Plaintext-related image encryption algorithm based on perceptron-like network

doi:10.1016/j.ins.2020.03.054

Information Sciences

Volume 526, July 2020, Pages 180-202

https://doi.org/10.1016/j.ins.2020.03.054 Get rights and content

Highlights

•
Proposed a perceptron-like network based on integer domain to diffuse image information through its weights’ memory function.
•
Introduced the perceptron-like network as the core of image cryptosystem, breaking through the traditional image encryption structure and constructing a new fast structure without round modules.
•
The proposed image cryptosystem is plaintext-related one with strong secret key sensitivity, equivalent key sensitivity, plain-image sensitivity and cipher-image sensitivity.
•
The pseudo-random numbers generated directly by the chaotic system is half the size of the image.

Abstract

A perceptron-like network based on integer domain was proposed, and then a new image cryptosystem based on the network was proposed in this paper. Different from the structure of classical image cryptosystem, the proposed image cryptosystem employed the perceptron-like network to achieve the diffusion of image information. It firstly generated the pseudo-random key streams from the secret key through chaotic system and S-box of AES. Then it obscured the sequence of plain image by XOR operation. Next, it used two perceptron-like networks to fulfill the information memory and diffusion of the image sequence. Finally, it obscured the diffused sequence using the equivalent keys to obtain the cipher image sequence. Performance analysis and comparison analysis show that the proposed image cryptosystem has the advantages of fast processing speed, strong system sensitivity and high security, and can be applied to the actual image communications.

Introduction

With the development of image information acquisition and processing technology, image information security has attracted wide attention. It has become a hot topic in information security and cryptology [3,5,42]. It is a well-accepted fact that image encryption is the most effective means of image information security [1,9,20]. At present, image information security is divided into two main branches. One is optical image encryption realized by optical technology, which encrypts images in the process of image acquisition. Its core technology is optical Fourier transform [29]. The other is digital image encryption realized by digital computer, which encrypts images in the process of image storage. Its core methods are called as confusion and diffusion [27,47]. In both fields, chaotic systems are frequently used to generate pseudo-random number sequences for encryption [28,49,50].

In the field of digital image cryptography, there are also two branches according to different research emphases. One is the image encryption technology which preserves the visibility of carrier images, such as hashing technology [30,37], visible or invisible image watermarking technologies [35], and image hiding technology [16,26], in order to achieve image integrity authentication or copyright authentication. The other is the image encryption technology for secure image storage or transmission, including cover encryption which encrypts the plain images into noise-like images [13,25] and deceptive encryption which encrypts the plain images into other visible images [43]. Currently, digital image cryptography has been greatly developed. Meanwhile, it is facing enormous challenges. As to the cover encryption, there are four main challenges in this field as follows.

