A Novel 1D Hybrid Chaotic Map-Based Image Compression and Encryption Using Compressed Sensing and Fibonacci-Lucas Transform

Tongfeng Zhang,Yide Ma,Min Yuan,Shouliang Li,Rongjun Ge

doi:10.1155/2016/7683687

Abstract

A one-dimensional (1D) hybrid chaotic system is constructed by three different 1D chaotic maps in parallel-then-cascade fashion. The proposed chaotic map has larger key space and exhibits better uniform distribution property in some parametric range compared with existing 1D chaotic map. Meanwhile, with the combination of compressive sensing (CS) and Fibonacci-Lucas transform (FLT), a novel image compression and encryption scheme is proposed with the advantages of the 1D hybrid chaotic map. The whole encryption procedure includes compression by compressed sensing (CS), scrambling with FLT, and diffusion after linear scaling. Bernoulli measurement matrix in CS is generated by the proposed 1D hybrid chaotic map due to its excellent uniform distribution. To enhance the security and complexity, transform kernel of FLT varies in each permutation round according to the generated chaotic sequences. Further, the key streams used in the diffusion process depend on the chaotic map as well as plain image, which could resist chosen plaintext attack (CPA). Experimental results and security analyses demonstrate the validity of our scheme in terms of high security and robustness against noise attack and cropping attack.

Highlights

With the fascinating development of computer networks and multimedia communications during the past decades, a great demand for secure image transmission is increased
Gao and Chen [8] presented a new image encryption scheme which employs an image total shuffling matrix to shuffle the positions of image pixels and uses a hyperchaotic system to confuse the relationship between the plain image and the cipher image
The experimental results of the four test images Lena, Cameraman, Baboon, and Boat are shown in Figure 5, where the first column, second column, and third column represent plain images, ciphered images, and decrypted images, respectively

Summary

Introduction

With the fascinating development of computer networks and multimedia communications during the past decades, a great demand for secure image transmission is increased. Chen et al [5] have proposed an image encryption algorithm which employs the three-dimensional cat map to shuffle the positions of the image pixels and uses another chaotic map to confuse the relationship between the encrypted and its original image. In [7], Pareek et al have proposed a new approach for image encryption based on chaotic Logistic maps. An external secret key of 80-bit length and two chaotic Logistic maps are employed. Gao and Chen [8] presented a new image encryption scheme which employs an image total shuffling matrix to shuffle the positions of image pixels and uses a hyperchaotic system to confuse the relationship between the plain image and the cipher image. Permutation and diffusion structure are usually adopted in the cryptosystems mentioned above, which suggests iterating the permutation and diffusion stage several rounds to earn good confusion and diffusion effect, whereas the permutation in those cryptosystem is almost the same in each round and independent of plain image

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Conclusion