Optical Encryption Evolves Beyond Double Random Phase Encoding, Review Finds

Optical information security has moved far beyond the double random phase encoding scheme that launched the field in 1995, according to a comprehensive review published in Applied Physics B. The review, authored by Raman Yadav, Harsh Vardhan, Aswathi K Sivarajan, Praveen Kumar, Sakshi Choudhary, Phool Singh, Gangi Reddy Salla, Sachin and Ravi Kumar, surveys roughly a decade of progress from 2015 to 2025 in optical cryptosystems, the techniques that encrypt images by manipulating the physical properties of light rather than the pixel values processed by conventional digital algorithms.

The appeal of optical encryption lies in physics. Traditional ciphers such as the Advanced Encryption Standard and the Data Encryption Standard process data sequentially and can struggle with the sheer volume of high-resolution images and video now transmitted across defense, healthcare and banking networks. Optical systems, by contrast, exploit inherent parallelism, multidimensional processing capability and large key spaces. Instead of scrambling pixel values, they embed information into the phase component of a complex wavefront, or decompose an image into holograms and diffraction patterns, using amplitude, phase, wavelength and polarization as security parameters.

The foundational scheme, double random phase encoding, was proposed by Refregier and Javidi in 1995 using two random phase masks in a 4-f optical setup. Researchers soon extended it to fractional Fourier, Hartley, fractional Hartley, wavelet and other hybrid transform domains. But the linear nature of the DRPE framework left it exposed. In 2006, Peng demonstrated that DRPE security could be compromised through known-plaintext and chosen-plaintext attacks, prompting a search for fundamentally more robust architectures.

A major response came from Qin and Peng, who introduced an asymmetric cryptosystem based on phase truncation and phase reservation in the Fourier domain, known as PTFT. Because PTFT is asymmetric, it resists plaintext attacks, which made it popular among researchers and spawned numerous variants. Yet vulnerabilities emerged there too: later analyses showed PTFT-based systems can be attacked through the relationship between phase and amplitude. The review traces a chain of successive fixes, each followed by new cryptanalysis. Equal modulus decomposition improved security but fell to attacks exploiting the equal modulus of the private key and ciphertext. Random modulus decomposition followed, only to be exposed to iterative attack algorithms. Unequal modulus decomposition addressed that weakness, and was itself shown susceptible to iterative attacks by Archana and colleagues. Polar decomposition, singular value decomposition, QR decomposition, unit equal modulus decomposition, QZ synthesis and Hessenberg decomposition have all since been proposed in the continuing contest between encryption design and attack.

Among the mathematical tools the review examines in detail is the QZ decomposition algorithm, originally proposed by Moler and Stewart in 1973 to solve eigenvalue problems of dense matrices with high speed through parallel processing. In optical encryption, QZ decomposition splits two matrices into two upper quasi-triangular matrices and two unitary matrices, and has been shown to strengthen PTFT-based asymmetric algorithms. It also allows users to encrypt multiple images simultaneously. A related QZ synthesis approach operates on two images at once, generating triangular matrices and unitary matrices that serve as private keys, reducing storage space while improving security. QZ synthesis has been combined with chaotic and hyperchaotic maps to increase randomness and resistance to differential attacks.

Singular value decomposition, a matrix factorization technique in which an image matrix is decomposed into orthogonal matrices and a diagonal matrix of singular values, offers another route. Because most image information concentrates in a few singular values, SVD is useful for compression, denoising, encryption and watermarking, and its stability under small perturbations makes it compatible with cryptographic applications. The generalized singular value decomposition extends this by factoring two matrices simultaneously through a common transformation matrix, enabling two images to be encrypted at once, and has been paired with compressive sensing and computer-generated holography.

Holography contributes a distinct physical layer of security. Since Dennis Gabor introduced the concept in 1948, holography has evolved into computer-generated holography, in which holograms are computed digitally and reproduced on film or spatial light modulators. Phase-only computer-generated holograms, also known as Kinoform holograms, offer high data security capacity within limited space and strong protection against attacks. Recent efficiency improvements include the patterned phase-only hologram and optimized random phase methods, which generate phase-only Fourier holograms by applying a pre-optimized random phase to the input image, and a random phase-free method that reduces speckle noise and improves recovered image quality. Interference-based encryption, introduced by Zhang and Wang in 2008, encodes an input image into two phase-only masks, later extended to three masks by Wang and Zhao to resolve the silhouette problem that arises when a single mask is exposed. Iterative attacks by Xiong and colleagues subsequently targeted the three-mask approach, driving further hardening.