(i)
Some scholars from chaos research have put forward many excellent pseudo-random number generating algorithms and proved that their pseudo-random numbers have good statistical characteristics. They applied these pseudo-random numbers to image encryption and proposed some simple image encryption schemes [8,31]. These schemes are basically equivalent to the one-time-pad system with little practical value [15,38]. Some schemes even used the information of plain images, such as the hash code of plain images, as the secret key directly [2,36]. These schemes are also one-time-pad systems and violate the basic principle of symmetric cryptography, which possess little theoretical and practical research value. Obviously, good pseudo-random sequences alone cannot guarantee the security of encryption schemes. How to combine good pseudo-random numbers with well-designed encryption algorithms to produce the image cryptosystems with sensitive equivalent keys is the first challenge of current image cryptography [21].
(ii)
A large number of image encryption schemes based on DNA coding have been proposed [33,39,40]. The four codes A, T, C and G of DNA are encoded by two-tuple binary numbers, then according to the rule of binary number system the addition/subtraction and XOR rules of DNA codes are designed. These image cryptosystems still used binary number image encryption algorithms in essence, and the operations of DNA codes can be substituted by binary operations in the encryption/decryption process without affecting the security of the scheme. Moreover, the usage of DNA coding cannot enhance the security of image cryptosystems. These image cryptosystems are vulnerable to chosen/known plaintext attacks [7,22,34]. With the help of DNA coding for image encryption, how to really get rid of the influence of binary arithmetic and realize the secure and fast image encryption algorithm is the second challenge of current image cryptography.
(iii)
Some image encryption algorithms based on quantum computing have been proposed [10,12,17], which may be the future direction of cryptography. With the help of quantum devices, some simple chaotic systems (such as Logistic map, Henon map and Arnold map) have been implemented, and some simple scrambling operations have been designed out. The core of the security of these schemes is based on the non-cloning property of quantum states. It is not the encryption algorithm itself that can resist various passive attacks, but the quantum communication itself that guarantees the security of quantum image information. At present, quantum replication has reached a very high level. In the near future, image encryption algorithm based on quantum computing should consider their ability to resist passive attacks such as chosen/known plaintext attacks. How to achieve good diffusion effect in image cryptosystem based on quantum computing is the third challenge of current image cryptography.
(iv)
Most of the existing image cryptosystems are based on confusion and diffusion technologies [4,23]. The confusion technology is to scramble the positions of pixels in the image without changing the pixels’ values. It has been proved that the image cryptosystem with confusion technology only is unsafe [11,14]. The diffusion technology is basically add-and-modulus operation or XOR operation which is carried out to spread the information of any pixel in the image to the whole cipher image. The image cryptosystems based on ‘confusion-diffusion’ technology also exposes some shortcomings. Firstly, they need a large number of pseudo-random numbers. However, the pseudo-random numbers are precious resource since it is difficult to produce a great quantity of pseudo-random numbers with good statistical characteristics in the digital computer. Secondly, the speed of encryption and the security of encryption are a pair of contradictions in these cryptosystems. When the number of rounds of the scheme grows larger, the security of encryption is enhanced with slower encryption speed as tradeoff; conversely, when the number of rounds is small, the speed of encryption is fast, but the security of encryption is significantly reduced. Many image cryptosystems are slower than AES in CBC mode applied to image encryption [44]. How to break through the existing image encryption structure and design the new fast and secure image cryptosystem is the fourth challenge of current image cryptography.

The work described in this paper focuses on the fourth challenge. This work abandoned the classical image encryption structure based on ‘confusion-diffusion’, and suggested an image encryption system based on perceptron-like network. The main innovations of this work are as follows: (i) A perceptron-like network based on integer domain is proposed to diffuse image information through its weights’ memory function; (ii) The perceptron-like network is introduced as the core of image cryptosystem, breaking through the traditional image encryption structure and constructing a new fast structure without round module; (iii) The proposed image cryptosystem is plaintext-related one with strong secret key sensitivity, equivalent key sensitivity, plain-image sensitivity and cipher-image sensitivity. The rest of this paper is organized as follows: Section 2 introduces the perceptron-like network based on integer domain; Section 3 details the proposed image cryptosystem based on perceptron-like network; Section 4 gives representative simulation results; Section 5 analyzes the security performance of proposed cryptosystem in detail; Section 6 makes a theoretical analysis on the system sensitivity; Section 7 makes a comparative analysis; Section 8 summarizes the full text.

Section snippets

Perceptron-like network

The M-P model (McCulloch-Pitts model) [18] of neurons simulating biological nervous system is shown in Fig. 1. A neuron is a processing unit (PU) of the neural network.

In Fig. 1, x₁,x₂,…,x_n are the inputs of the neuron, y is the output of the neuron, w₁,w₂,…,w_n are the weights, b is the threshold, and f is the activation function. According to Fig. 1, the output y is $y = f (\sum_{i = 1}^{n} w_{i} x_{i} - b)$

A three-layer perceptron network with multiple inputs and single output is shown in Fig. 2.

In Fig. 2, the inputs x₁

Image cryptosystem

The traditional image encryption scheme mainly has the ‘confusion-diffusion’ structure, as shown in Fig. 5.

In the scheme shown in Fig. 5, the inputs are the plain image and the secret key, and the output is the cipher image. The chaotic system is employed to generate the key streams, and the encryption process includes several rounds of confusion and diffusion.

