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Block Ciphers
Published in Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone, Handbook of Applied Cryptography, 2018
Alfred J. Menezes, Paul C. van Oorschot, Scott A. Vanstone
7.52 Example (Hill cipher – historical) An n-gram substitution may be defined using an invertible n × n matrix A = aij as the key to map an n-character plaintext m1 … mn to a ciphertext n-gram ci=∑j=1naijmj, i = 1, …, n. Decryption involves using A−1. Here characters A–Z, for example, are associated with integers 0–25. This polygram substitution cipher is a linear transformation, and falls under known-plaintext attack.
A novel image encryption using random matrix affine cipher and the chaotic maps
Published in Journal of Modern Optics, 2021
Parveiz Nazir Lone, Deep Singh, Umar Hussain Mir
In order to provide an efficient and secure cryptosystem, it becomes natural from the last decade to employ the chaotic maps. Due to the intrinsic characteristic of chaos map including non-periodicity, initial condition, ergodicity, highly random like behaviour, etc., highlighted its use in image encryption. In [14], authors proposed multi-layer security to image data rely on the logistic map with RP2DFRFT (reality preserving two dimensional discrete fractional Fourier transform) based on time domain as well as frequency domain. The authors performed analysis but no attempt has been made against the differential attacks. Similar is the case in [24], authors combined Arnold transform with Hill cipher technique to encrypt image data over domain for the secure transmission of information. A first approach to color image encryption by RMAC technique associated with the discrete wavelet transform is proposed by [25], where the minimum loss of information is observed during reconstruction, and the analysis is only based on MSE (mean square error) not give a clear indication for the system to be secure. In [23], authors presented a secure encryption method using advanced Hill cipher with a lossless compression technique supported by discrete wavelet transform for the security of RGB images. The authors in [12] proposed a novel scheme of encryption using the Galois field and coupled hyper chaotic system to confuse and diffuse the pixel information by polynomial addition and multiplication operated over the Galois field. Recently in [5], a new encryption method is proposed combining DNA encoding and chaotic system where the diffusion is achieved by the XOR operation and pixel permutation is done through the shift algorithm taking inputs from a mandelbrot set. Further in [11], authors took help of chaos game theory to generate pseudo random number generators (PRNG) for the encryption technique. In addition, the use of Lyapunov exponent and bifurcation diagram analysis guarantees the chaotic characteristic and can be used as a secure PRNG for cryptographic techniques. Besides in the medical field, there is also an important need for encryption to transmit confidential images of the patients over the public channels. In [6], authors have shown the use of medical image encryption in e-health, telemedicine applications, etc., by using DNA approach and dual hyper chaos technique to provide high security for digital medical images. Optical encryption techniques for security of image data have been extensively researched for data communication [20–22]. The method [22] made use of two series of keys, one for fractional order and other for wavelet packet filter to encrypt the image information. In optical domains, encoding methods have shown a good potential for the protection of image data, with a large degree of freedom for phase, wavelength, amplitude, and polarization.