Software and hardware realizations for different designs of chaos-based secret image sharing systems

Journal of Real-Time Image Processing (2024) 21:83 https://doi.org/10.1007/s11554-024-01450-8 RESEARCH Software and hardware realizations for different designs of chaos‑based secret image sharing systems Bishoy K. Sharobim1,4 Ahmed G. Radwan2,3 · Muhammad Hosam1 · Salwa K. Abd‑El‑Hafiz2 · Wafaa S. Sayed2 · Lobna A. Said1 · Received: 14 December 2023 / Accepted: 1 March 2024 / Published online: 6 May 2024 © The Author(s) 2024 Abstract Secret image sharing (SIS) conveys a secret image to mutually suspicious receivers by sending meaningless shares to the participants, and all shares must be present to recover the secret. This paper proposes and compares three systems for secret sharing, where a visual cryptography system is designed with a fast recovery scheme as the backbone for all systems. Then, an SIS system is introduced for sharing any type of image, where it improves security using the Lorenz chaotic system as the source of randomness and the generalized Arnold transform as a permutation module. The second SIS system further enhances security and robustness by utilizing SHA-256 and RSA cryptosystem. The presented architectures are implemented on a field programmable gate array (FPGA) to enhance computational efficiency and facilitate real-time processing. Detailed experimental results and comparisons between the software and hardware realizations are presented. Security analysis and comparisons with related literature are also introduced with good results, including statistical tests, differential attack measures, robustness tests against noise and crop attacks, key sensitivity tests, and performance analysis. Keywords Chaos · FPGA · Secret image sharing · SHA-256 · Visual secret sharing 1 Introduction Digital data have become essential to modern telecommunications, especially where vast images are stored and transferred. This increased the awareness of privacy and information security, and made protecting digital images a very important requirement. As a result, research efforts This work is supported by the Science, Technology, and Innovation Funding Authority (STIFA), Egypt, under grant number 45631. * Bishoy K. Sharobim 1 Nanoelectronics Integrated Systems Center (NISC), Nile University, Giza 12588, Egypt 2 Engineering Mathematics and Physics Department, Faculty of Engineering, Cairo University, Giza 12613, Egypt 3 School of Engineering and Applied Sciences, Nile University, Giza 12588, Egypt 4 Centre of Informatics Science, School of Information Technology and Computer Science, Nile University, Giza, 12588, Egypt increased in the information security fields such as cryptography, information hiding, and secret sharing (SS) [1]. SS is a relatively new idea introduced by Shamir in 1979, where a secret number is sent to a group of participants as n shares of the secret in a meaningless form [2]. Each share alone does not give any information about the secret number, while a group of k or more shares can reveal the secret, where k ≤ n. The idea was based on polynomial interpolation, and it is useful when the recipients are mutually suspicious or must cooperate. It is also used in cloud computing and distributed storage [1]. The idea of SS was improved to work for images in 1995 by Naor and Shamir, who introduced Visual Secret Sharing (VSS) [3]. In VSS, the recovery process is as easy as stacking the shares to recover the secret image using the human visual system. Stacking images is equivalent to the boolean OR operation between the images [4]. More secure systems were needed, which led to the introduction of Secret Image Sharing (SIS) by Thien and Lin in 2002 [5]. They used polynomial interpolation with shares of size 1/k of the secret image, but it needed more computation power compared to VSS. Vol.:(0123456789) 83 Page 2 of 16 The need for acceleration and easily integrating encryption into existing systems led to the use of field programmable gate arrays (FPGAs) as pivotal tools in the realms of both cryptographic operations and VSS. Their distinctive ability to be customized for specific tasks, coupled with their prowess in parallel processing, has propelled them to the forefront of secure data processing [6]. Security applications often favor FPGAs over general-purpose computers because of their low power consumption, high throughput, design adaptability, cost-effectiveness in development per unit, rapid processing speed, resilience to noise, and elevated security levels [7, 8]. This work presents a VSS system as a main block for SIS to ensure fast recovery. Then, two new lossless (n, n)-SIS systems are introduced for sharing binary, grayscale, or color images using the VSS system as the backbone. The first SIS system uses the Lorenz chaotic system as a source of randomness, utilizes the generalized Arnold transform to perform permutations, and has a long and sensitive system key. The second SIS system further enhances security and robustness using SHA-256 and RSA public-key cryptosystem. Software implementations and FPGA realizations, including all the used modules, are presented for the three systems. Security analysis is performed between the secret image and shares, and validated hardware results are presented. The experimental results show the systems’ effectiveness when deployed on FPGAs, exhibiting real-time processing capabilities and minimal resource utilization. Performance analysis and comparisons with recent approaches are also presented. The results demonstrate that the proposed enhanced system is a secure, robust and efficient SIS system. The next section of this paper briefly reviews the recent related approaches of secret sharing. Section 3 describes the background needed for the proposed systems. Section 4 describes the VSS system, and Sect. 5 describes how the VSS system is modified to create the first SIS system. Section 6 describes the second SIS system. Section 7 describes the hardware implementations for the three systems. Section 8 gives the results and comparisons, and Sect. 9 briefly gives the conclusions and future work. 2 Related work Most VSS systems use halftoning to convert all types of images into binary images and process them. Halftoning represents the image as dots, which affects the quality of the images [9]. Due to data loss when OR is used in recovery, XOR is used in recent literature to provide better quality for the recovered images [10]. There are different types of VSS introduced for different purposes, such as weighted VSS, which gives different weights for shares, and the total weight available in the recovery process defines the quality Journal of Real-Time Image Processing (2024) 21:83 of the recovered image [11]. Another type is the tagged shares, which adds information in each share to differentiate between shares by folding the share, for example, to show the tag [12]. Others added features like meaningful shares [13] or sharing multiple images [14]. As previuosly mentioned, the reco (...truncated)