The project is led by principal investigator Edoardo Persichetti, Ph.D., a professor in FAU’s Department of Mathematics and Statistics and director of the university’s Center for Cryptology and Information Security within the Charles E. Schmidt College of Science. Co-principal investigator is Veronika Kuchta, Ph.D., an assistant professor in the same department. Together, the team will build the mathematical foundations for post-quantum protocols that offer advanced capabilities rather than just basic protection, aiming to strengthen digital security as quantum technology advances and to develop more efficient, scalable tools for safeguarding information in complex security applications.

To understand why this matters, it helps to look at how most of today’s public-key cryptography works. The security of the systems protecting online banking, messaging and commerce rests on mathematical problems that are easy to compute in one direction but extraordinarily hard to reverse with conventional computers, such as factoring enormous numbers or computing discrete logarithms. In 1994, mathematician Peter Shor showed that a sufficiently powerful quantum computer running his algorithm could solve those problems efficiently, which means a mature quantum machine could theoretically unravel the public-key infrastructure the digital world depends on. Post-quantum cryptography responds by building new methods on mathematical problems believed to remain hard even for quantum attackers.

Recent international efforts, including the standardization process run by the U.S. National Institute of Standards and Technology, have concentrated on the foundational primitives of that new arsenal: encryption schemes and digital signatures. But many emerging applications demand more sophisticated machinery. Decentralized systems, privacy-preserving technologies and multi-party protocols need cryptographic tools that do far more than encrypt a message or sign a document. The FAU research targets precisely this gap, designing and analyzing post-quantum protocols that can deliver advanced functions for applications where multiple parties must interact securely while protecting sensitive information and verifying the integrity of digital processes.

“This NSF support gives us an opportunity to take the next step in post-quantum cryptography by moving beyond basic encryption and signatures toward more advanced protocols that can address the increasingly complex security needs of emerging technologies,” said Persichetti. “The grant will allow us to develop new cryptographic constructions, rigorously analyze their security and investigate how they can be made more efficient and scalable. It also will help us train the next generation of researchers in an area that will be increasingly important as quantum computing advances.”

The technical heart of the project lies in algebraic structures drawn from several mathematical frameworks, including lattices, error-correcting codes, group actions and isogeny-based cryptography. Lattices, for instance, underpin schemes whose security rests on the difficulty of finding the shortest vector in a high-dimensional grid, a problem with no known efficient quantum solution. Code-based cryptography, meanwhile, leans on the decades-old difficulty of decoding arbitrary linear error-correcting codes, while isogeny-based approaches exploit the intricate structure of mappings between elliptic curves. By working across these families, the researchers can compare trade-offs in key sizes, computational cost and security assumptions, and combine their strengths in hybrid constructions.

On top of these foundations, the team will investigate protocols supporting advanced cryptographic functions such as blind signatures, threshold signatures, multisignatures and verifiable random functions. A blind signature allows someone to obtain a signed document without the signer seeing its contents, a property crucial for private electronic voting and anonymous credentials. Threshold signatures distribute signing power among several parties so that only an authorized subset acting together can produce a valid signature, eliminating single points of failure. Multisignatures compress the approvals of many participants into one compact object, and verifiable random functions generate randomness that anyone can check was computed honestly, a building block for blockchain consensus and secure lotteries. Making all of these quantum-resistant, efficient and scalable is a formidable mathematical challenge.

A vital component of the work will be the development of rigorous security proofs grounded in well-defined computational assumptions, the gold standard that separates genuine cryptographic guarantees from wishful thinking. The researchers will also employ zero-knowledge proofs, which let one party convince another that a statement is true without revealing any information beyond the truth of the statement itself, along with group-action frameworks that provide a clean algebraic language for constructing such proofs. The emphasis throughout will be on improving efficiency, security and scalability, because a protocol that is provably secure but too slow or too bulky for real systems protects nothing in practice.

