Color image encryption based on discrete trinion Fourier transform and random-multiresolution singular value decompositi

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Color image encryption based on discrete trinion Fourier transform and random-multiresolution singular value decomposition Qijun Yao 1 & Zhuhong Shao 1 Rui Zeng 4 & Qingbin Tong 5

& Yuanyuan Shang

1,2

1

3

& Hui Ding & Xilin Liu &

Received: 20 July 2019 / Revised: 24 April 2020 / Accepted: 29 June 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020

Abstract

With more and more color images are spread and shared in the untrusted cloud server remotely over the open Internet, some private or confidential information may be contained, it is necessary to develop cryptosystem for these images to free from serious threats. This paper investigates a secure and robust cryptosystem for color image based on discrete trinion Fourier transform and random-multiresolution singular value decomposition. Firstly, a color image is represented into a trinion matrix by precoding and followed by block-wise discrete trinion Fourier transform. Then a mapping from trinion number domain to real number domain is implemented to facilitate random-multiresolution singular value decomposition. To further enhance the randomness of the transformed data, the scrambling based on chaotic sequence is applied to obtain the cipherimage. Experimental results have demonstrated that the proposed color image encryption algorithm is feasible. The adoption of logistic map ensures that the proposed cryptosystem attains high level security. Furthermore, the quality of the retrieved image is better than that of the algorithm based on single color channel processing separately and quaternion matrix based algorithms when it is decrypted correctly or under Gaussian noise and shear attacks. Moreover, employing a trinion matrix to represent a color image is more compact than using quaternion matrix. It would have potential applications in digital image protection. Keywords Color image encryption . Discrete trinion Fourier transform . Multiresolution singular value decomposition . Logistic map

* Zhuhong Shao [email protected] Extended author information available on the last page of the article

Multimedia Tools and Applications

1 Introduction Under the current era, large amounts of multimedia are being propagated over the open Internet at all times. According to the top 20 valuable Facebook statistics, there were over 2.38 billion monthly active users (MAU) worldwide as of March 31, 2019 and up to 300 million photos were uploaded per day (https://zephoria.com/top-15-valuable-facebookstatistics/). On the other hand, these big data stored in the untrusted cloud server remotely over the Internet may contain the private or confidential information, which leads the privacy and access control issues [27]. Adversary attacks to obtain the content of images for illegal usage, which imposes serious threats and motivates research in information security. Image encryption is a very useful technique that transforms a meaningful image into a noise-like data, which makes it difficult for illegal user to obtain image content without the granted keys. S