Perhaps the most visually striking frontier involves structured light beams. Optical vortex beams, which carry orbital angular momentum and possess a phase singularity of undefined phase, offer encoding degrees of freedom far beyond conventional polarization’s two orthogonal states, since the topological charge can take any integer value. Any disturbance to the beam alters its singularity structure in a detectable way, adding a natural security layer. Fang and colleagues introduced OAM holography, in which different holographic images are encoded in different orbital angular momentum modes and reconstructed only with the correct topological charge. Ma and colleagues combined OAM holography with ghost imaging for multiplexed encryption, while Yuan and colleagues proposed large-capacity encryption using multiple topological charge channels for parallel encryption of high-resolution images. Vortex arrays, containing several spatially separated phase singularities, provide independent encoding channels, though the review notes limitations including restriction to binary images, finite spatial light modulator resolution, low refresh rates and misalignment sensitivity. Random-vortex-array schemes overcome some of these constraints, supporting grayscale and color encryption. Vector vortex beams, formed by superposing orthogonally polarized OAM modes, add spatially varying polarization as an independent carrier, and a recent scheme encodes information into the polarization-phase structure of optical skyrmion beams.

The review devotes substantial attention to cryptanalysis, the systematic effort to break encryption schemes in order to expose their weaknesses. Following Kerckhoff’s principle, formulated in 1883, a cryptosystem must remain secure even if the attacker knows everything except the key. DRPE-based schemes fall to known-plaintext attacks using phase retrieval techniques such as the Gerchberg-Saxton or hybrid input-output algorithms, to chosen-plaintext attacks employing impulse function sequences, to chosen-ciphertext attacks, and to ciphertext-only attacks that exploit phase retrieval from a single intensity measurement. Artificial intelligence has entered the offensive arsenal as well: the DecNet attack integrates chosen-plaintext attack with deep learning against DRPE, AI-based frameworks have targeted the DIBE approach, and learning-based attacks have broken asymmetric techniques such as PTFT. A hybrid attack combining known-plaintext and ciphertext-only stages broke an interference scheme with fixed phase masks, and modified plaintext attacks defeated a DRPE system with perfect forward secrecy when the same secret key was reused.

The authors also catalog the standard metrics used to evaluate encryption security: histogram uniformity, near-zero correlation between adjacent pixels, information entropy approaching eight bits for ideal 8-bit grayscale images, Number of Pixel Change Rate values around 99.6 percent and Unified Average Changing Intensity near 33 percent as indicators of differential attack resistance, plus key space and key sensitivity analysis, robustness to noise and occlusion measured by PSNR, MSE and SSIM, and NIST randomness testing for chaotic sequences. Despite this mature toolkit, obstacles to real-world deployment remain. Most work relies on simulation rather than experiments with real optics, no uniform benchmarking protocol exists, secure key management and scalability are unresolved, compatibility with the Internet of Things and edge computing is untested, and quantum attacks pose a future threat. The authors call for fast, energy-efficient algorithms, standardized datasets and unified systems combining encryption, authentication, integrity verification, watermarking and key management as the path toward practical optical security.

Subject of Research: A review of the evolution of optical image encryption techniques and the attacks against them

Article Title: A comprehensive review on evolution of optical information security techniques

Article References: Yadav, R., Vardhan, H., Sivarajan, A. K., Kumar, P., Choudhary, S., Singh, P., Salla, G. R., Sachin, & Kumar, R. (2026). A comprehensive review on evolution of optical information security techniques. Applied Physics B, 132(10), Article 101. https://doi.org/10.1007/s00340-026-08713-1

Image Credits: AI Generated

DOI: 10.1007/s00340-026-08713-1

Keywords: optical encryption, cryptosystems, double random phase encoding, holography, orbital angular momentum, vortex beams, singular value decomposition, cryptanalysis, phase truncation, structured light, image security, deep learning attacks