The award builds on FAU’s growing national leadership in the field. Persichetti has played a significant role in preparing cryptographic systems for the quantum era: he submitted four algorithms to NIST’s post-quantum cryptography competition, three of which advanced to the final round, and his Hamming Quasi-Cyclic (HQC) algorithm was ultimately selected by NIST for standardization as part of its Post-Quantum Cryptography project. HQC, a code-based scheme, is designed to provide secure key exchange while protecting communications against attacks from future quantum computers. Notably, FAU is the only university in the United States represented among the authors of the two key-encapsulation mechanisms NIST selected for standardization, HQC and ML-KEM, and FAU faculty have also contributed to the CRYSTALS-DILITHIUM digital signature algorithm, another NIST selection. “This new NSF award builds directly on the expertise and research foundation we have developed through our work in post-quantum cryptography,” said Persichetti. “The selection of HQC for standardization demonstrated the importance of developing cryptographic systems that can withstand quantum threats. This project expands that effort into advanced functionalities that will be needed to protect increasingly sophisticated digital systems in the years ahead.”

Beyond the mathematics, the grant carries an investment in people. The project will support training and mentoring students through research experiences and outreach activities, cultivating the next generation of cryptographers and cybersecurity researchers who will confront security challenges that do not yet fully exist. “This award reflects Florida Atlantic’s growing strength at the intersection of mathematics, cryptography, cybersecurity and emerging technologies,” said Valery Forbes, Ph.D., dean of the Charles E. Schmidt College of Science. “Our faculty are not only contributing to the development of technologies designed to protect the nation’s digital infrastructure but are helping shape the next generation of post-quantum security. With nationally recognized research such as the work of Dr. Persichetti and our cryptography team, FAU is at the forefront of this rapidly evolving field.” The effort also aligns with FAU’s broader identity as Florida’s first quantum university: through its Center for Quantum Technologies, the institution unites faculty, students and industry partners to advance quantum research, and its Boca Raton campus now hosts a D-Wave Advantage2 annealing quantum computer, giving researchers hands-on access to leading-edge quantum hardware. As quantum computing inches closer to practical reality, work like this ensures that when the quantum era arrives, the mathematics defending the world’s data will already be waiting for it.

Subject of Research: Post-quantum cryptography protocol design funded by a National Science Foundation grant at Florida Atlantic University

Article Title: FAU receives $400,000 NSF grant to advance post-quantum cryptography

Article References: FAU receives $400,000 NSF grant to advance post-quantum cryptography. Original publication (Bibliographic details unavailable.)

Image Credits: AI Generated

DOI: Not provided

Keywords: post-quantum cryptography, quantum computing, NSF grant, Florida Atlantic University, cryptography, lattices, error-correcting codes, zero-knowledge proofs, digital signatures, NIST standardization, cybersecurity, HQC

Image encryption has long relied on two complementary operations. Confusion, or permutation, shuffles the positions of pixels so the picture becomes spatially meaningless, while diffusion alters the actual intensity values of the pixels so that even a single changed input ripples across the whole encrypted output. Chaotic maps, mathematical functions that are exquisitely sensitive to their initial conditions, are the workhorses of both stages: feed in a secret starting value and the function spews out a sequence that looks random but can be regenerated exactly by anyone holding the same key. The weakness of many published schemes is that the key material used for diffusion is either derived from the same sequences used for scrambling or produced by simple, predictable rules, leaving an opening for chosen-plaintext and known-plaintext attacks in which an adversary encrypts specially crafted images to expose the underlying key stream.

The new work attacks both vulnerabilities at once. For confusion, the team introduced what they call the 4D Non-monotonic Sinusoidal Chaotic Map, or NSCM. A conventional monotonic function generates sequences that steadily rise or fall, which is useless for cryptography because the output is predictable. The researchers folded a sinusoidal term into the monotonic recurrence, converting the non-random ascending or descending sequence into a genuinely random, non-monotonic one. The map produces four coupled random sequences from three initial values and one control parameter, all specified to fifteen decimal places. According to the authors’ analysis, the sequences yield positive Lyapunov exponents of 0.85 and 0.69 above control parameter thresholds of 3.6 and 3.7 respectively, and bifurcation diagrams show the system descending into full chaos as the parameter climbs past roughly 3.5. A 0-1 test returned 0.84 for one sequence, further confirming chaotic behavior.

