An image encryption scheme based on rotation matrix bit-level permutation and block diffusion

doi:10.1016/j.cnsns.2013.06.031

Communications in Nonlinear Science and Numerical Simulation

Volume 19, Issue 1, January 2014, Pages 74-82

https://doi.org/10.1016/j.cnsns.2013.06.031 Get rights and content

Highlights

•
Rotation matrix bit-level permutation and block diffusion are used to encrypt image.
•
Confusion operation relies on plaintext against known/chosen-plaintext attacks.
•
The scheme is robust against noise and applies to communication on noisy channels.
•
The proposed scheme is suitable for running in a parallel computing environment.

Abstract

This paper proposes a novel image encryption scheme based on rotation matrix bit-level permutation and block diffusion. Firstly, divide plain image into non-overlapping 8 × 8 pixels blocks with a random matrix, then transform each block into an 8 × 8 × 8 three-dimensional (3-D) binary matrix, which has six directions just as a cube. Permutation is performed by multiplying the 3-D matrix by the rotation matrix that relies on plain image according to different direction. Secondly, use block diffusion to further change the statistical characteristics of the image after confusion. Experiment results and analysis show that the scheme can not only achieve a satisfactory security performance, but also have the suitability for a parallel mode and the robustness against noise in communication system.

Introduction

In recent years, the transmission of digital images over communication media has developed greatly. The security of multimedia data is receiving more and more attention due to the widespread transmission over various communication networks. It has been noticed that image encryption is different from traditional text encryption due to some inherent features of the image, such as bulk data capacity, high redundancy, and strong correlation among adjacent pixels. To meet a great demand for secure image transmission over networks, a variety of encryption schemes have been proposed [1], [2], [3], [4], [5], [6], [7], [8], [9].

Chaotic cryptosystems have been studied extensively due to its ergodicity, pseudo-randomness and sensitivity to initial conditions and control parameters, which are close to confusion and diffusion in cryptography. These properties make chaotic systems a potential choice for constructing cryptosystems [3], [4], [5], [6], [7], [8], [9], [10]. According to the difference of the basic permutation unit, the existing chaotic image cryptosystems can be classified into two groups. In the first group, which most the existing cryptosystems belong to, the basic permutation unit is each pixel. While in the second group, a pixel is further divided into 8 bits, and each bit is chosen as the basic permutation unit. Since each pixel bit contains percentage of the pixel information, the confusion performance at the bit-level is quite different. In [11], Chen et al. designed a new typical bit-level system called Two-Dimensional Circulation Encryption Algorithm (TDCEA). Authors define two bit-circulation functions for one-dimensional binary array transformation and exploit a chaotic system to control them. Then, each eight 8-bit data element is regarded as a set and fed into an 8 × 8 binary matrix being transformed on each row and each column of the matrix by these two bit-circulation functions. Unfortunately, TDCEA was cryptanalyzed in [12], [13] due to its permutation-only operation which is unsafe under a known/chosen-plaintext attack [14], [15]. Because of this vulnerability, Zhu et al proposed an image cryptosystem with the architecture of confusion and diffusion employing the Arnold cat map for bit-level permutation and the logistic map for diffusion (BLP) in [16]. In [17], lightweight bit-level confusion and cascade cross circular diffusion were used to encrypt image. However, in our opinion, to ensure the transmission of digital images, besides the security of a cryptosystem, the robustness of cipher image against noise or other external disturbances is also important.

Based on the above analysis, a novel image encryption scheme with confusion-diffusion is proposed in this paper, where rotation matrix is used in its confusion phase. Meanwhile, block diffusion is adopted for secure communication on noisy channels.

The rest of the paper is organized as follows: In the next section, the concept of the rotation matrix is introduced simply. Then, the proposed image cryptosystem is described in Section 3. Performance and security analysis are reported in Section 4. Finally, main conclusions are given in Section 5.

Section snippets

Rotation matrix

In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space [18]. For example, the matrix $(\begin{matrix} \cos θ & - \sin θ \\ \sin θ & \cos θ \end{matrix})$ rotates points in the xy-Cartesian plane counterclockwise through an angle θ about the origin of the Cartesian coordinate system. Rotation matrices are square matrices, with real entries. More specifically, they can be characterized as orthogonal matrices with determinant ±1: $R^{T} = R^{- 1}, \det (R) = \pm 1 .$

The set of all such matrices of size n forms a group,

The proposed cryptosystem

As we know in cryptography, confusion and diffusion are two desired properties of a secure cipher which were identified by Shannon [19], so the general image encryption algorithm is composed of confusion-diffusion.

Experimental results and performance analysis

In this section, the experimental results and performance analysis on the proposed image encryption scheme are discussed. For comparison, we implement ‘Lena’ image encryption schemes based on ETDCEA and BLP which were firstly proposed as a comparable bit-level encryption schemes in [11], [16]. We have used Matlab 7.10.0 (R2010a) to run encryption and decryption programs in a personal computer with a Intel(R) Celeron(R) CPU 2.7 GHz, 2 GB memory and 250 GB hard-disk capacity, and the operation

Conclusion

In this paper, an image encryption scheme based on rotation matrix bit-level permutation and block diffusion is proposed. Experiment results and analysis show that the proposed scheme has a satisfactory security performance. Moreover, unlike previous algorithms, it is suitable for running in a parallel and noisy environment.

Acknowledgement

The work was funded by the Natural Science Foundation Project of CQ CSTC (Grant no. 2011jjjq40001).

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An image encryption scheme based on rotation matrix bit-level permutation and block diffusion

Highlights

Abstract

Introduction

Section snippets

Rotation matrix

The proposed cryptosystem

Experimental results and performance analysis

Conclusion

Acknowledgement

Commun Nonlinear Sci Numer Simulat

Commun Nonlinear Sci Numer Simulat

Comput Math Appl

Commun Nonlinear Sci Numer Simulat

Chaos Solitons Fract

Commun Nonlinear Sci Numer Simulat

Opt Commun

Phys Lett A

Inform Sci

Signal Process-Image

Signal Process