A Novel Image Encryption Scheme Based on Collatz Conjecture

Abstract

Image encryption methods aim to protect content privacy. Typically, they encompass scrambling and diffusion. Every pixel of the image is permuted (scrambling) and its value is transformed according to a key (diffusion). Although several methods have been proposed in the literature, some of them have been cryptanalyzed. In this paper, we present a novel method that deviates the traditional schemes. We use variable length codes based on Collatz conjecture for transforming the content of the image into non-intelligible audio; therefore, scrambling and diffusion processes are performed simultaneously in a non-linear way. With our method, different ciphered audio is obtained every time, and it depends exclusively on the selected key (the size of the key space equal to 8 . 57 × 10 506 ). Several tests were performed in order to analyze randomness of the ciphered audio signals and the sensitivity of the key. Firstly, it was found that entropy and the level of disorder of ciphered audio signals are very close to the maximum value of randomness. Secondly, fractal behavior was detected into scatter plots of adjacent samples, altering completely the behavior of natural images. Finally, if the key was slightly modified, the image could not be recovered. With the above results, it was concluded that our method is very useful in image privacy protection applications.

A Dynamic DNA Color Image Encryption Method Based on SHA-512

“…Aashiq et al [ 14 ] presented an image encryption method based on chaotic attractors; on the frequency domain they used the integer wavelet transform to encrypt the image while on the spatial domain they used the DNA sequence. Ballesteros et al [ 15 ] presented a novel method that deviated from traditional schemes, in which variable-length codes based on the Collatz conjecture were used to transform the content of the image into unintelligible audio. Moreover, Ouyang et al [ 16 ] proposed a color image encryption method using the memristive hyperchaotic system and DNA encryption, and Zhu et al [ 17 ] reported an image encryption algorithm based on a matrix of Kronecker products and DNA operations over finite fields.…”

An Image Encryption Scheme Based on Block Scrambling, Modified Zigzag Transformation and Key Generation Using Enhanced Logistic—Tent Map

“…Previously, various encryption techniques that are dependent on chaos have been examined and broadly contemplated. Image encryption algorithms have been constructed based on a logistic and two-dimensional (2D) chaotic economic map [ 6 ], variable length codes that are based on Collatz conjecture [ 7 ], 2D discrete wavelet transform and Arnold mapping [ 8 ], logistic mapped convolution and cellular automata [ 9 ], cat map [ 10 ], 2D Chebyshev-sine map [ 11 ], 2D Sine Logistic modulation map [ 12 ], one-dimensional (1D) delay with linearly coupled Logistic chaotic map [ 13 ], a hyper-chaotic system that combines Dynamic Filtering, DNA computing, and Latin Cubes (DFDLC) [ 14 ], Arnold Transform followed by Qubit Random Rotation [ 15 ], 2D Baker’s map with diffusion process based on XORing [ 16 ], ant colony optimization [ 17 ], Chebyshev Map followed by Rotation Equation [ 18 ], an algorithm combining Julia fractal and Hilbert curve [ 19 ], four-dimensional (4D) hyper-chaotic nonlinear Rabinovich system [ 20 ], Josephus traversing and mixed chaotic map [ 21 ], 2D logistic-modulated-sine-coupling-logistic chaotic map [ 22 ], multiple permutation of pixels followed by the 2D Chebyshev function [ 23 ], chaos map with pixel permutation [ 24 ], improved hyperchaotic sequences [ 25 ], high-dimension Lorenz chaotic system with a perceptron model [ 26 ], rotation matrix bit-level permutation with block diffusion [ 27 ], and discrete Chirikov map with chaos-based fractional random transform [ 28 ].…”

Distributed Steganography in PDF Files—Secrets Hidden in Modified Pages

“…Concealing data in an inconspicuous way is called steganography [ 1 ] and is mainly used to communicate secretly. This attribute differentiates it from cryptography [ 2 , 3 ]—when information is encrypted, it cannot be read, but everyone knows of its existence. In steganography, the primary goal is undetectability of secret message.…”