Randomness was also verified against the official benchmark. The team ran their sequences through the full NIST statistical test suite, the standard battery used by the US National Institute of Standards and Technology to certify pseudorandom number generators for cryptographic use. All fifteen tests passed, including the frequency, runs, approximate entropy, discrete Fourier transform, and cumulative sums tests, with p-values ranging from 0.0108 to 0.9999. That matters because the statistical quality of the random sequences directly determines how flat and uninformative the encrypted image appears.

The more unconventional half of the scheme is the diffusion key. Instead of expanding a key image by interpolation or pseudo-random number generation, both of which carry known weaknesses, the researchers harvest sixteen elements from the fourth sequence of the NSCM and arrange them into a 4 by 4 matrix. This tiny matrix is then fed through a six-layer convolutional neural network built from transposed convolution layers, which progressively upsample the input: 4 by 4 becomes 8 by 8, then 16, 32, 64, 128, and finally 256 by 256, matching the size of the plaintext image. Each layer applies transposed convolution to enlarge the spatial dimensions, a rectified linear unit to inject non-linearity, and batch normalization to stabilize the values. The final output is normalized to the 0-to-255 intensity range and reshaped into a key map that looks like pure noise, with essentially no correlation between neighboring pixels.

Crucially, the network never needs training. Because it performs no classification, regression, or feature learning, there is no backpropagation and no dataset; it operates purely as a deterministic forward mapping with fixed parameters. Those parameters, including kernel sizes, strides, and the number of filters, are not fixed by the algorithm but chosen by the user and known only to sender and receiver, so the architecture itself becomes part of the secret key. This design sidesteps the time cost that plagues learning-based encryption schemes while still reaping the non-linear complexity that neural layers provide.

Encryption proceeds in three rounds of confusion followed by one of diffusion. The 256 by 256 plaintext is first divided into 1,024 blocks of 8 by 8 pixels, and the blocks themselves are shuffled using a permutation derived from the first NSCM sequence. Two further pixel-wise shuffles follow, driven by the second and third sequences. Finally, the thrice-scrambled image is XORed bit by bit with the neural key map to produce the ciphertext. Decryption simply reverses the pipeline: XOR with the key map, then undo the permutations in reverse order using the de-scrambling indices.

The experimental results are strong across the standard battery of cryptanalytic metrics. Information entropy of the encrypted images reached 7.9974 on an 8-bit scale whose theoretical maximum is 8, indicating near-perfect randomness. Correlation coefficients between adjacent pixels, which hover near 1 in natural images, collapsed to values within a few thousandths of zero in the ciphertext. The number of pixels change rate and unified average changing intensity, the two canonical measures of resistance to differential attacks, came in above 99.5 percent and above 33 percent respectively for every test image, matching or approaching the ideal thresholds. Histograms of encrypted images were flat and image-independent, denying attackers any statistical fingerprint of the original content.

Robustness testing pushed the scheme further. When encrypted images were cropped by 25, 50, or even 75 percent, simulating an occlusion attack, the decrypted pictures remained recognizable, with peak signal-to-noise ratios declining gracefully from about 15.8 to 11.0 decibels. Salt-and-pepper noise injected into up to half of the ciphertext still allowed recovery of the plaintext. Against chosen-plaintext attacks, the team encrypted all-black and all-white images, the classic probe for exposing permutation-only ciphers, and found the difference between the two ciphertexts revealed no patterns; pixel correlation in the encrypted all-black image was a negligible 0.00113, and XORing two ciphertexts did not leak the key stream.

Perhaps the most striking figure is the key space. The three initial values and control parameter, each precise to ten to the minus fifteen, contribute roughly 2 to the power 199 possible keys, while the sixteen-element input vector at ten to the minus four precision adds another 2 to the power 212, for a combined space of about 2 to the power 411, vastly exceeding the 2 to the power 100 lower limit generally considered safe against brute force. If the input vector were specified to fifteen decimal places, the space would balloon to 2 to the power 996. Key sensitivity is equally fierce: perturbing a key by one part in ten to the fifteen renders decryption impossible. And the whole operation is fast, encrypting a 256 by 256 grayscale image in about 2.0 seconds on an ordinary Intel Core i5 machine with 8 gigabytes of RAM, quicker than several competing schemes the authors compared against. With medical imaging, satellite data, and the Internet of Things all demanding lightweight yet attack-proof visual security, a scheme that marries chaos theory to the geometry of transposed convolutions offers a compelling template for the next generation of lossless image ciphers.

