The rapid proliferation of digital communication platforms and the growing dependence on cloud-based storage have led to an unprecedented rise in the transmission of visual information. Images constitute a substantial portion of exchanged data in fields such as medical diagnostics, remote monitoring, legal documentation, surveillance and multimedia services. Owing to their rich structure and high redundancy, image datasets are inherently vulnerable to unauthorized access, interception and manipulation. Ensuring confidentiality, authenticity and robust protection against tampering has therefore become a critical requirement in modern communication systems. While conventional cryptographic standards provide good security for general data, they are not always a suitable fit for image data, which often requires special processing strategies to consider spatial correlations, large volumes and real time constraints. Several classical encryption algorithms such as AES [1] and DES [2] have been widely used for digital information security. However, when they are applied directly to images, these schemes often suffer from increased computational overhead, the lack of diffusion behaviour and vulnerability to certain types of statistical attack, especially when dealing with structured or coherent visual patterns. The demand for higher speed, greater key diversity and more flexible encoding mechanisms has motivated the exploration of optical and transform domain encryption techniques.

Optical encryption frameworks, in particular, benefit from parallel processing capabilities, low computational cost and the ability to incorporate physically meaningful parameters as cryptographic keys. Refregier and Javidi [3] laid the foundation of optical encryption techniques by proposing Double random phase encryption technique in Fourier domain which was later extended to multiple domains[[4], [5], [6], [7], [8], [9]]. This was later found vulnerable to various attacks like Ciphertext-only attack (COA), known-plaintext attack (KPA), chosen-plaintext attack (CPA), and chosen-ciphertext attack (CCA) [[10], [11], [12], [13], [14]], due to symmetric and linear nature of the scheme. Therefore, asymmetric schemes such as phase truncated Fourier transform [15] and its variants [[16], [17], [18]] were introduced, but were later found vulnerable to iterative transform based attacks [19,20]. Cai et al. [21] introduced asymmetric coherent decomposition technique named equal modulus decomposition which formed basis for various schemes [[22], [23], [24]]. It was also found susceptible to specific type of attack [25]. Later random modulus decomposition [26] and unequal modulus decomposition [27] techniques were proposed and utilized in multiple works[[27], [28], [29], [30], [31]]. Random decomposition technique was found vulnerable to simple cryptographic attacks [32]. Computer generated holography (CGH) [33] is one such promising approach. Instead of physically capturing holograms through optical interference, CGH synthesizes them numerically by modelling light propagation using diffraction integrals. This approach enables the use of parameters such as wavelength, propagation distance and sampling intervals as part of an extended key space. Transforming an image into a complex valued optical field via CGH yields intensity patterns resembling white noise that obscure the core structure, establishing CGH as a promising component for secure image encryption systems. CGH gets even more powerful on being combined with advanced transform domain operations and techniques [[34], [35], [36], [37], [38], [39], [40], [41], [42]] that provide additional layers of scrambling and parameter control. Meanwhile, recent studies have explored hybrid and intelligent encryption designs to enhance security. Compressive sensing combined with chaotic scrambling, diffusion, and steganography has enabled carrier-free and visually secure encryption [43]. Quantum transform-based approaches integrating Baker maps, DCT and wavelets have been used for joint encryption and authentication [44]. Computational ghost imaging with fractional angular transforms and chaotic systems has improved colour image security and authentication capability [45]. Memristor-based chaotic systems with CNN-generated keys have demonstrated hardware-backed randomness and robustness [46]. Deep-learning-assisted ROI-based encryption has also been applied for secure medical image protection [47]. These developments indicate a shift toward hybrid, application-aware optical encryption while highlighting the need for robust and scalable designs.

