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Open AccessArticle

A Novel Image Encryption Scheme Based on Collatz Conjecture

Telecommunications Engineering, Universidad Militar Nueva Granada, Carrera 11 No. 101-80, Bogotá 110111, Colombia
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Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Entropy 2018, 20(12), 901; https://doi.org/10.3390/e20120901
Received: 24 October 2018 / Revised: 11 November 2018 / Accepted: 21 November 2018 / Published: 25 November 2018
(This article belongs to the Special Issue Information Theory Applications in Signal Processing)
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. View Full-Text
Keywords: image encryption; Collatz conjecture; ciphered audio; scrambling; diffusion image encryption; Collatz conjecture; ciphered audio; scrambling; diffusion
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Ballesteros, D.M.; Peña, J.; Renza, D. A Novel Image Encryption Scheme Based on Collatz Conjecture. Entropy 2018, 20, 901.

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