Plaintext Attack to Two Cryptosystems Based on the BB Equation, IEEE Transactions on Circuits and Systems II: Express Briefs Vol. 55, Issue 5, pp. 423-6, 2008.

  2. A M Youssef, A comment on Cryptographic applications of Brahmagupta-Bhakara equation, IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 54, no. 4, pp. 927-8, 2007.

6.N Rama Murthy and M N S Swamy, Authors reply, IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 54, no. 4, pp. 928-9, 2007.


Mr. Ishwar Lal Paliwal is presently in M.E. final year in Digital Communication branch in Shrinathji Institute of Technology & Engineering Upli Oden, Nathdwara, Rajasthan ishwarpaliwal1339@gmail.com

Mr. Mahesh K. Porwal is presently working as Associate Professor in Electronics and Communication Department in Shrinathji Institute of Technology & Engineering Upli Oden, Nathdwara, Rajasthan


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