Subject of Research: Deep network-guided key map generation and a 4D non-monotonic sinusoidal chaotic map for lossless image encryption

Article Title: Deep network-guided key map generation for lossless image encryption

Article References: Mahapriya, C., Thanikaiselvan, V., & Thomas, S. B. (2026). Deep network-guided key map generation for lossless image encryption. Frontiers in Artificial Intelligence, 9, Article 1913975. https://doi.org/10.3389/frai.2026.1913975

Image Credits: AI Generated

DOI: 10.3389/frai.2026.1913975

Keywords: image encryption, chaotic map, deep learning, convolutional neural network, cryptography, diffusion, confusion, XOR, key space, NIST randomness tests, differential attack, lossless decryption

The study, published in the journal Cluster Computing, introduces what the authors call EQR-MCPABE, short for an efficient and quantum-resistant multi-authority ciphertext-policy attribute-based encryption scheme. The work was carried out by Sravya Gudipati and R. Padmavathy of the National Institute of Technology Warangal, together with Syam Kumar Pasupuleti of the Quantum-Safe Cryptography Lab at the Institute for Development and Research in Banking Technology in Hyderabad. Gudipati and Pasupuleti contributed equally to the research.

Attribute-based encryption is a family of techniques that rethinks who holds the keys to a piece of data. Instead of encrypting a file for one specific recipient, the data owner encrypts it under a policy written in terms of attributes, such as department, clearance level, or role. Only users whose credentials satisfy the policy can decrypt the content. In the ciphertext-policy variant, the encryptor dictates the policy, which makes the approach a natural fit for fine-grained access control in cloud environments where files may be read by many different people over long periods.

Multi-authority versions of the scheme add another layer of practicality. Rather than relying on a single trusted authority to issue every key, a dangerous single point of failure, multiple independent authorities each manage their own set of attributes. A hospital might have one authority for medical roles and another for administrative clearances, and no single entity can reconstruct a user’s full secret key. This decentralization has made multi-authority ciphertext-policy attribute-based encryption, or MCP-ABE, one of the most promising building blocks for privacy-preserving cloud applications.

Yet nearly all of the classical MCP-ABE schemes rest on number-theoretic assumptions, problems such as factoring and computing discrete logarithms that Shor’s algorithm, running on a future quantum computer, is known to solve efficiently. That looming vulnerability has pushed cryptographers toward lattice-based constructions, whose security rests on problems like Learning with Errors that have resisted both classical and quantum attack strategies for nearly two decades. Lattice problems involve finding short vectors in high-dimensional geometric structures, and no known quantum algorithm breaks them.

Existing lattice-based MCP-ABE schemes, however, carry a heavy computational burden. Most are built on the Learning with Errors problem or its ring-based variant, Ring-LWE, and they rely on Gaussian sampling algorithms, procedures that draw random values from a bell-shaped distribution over a lattice. Gaussian sampling is notoriously expensive and delicate to implement correctly, and it has historically been a major source of inefficiency in lattice cryptography. On top of that, many of these schemes lack effective attribute revocation, the ability to cleanly remove a user’s access when attributes change, which is essential for any system handling dynamic organizations where people join, leave, and change roles constantly.

The new scheme sidesteps both problems. EQR-MCPABE is constructed from module lattices, a middle ground between general lattices and ideal lattices that offers a balance of security confidence and efficiency. Module lattices have gained prominence in post-quantum cryptography; the standardized key-encapsulation mechanism CRYSTALS-Kyber, selected by standards bodies for quantum-safe encryption, is itself built on module lattices. Crucially, the new construction avoids Gaussian sampling algorithms altogether, which the authors identify as the key to reducing computation cost while preserving resistance to quantum attacks.

