An improved digital logistic map and its application in image encryption
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An improved digital logistic map and its application in image encryption Hongyue Xiang 1 & Lingfeng Liu 1 Received: 31 March 2020 / Revised: 10 July 2020 / Accepted: 11 August 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract
Chaos maps are widely used in image encryption systems due to their intrinsic advantages such as extreme sensitivity to initial values., ergodicity and pseudo-randomness. 1D Logistic map has attracted the attention of researchers due to its simple structure and easy implementation, but also because of this, the map is easy to be affected by finite precision, resulting in dynamic degradation, at low precision, the sequence generated by this map not only enters a period quickly, but also has a shorter period. Thus, taking 1D Logistic map as an example, we proposed a method to suppress the dynamic degradation of digital chaotic systems by using parameter variables and state variables to influence each other, and using sine function as feedback function to destroy the state space. The simulation results show that the improved logistic mapping with the proposed method has better randomness and higher complexity than the original logistic mapping. To prove the practicability and applicability of the improved chaotic map, we design a new image encryption algorithm, which is suitable for both color image and grayscale image. The numerical results indicate that the proposed algorithm has high encryption efficiency, good resistance to various attacks and certain competitiveness with other encryption algorithms. Keywords Chaos . Digital chaotic map . Image encryption
1 Introduction With the development of information technology, a lot of information is being generated all the time. Senders and receivers of information do not want information to be accessed by unauthorized others. Thus, they encrypt information in ciphertext forms that are difficult for third parties to understand. Among all forms of information, image information is widely used because of its intuitive, visual and information-rich characteristics. It is regrettable that the
* Lingfeng Liu [email protected]
1
School of Software, Nanchang University, Nanchang 330029 Jiangxi, China
Multimedia Tools and Applications
traditional encryption methods, such as Advanced Encryption Standard (AES) and RivestShamir-Adleman (RSA), are not suitable for image encryption. Such methods are characterized by poor encryption effect, slow speed, and poor practicability when used for encrypting information with a large amount of data or strong correlation between adjacent pixels, such as images or videos. Fields such as medicine [28], aerospace, education, the military, and others all need to encrypt images. Therefore, an encryption algorithm suitable for images is needed to achieve good encryption effect, high efficiency, effectively reduce the correlation of adjacent pixels, and have the ability to resist various attacks. And numerous encryption algorithms have been proposed, including the DNA code [5, 23, 29, 33],
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