1. Introduction
The rapid development of the internet has brought convenience to daily life, but privacy leakage incidents occur frequently. The issue of security has garnered extensive attention. Optical encryption, compressed sensing (CS), and network learning are effective means of protecting image security [
1,
2,
3]. In 1995, Refregier and Javidi introduced the double random algorithm [
4], which utilizes four optical processors and has garnered significant attention. To enhance security and increase the range of possible keys, the DRPE technique has been expanded into additional domains. However, it needs to be pointed out that these double-random phase-encoding (DRPE)-based encryption systems are linear systems [
4,
5,
6,
7], and these encryption methods are all types of symmetrical encryption systems. Due to the inherently linear nature of mathematics and optical transformation, the vulnerability of various encryption schemes to plaintext assaults is rather high [
8].
Consequently, many nonlinear optical image encryption systems that can enhance security and resist plaintext attacks have been recently put forward [
9,
10,
11,
12]. An image encryption technique based on a chaotic system and transform was presented by Zhou et al. [
9]. FRMTs of varying orders alter distinct annular areas of the original image, and this can be used to overcome the disadvantage of using linear transforms and having large key space. Since then, both signal processing and encryption have involved the more flexible linear canonical transform (LCT), which has three free parameters [
13,
14]. On the basis of the LCT, Wei et al. proposed the random discrete linear regular transform (RDLCT) [
13]. The randomness of the RDLCT’s output phase and magnitude can strengthen an encryption system’s security. Recent designs have included further techniques based on the 2D LCT [
14,
15]. The 2D LCT has the natural advantage of multiple parameters, which can expand the key space and improve the security of an algorithm.
Chaos-based encryption schemes have frequently been utilized to further increase security [
16,
17,
18,
19,
20]. This is because of their significant sensitivity to beginning circumstances, good pseudo-randomness, and ergodicity. In 1998, Fridrich proposed the classic framework of image encryption [
16]. An image encryption technique based on spatiotemporal chaos was created using the framework mentioned above [
17]. However, both of them were proven to be unable to resist chosen plaintext attacks [
19,
21]. Image encryption systems use an increasing amount of high-dimensional chaos due to their increasingly complicated dynamic nature, and they are more sensitive to initial values and higher security than to low-dimensional chaos [
22]. Saljoughi presented an encryption algorithm using three-dimensional logistic maps [
23]. A scale-invariant digital image encryption technique based on chaotic 3D maps was introduced by Hamed et al. [
24], and it had excellent security capacity and high efficiency. Additionally, a number of hyper-chaotic systems were incorporated to enhance security [
25,
26,
27]. To sum up, hyper-chaotic systems provide sequences with high pseudo-randomness that are ideal for encryption.
Meanwhile, CS is widely used because it allows data to be compressed directly at the time of collection, rather than being transmitted or stored after collection [
28,
29,
30]. This can reduce the amount of data transferred and stored, increasing efficiency. At the same time, the nature of random measurements makes it more difficult to reconstruct information from raw data, which can increase the strength of encryption. Measurement matrices are typically thought of as the key in compressive-sensing-based algorithms [
31,
32,
33]. However, the most popular approach generates an image-encrypted measurement matrix using a chaotic system [
31,
32,
34,
35,
36]. Zhou developed an approach that employed two measurement matrices under the control of a logistic map to compress and encrypt pictures [
31]. Nevertheless, the aforementioned techniques’ secret keys were unrelated to plaintext pictures, making them susceptible to specific plaintext assaults. Some recent methods can reduce these problems. The work in [
37] introduced parallel compressive sensing (PCS), which was resistant to specific plaintext assaults. Above all, we created a unique image encryption technique based on CS and 2D LCT that could withstand typical assaults and had a huge key space.
In this study, we introduced a unique image encryption technique based on CS and the 2D LCT to further increase security. First, CS offers trustworthy and effective encryption and compression services, and a plaintext image controls the CS measurement matrix’s construction parameters. Second, to prevent certain plaintext assaults, the hyper-chaotic system’s initial values were generated by using the SHA 256 value of the original image. Third, the 2D LCT had six free parameters, which greatly enhanced the key space. The suggested scheme’s security against various assaults was demonstrated by the findings in security analysis and testing.
The following is the format for the remainder of this paper:
Section 2 presents a few foundational theories.
Section 3 provides a detailed explanation of the recommended image encryption method. A number of presentations and simulations are presented in
Section 4. In
Section 5, a succinct summary of the findings is provided.
5. Conclusions
In this study, we illustrated a novel approach to image encryption in 2D LCT domains by utilizing CS, Lorenz’s hyper-chaotic system, and chaotic random phase encoding. SHA-256 helps strengthen defenses against specific plaintext attacks. The measurement matrix in CS is connected to the total of an image’s pixels, which may further increase the sensitivity to plaintext. CS can also efficiently minimize the size of encrypted images. Two positive Lyapunov exponents and a vast parameter space characterize Lorenz’s hyper-chaotic system. It is, therefore, ideal for applications involving image encryption. Additionally, the image is re-encrypted using the 2D LCT based on chaotic random phase masks. The suggested approach has a wide key space and high key sensitivity, and it is especially sensitive to plaintext, according to the simulation findings and security assessments. As such, it is resistant to well-known attacks, such as chosen-plaintext, known-plaintext, and brute-force attacks.