Abstract
The chapter intends to propose a hybrid cryptosystem based on a chaotic map and a fractal function. The sequential order of process execution provides a computationally less expensive and simple approach that still designed a secure cryptosystem. A one-dimensional Ricker map and its modified form are employed to initially shuffle the image pixels twice, and also a pseudo-random sequence is generated using both maps. The algorithm implemented a sequence of pixel confusion-diffusion steps using the image rotation and a transcendental anti-Mandelbrot fractal function (TAMFF) and its Mann-iterated fractal function (Sup-TAMFF). Finally, the pixel value of an image obtained in the last step and the recent two pixels of the encrypted image is XORed with the corresponding pseudo-random matrix value to get the cipher image. Subsequently, various performance tests are conducted to verify the suitability of the given method to be used in real-world information transmission.
TopIntroduction
Today’s internet world is glorified with the use of vast digital media communication, resulting in the transmission of enormous data over the network. An organization having a growing network of interconnected devices strengthen the protection requirement of its cybersecurity assets. They must be aware of the cybersecurity laws and regulations to formalize the applicable security standards to secure and protect their organizational data. Failing to which, could arise the threatening situation for the association.
With the advancement in the internet world, digital media transmission has increased tremendously. It can be in the form of text, images, audio, or video. The data transmitted over the channel is expected to be received securely on the receiver side. The number of cyber threats challenges to create a credible secure system to protect the sensitive and confidential information produced in various fields like in the military, medical, financial and many more. There have been many conventional ciphers like Data Encryption Standard (DES) (Smid & Branstad, 1988), International Data Encryption Algorithm (IDEA) (Lai & Massey, 1991), RSA algorithm (Rivest, Shamir, & Adleman, n.d.), Advanced Encryption Standard (AES) (FIPS 197, Advanced Encryption Standard (AES), n.d.), etc., provide high data security measure. However, the above-mentioned algorithms provide effective results to encrypt text data but are expensive and time consuming for image encryption. Due to the inherent image features such as large data volume, strong pixels correlation, high redundancy, etc., need a high computational efficient and time-sensitive image encryption algorithm.
In the past decade, a dynamical chaotic system was studied extensively by the researchers. The non-linear complex chaotic map has ergodic property, unpredictable trajectories, pseudo-randomness, sensitiveness and dependence on its initial condition. There will be completely a different chaotic sequence for a minute changed map’s initial parameter which implies its great importance in the cryptography field. These characteristics make the chaotic map advantageous in many disciplines such as mathematics, physics, computer science, and engineering. A competent image cryptosystem generally designed using confusion and diffusion processes. The confusion property or pixel permutation is achieved by the random pixel shuffling within the image to minimize the correlation between the adjacent pixels. It helps to enhance the computational complexity of a chosen-plaintext attack. The diffusion property or pixel replacement is obtained by changing pixel values in such a manner that by making a small change in a plain image effect in almost all pixels in the cipher image. One can design a cryptosystem by applying single or multiple rounds of confusion/diffusion process depending upon the system requirement.
The chapter discusses a cryptosystem which combines the complex features of the chaotic map and a fractal function. A fractal image is the graphical representation of a complex function at the local and the global irregularity level (Pickover, 2001). It is generated by iterating a mathematical function for a pre-determined number of times. Because of the non-linear behavior and fractional dimension, the fractal function has been popularized to solve complex mathematical problems. Fractal functions can be visualized in the whole universe in different forms which further help to investigate the things on the practical ground. Few examples include the Coast of Britain, Alzheimer's brain, special effects in shows such as Star Trek and Star Wars, a biological pattern like growth patterns of bacteria and so on (Addison, 1997). Unlimited resources are available to generate fractal images including ChaosPro, Fractint, Fraqtive, Ultra Fractal, etc.
Key Terms in this Chapter
Cybersecurity: Cybersecurity is an act to protect data, devices, applications, servers, network from the malicious attack through various tools and techniques. The process also ensures the confidentiality, integrity, availability, and non-repudiation of the content.
Visual Cryptography: A visual cryptography technique works by splitting the secret image into two or more non-identical meaningless images. The image reconstruction is possible only in case of all images stacked together.
Chaotic Cryptography: A system utilizing the randomness, unpredictable behavior, and sensitivity on the initial condition of the chaotic function to construct a robust cryptosystem.
Cryptanalysis: Cryptanalysis refers to the study of the cryptosystem or ciphertext to crack the confidentiality of the underlying information and try to gain unauthorized access to the content.
Lightweight Cryptography: A lightweight cryptography refers to a cryptosystem with low computational cost and suitable for high-constrained devices. The concept was initiated by the National Institute of Standards and Technology (NIST) to develop a cryptographic algorithm that can work with small electronic devices in the IoT environment.
Cryptosystem: A cryptosystem includes a complete process of key generation, encryption, and decryption techniques for secure data communication over the insecure channel.
Fractal Cryptography: A fractal cryptography is a technique in which either a single process (key generation/encryption and decryption) or multiple processes designed by using the fractal function.