However, the structure of proposed image encryption scheme is completely different from that of traditional system shown in Fig. 5. The

Simulation

The computer used is configured with Microsoft Windows 10 Home (64-bit), Intel Core [email protected] GHz, 16GB DDR4@2666 MHz memory. The simulated program is designed in C# language under the integrated development environment –– Microsoft Visual Studio Community 2019 V16.2.4 with Microsoft .NET Framework V4.8. Without loss of generality, the simulation uses a random secret key K = ‘315D3F0C7089352A952AD5BB3972AF4E1DBA42E 8377FC17F5A8D6A57DBCE863ED80A4F7EE3CBDE0CC4C93A41CE6BBFC3857B5685835C

Security analysis

This section starts with the discussion of encryption/decryption speed. Then under such encryption/decryption speed, it will discuss the size of key space and the system's ability to resist exhaustive attacks. Next, the statistical characteristics of cipher images are analyzed. And finally, the system sensitivities –– key sensitivity, equivalent key sensitivity, plaintext sensitivity, and cipher-text sensitivity –– are analyzed. These performance analyses will confirm that the proposed image

Theoretical analysis of system sensitivity

In Section 5.4, the simulation results show that the proposed image cryptosystem is sensitive to the secret key, equivalent key, plain images and cipher images. However, the simulation tests cannot exhaust all the cases, and have some limitations. This section will prove in theoretical that the proposed image cryptosystem is sensitive.

Comparison analysis

Generally, the noise-like cipher images produced by any image cryptosystem possess good statistical characteristics, such as flat histogram, little correlation, and large information entropy [1,9,20]. So the important indexes for comparing the performance of different image cryptosystems are their system sensitivity and encryption/decryption speed. Those image cryptosystems with faster encryption/decryption speed are better under the condition that they all have the excellent system

Conclusion

The proposed image cryptosystem employs chaotic system to generate the pseudo-random sequence with half the size of plain image for image encryption. Unlike traditional image cryptosystems with the ‘confusion-diffusion’ structure, the proposed image cryptosystem adopts the perceptron-like network as the core to realize the information memory and spread of plain images. The perceptron-like network is a one-time-learning neural network based on integer domain. Its feedback learning makes the

CRediT authorship contribution statement

Yong Zhang: Conceptualization, Methodology, Software, Writing - original draft. Aiguo Chen: Project administration, Formal analysis. Yingjun Tang: Software, Validation, Visualization. Jianwu Dang: Methodology, Writing - review & editing. Guoping Wang: Conceptualization, Supervision.

Declaration of Competing Interest

This manuscript is our original work and has not been published nor has it been submitted simultaneously elsewhere. All authors have checked the manuscript and have agreed to the submission.

Acknowledgment

This work was supported by National Natural Science Foundation of China [Nos. 61762043 and 61562035], Natural Science Foundation of Jiangxi Province [No. 20192BAB207022], and Science and Technology Research Project of Jiangxi Provincial Department of Education [No. GJJ190249].

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Plaintext-related image encryption algorithm based on perceptron-like network

Highlights

Abstract

Introduction

Section snippets

Perceptron-like network

Image cryptosystem

Simulation

Security analysis

Theoretical analysis of system sensitivity

Comparison analysis

Conclusion

CRediT authorship contribution statement

Declaration of Competing Interest

Acknowledgment

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Chaos Solitons Fractals

Inf. Sci.

Inf. Sci.

Signal Process.

Signal Process. Image Commun.

Comput. Biol. Med.

Signal Process.

Appl. Soft Comput.

Inf. Sci.

Inf. Sci.

Inf. Sci.

Inf. Sci.

Opt. Lasers Eng.

A novel image encryption scheme based on DNA sequence operations and chaotic systems

Neural Comput. Appl.

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Nonlinear Dyn.

Impulsive synchronization of reaction-diffusion neural networks with mixed delays and its application to image encryption

IEEE Trans. Neural Netw. Learn. Syst.

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Cryptanalysis and improvement of the hyper-chaotic image encryption scheme based on DNA encoding and scrambling

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