Although numerous optical and transform domain encryption schemes have been presented, many are limited by a narrow key space, linear processing stages or reliance on a single transform. The Fractional Fourier Transform [[7], [48], [49]] (FrFT) offers a continuum between spatial and frequency domains via its fractional order parameter, which can serve as a sensitive and powerful cryptographic key. Meanwhile, nonlinear or hybrid transforms have been studied to enhance security by making it more resistant to reconstruction and inverse modelling. The Hyperbolic Sine Cosine Transform (HSCT) [50] introduces a hyperbolic sine modulation along with a cosine modulation, which introduce an adaptable transform space with adjustable nonlinearity controlled by a scaling factor. Such nonlinearity makes the scrambling more severe and the overall mapping between plaintext and ciphertext more complex.

The existing classical optical encryption schemes exhibit notable security limitations. DRPE, and its variants suffer from linearity, symmetry and limited key diversity, which make them vulnerable to Cipher only attack, known plaintext attack, Chosen plaintext attack and Chosen ciphertext attack. PTFT based schemes remain susceptible to iterative phase-retrieval/transform attacks. Decomposition-based methods (EMD, RMD, UMD) improve asymmetry but still expose structural and statistical weaknesses exploitable by tailored cryptanalysis. Recent hybrid approaches incorporating ghost imaging, chaos, quantum transforms, memristor-based systems, and deep-learning-assisted encryption have shown promising advances in functionality and application-specific security. At the same time, their multi-component structures may increase computational complexity, motivating continued exploration of numerically efficient and structurally streamlined optical encryption models. To overcome these limitations, the proposed scheme integrates computer-generated holography (CGH) for complex field conversion and parameterized key expansion, fractional Fourier transform FrFT for highly sensitive fractional-order keys, block-wise Hyperbolic Sine Cosine Transform (HSCT) for nonlinear scrambling, and unequal modulus decomposition for generating complementary amplitude-phase masks that enlarges key entropy. The key novelty of this work lies in the synergistic multi-domain fusion of CGH, HSCT, FrFT, and UMD within a unified optical–transform framework, which is not jointly explored in prior schemes. This integration significantly enhances key space, and statistical security while maintaining computational practicality. The scheme demonstrates near-ideal entropy, strong NPCR/UACI performance, and improved resistance to common attacks, thereby providing a secure and scalable alternative to existing optical encryption methods.

In this paper, an asymmetric image encryption scheme is proposed that utilizes computer generated holography with unequal modulus decomposition in a unique integration of block-wise Hyperbolic Sine Cosine Transform with fractional Fourier transform domain. Here, Computer-generated holography maps the image into a complex optical field, where wavelength, propagation parameters, and sampling interval direct optical propagation. The block-wise Hyperbolic Sine Cosine Transform adds strong nonlinear modulation and efficient energy compaction, making statistical reconstruction infeasible. Unequal modulus decomposition produces two complementary masks with diverse amplitude-phase characteristics, thereby significantly enlarging the key space. Fractional Fourier transform introduces an additional highly sensitive key parameter, namely, fractional order, strengthening the overall encryption process. Moreover, the proposed framework is fundamentally derived from optical wave propagation and holographic imaging principles, where each processing stage corresponds to a physically realizable optical operation. The use of parameters such as wavelength, propagation distance, and fractional order further confirms the practical feasibility of implementing the scheme within real optical architectures, thereby aligning the work with the scope of optical encryption research.

This paper is organized into several sections to ensure coherence and clarity. Section 1 provides a thorough literature review and establishes motivation behind the research, while highlighting the strategic contributions of the proposed mechanism. Section 2 presents the mathematical foundations and analytical details of the fundamental techniques employed. Whereas in section 3 of the manuscript encoding and decoding processes are detailed in a stepwise manner. Section 4 reports the results obtained through the MATLAB based numerical simulations including the statistical analysis, key sensitivity analysis and resistance to various attacks, thereby validating the mechanism's effectiveness. Comparison analysis against state-of-the-art encryption mechanism has been carried out and demonstrated in section 5 to highlight the advantages and significance of the proposed work. Finally, Section 6 provides the concluding remarks of the proposed scheme.