IEEE-32331
A Novel Image Encryption Algorithm Using Hyper-chaos Key Sequences, Multi Step Group Based Binary Gray Conversion and Circular Bit Shifting Logic Sk Safikul Alam* Department of Computer Sc & Engineering Calcutta Institute of Technology Kolkata, India
[email protected]
Siddhartha Bhattacharyya Department of Information Technology RCC Institute of Information Technology Kolkata, India
[email protected]
Abstract— This paper is introducing a new image encryption method using hyper chaos based keys, multi step group-based binary gray encryption, bit shifting logic and finally prepares a cipher image, an encrypted image recognizing the plaintext image is very next to impossible. The principal advantage of chaos base encryption is there are sequences of key for multiple times execution of the encryption process. Initially enormous Hyperchaos numbers are to be generated considering a set of equation and finally generating a decimal key and bit shifting key using these Hyper-chaos numbers. These keys are the entity of the multi step group based binary gray conversion and bit shifting logic performed on every individual pixel of plain image. And lastly a set of comparison studies like histogram analysis, information entropy, correlation coefficient, sensitivity test of the plain image with cipher image have been run. The experimental results show the key space analysis and the security in the encryption algorithm. It is shown here the encryption scheme deal with the bit-wise operation on the plain image pixel provides high performance on security and reliability, robustness and invisibility. Keywords— Chaos; Lissajous Curve; Hyper-chaos; Multi Step Group Based Binary Gray Conversion; Circular Bit Shifting
I.
INTRODUCTION
With the technological advancement of computer network, high performance computing, computer multimedia, digital communication, it is required to introduce advanced encryption techniques to incorporate more security on digital information especially digital image. A digital image consists of enormous small fragment of digital information called pixel or voxel (for 3D Image) and therefore a public key encryption or public private key encryption may not be an efficient one because it takes long time to decrypt a digital image. A robust encryption scheme has the following fundamental characteristics [1]: a. Mapping the plaintext to the random cipher text; b. Sensitive to the plaintext; c. Sensitive to the secret key. For security reason and to minimize execution time the digital image should be encrypted with multiple keys. In last few years a good numbers of chaos based image encryption schemes have been introduced that deals with mainly security
Sourabh Chandra Department of Computer Sc & Engineering Calcutta Institute of Technology Kolkata, India
[email protected]
and execution time of encryption process of the plaintext image. The chaos is an interesting phenomenon what are observed everyday in nature like weather, climate, population growth in ecology and also in laboratory like electrical circuit, chemical reaction, mechanical system etc. The chaotic sequences should consist of real numbers generated by a set of equation and it has many potential applications in digital communications like in digital cryptography, data modulation and data compression etc.[2] D. Solev, P. Janjic, and L. Kocarev [2] stated the main features of a nonlinear dynamical system exhibiting deterministic chaos for given values of the parameters are sensitive dependence on initial conditions. X. Deng , C. Liao, C. Zhu, Z. Chen[3] introduced permutation and diffusion process to diffuse the permuted image for encrypting an image using hyper chaos key sequences. Guan et al [4] used Arnold 2D cat map to shuffle the positions of the image pixels. Lian et al and V. Patidar, N. K. Pareek, and K. K. Sud [5][12] proposed the substitution through a chaotic standard map; a logistic map for the diffusion and a chaotic skew tent map for the keys generation. Wang et al [6] proposed an image encryption scheme with combined permutation and diffusion stages using an efficient method for generating pseudorandom numbers from patio-temporal chaos. L. Lihong ,B. Feng-ming,H. Xue-hui [7] introduced two round of encryption image encryption based on double kinds of keys created by Hyperchaos system. Lin et al [8] introduced a chaos based bit level permutation scheme for more secured efficient cipher image. II.
PRELIMINARIES
In mathematics following equations are used to create the Lissajous Curve and is popularly known as Lissajous figure [9][10] x= A sin (at + į), y = B sin (bt) (1) The appearance of the figure is highly sensitive to the ratio a/b. For a ratio of 1, the figure is an ellipse, with special cases including circles (A = B, į = ʌ/2 radians) and lines (į = 0).
Veltech Multitech Dr.Rangarajan Dr.Sakunthala Engineering College, Avadi, Chennai (Sponsors)
International Conference on Science, Engineering and Management Research (ICSEMR 2014) 978-1-4799-7613-3/14/$31.00 ©2014 IEEE
IEEE-32331 Another simple Lissajous figure is the parabola (a/b = 2, į = ʌ/2). Other ratios produce more complicated curves, which are closed only if a/b is rational [9].
Fig.1. Lissajous Curve for a =3,b=4
The visual form of these curves is often suggestive of a three-dimensional knot, and indeed many kinds of knots, including those known as Lissajous knots, project to the plane as Lissajous figures[9][10]. III.
Fig.4. The modified Lissajous Curve for a=3,b=4 and
G
Fig.2. Lissajous Curve for a=4,b=5
THE MODIFIED LISSAJOUS EQUATION FOR CREATING HYPERCHAOTIC ARRAY
The said Lissajous Curve [9] equations have many interesting applications and it can be used to create enormous non-periodic numbers which always range within certain limit. It is known to us that in digital image processing an image of resolution MxN is nothing but a matrix of numbers within certain range. To create the digits for Hyper-chaos Sequences of size MxN the following is the modified equation: xij=m*sin(a*(i*j)mod 360 + G ) yij=n*sin(b*(i*j)mod 360)
3 / 8S Matrix Size 45x55
Now the X and Y components of the Lissajous Curve can be used to create a set of decimal digits forming Hyper-chaos decimal sequences. The following is the equation for the same Keyij=floor(Xij)x
+ floor(Yij)
(3)
where 1