Revocation is handled through a server-assisted mechanism. Instead of forcing every authority to reissue keys whenever an attribute must be revoked, the scheme delegates part of the revocation workload to the cloud server, allowing access to be cut off efficiently without imposing a heavy burden on users or authorities. The design achieves both forward and backward security, meaning that a revoked user cannot read data encrypted after the revocation, and cannot recover data encrypted before it either, closing the window that poorly designed revocation systems often leave open.

On the theoretical side, the authors prove that EQR-MCPABE is secure against chosen-plaintext attacks under the Module-LWE assumption, the module-lattice analogue of the Learning with Errors problem. Chosen-plaintext security is a standard formal guarantee: an adversary who can obtain encryptions of messages of their choosing still cannot extract information about other encrypted content. Grounding the proof in Module-LWE ties the scheme’s security to a well-studied lattice problem, aligning it with the assumptions underpinning the leading post-quantum standards.

Performance analysis presented in the paper shows that the scheme outperforms existing lattice-based MCP-ABE constructions, a result the researchers attribute largely to the elimination of Gaussian sampling and the efficiency of the module-lattice setting. As organizations worldwide begin the long migration to quantum-safe cryptography, work like this points toward access-control systems that can protect fine-grained, multi-authority cloud data not just against today’s attackers, but against the quantum machines of tomorrow, without the performance penalties that have kept earlier lattice-based designs out of practical deployment.

Subject of Research: A quantum-resistant multi-authority attribute-based encryption scheme for secure cloud storage

Article Title: Efficient and quantum-resistant multi-authority CP-ABE with attribute revocation for cloud Storage

Article References: Gudipati, S., Pasupuleti, S. K., & Padmavathy, R. (2026). Efficient and quantum-resistant multi-authority CP-ABE with attribute revocation for cloud Storage. Cluster Computing, 29(15), Article 849. https://doi.org/10.1007/s10586-026-06660-2

Image Credits: AI Generated

DOI: 10.1007/s10586-026-06660-2

Keywords: cryptography, post-quantum cryptography, lattice-based cryptography, cloud storage, attribute-based encryption, Module-LWE, attribute revocation, access control, multi-authority encryption, quantum computing, data security, Efficient

A research team led by Shitong Bai and Jun Wu of Fudan University, together with Jiawei Zhang of Xidian University, has now unveiled a cryptographic scheme designed to restore that control. Published in the open-access journal Cybersecurity, their work describes a revocable and time-based secure file hierarchy sharing scheme for cloud-assisted IoT, built on an advanced form of Ciphertext-Policy Attribute-Based Encryption, or CP-ABE. The scheme promises to cut encryption time by more than 30 percent and decryption time by more than 50 percent compared with leading prior designs, while saving over 50 percent of ciphertext storage on the cloud server.

CP-ABE has long been the workhorse of fine-grained access control for encrypted data. Instead of sharing a decryption key with a named individual, the data owner attaches an access policy to the ciphertext itself, written in terms of attributes such as doctor, pharmacist or researcher. A user whose attributes satisfy the policy can decrypt; everyone else sees only noise. The technique was first proposed by Bethencourt, Sahai and Waters in 2007 and has since spawned a rich family of extensions addressing user privacy, revocation and large attribute universes in decentralized settings.

Yet the Fudan and Xidian team identified three persistent gaps that keep existing CP-ABE schemes from working well in real cloud-assisted IoT deployments. First, most designs treat the cloud as an unlimited resource pool and ignore the long-term cost of storing ever-growing ciphertexts. File Hierarchy CP-ABE, introduced by Wang and colleagues in 2016, partially addressed this by exploiting the hierarchical structure of shared files, but early versions suffered from a collusion problem in which users at the same hierarchy level could decrypt each other’s files, and the fix that followed came at a steep computational price in both encryption and decryption.

Second, time matters. In healthcare IoT, patient health records must be read by doctors immediately for timely diagnosis, while pharmacists and researchers legitimately need access only later, for follow-up care and monitoring. Time-based CP-ABE schemes that fuse a time factor with attributes have been proposed, notably by Hong and colleagues in 2017, but they fail to handle dynamic users who join and leave the system. Conversely, schemes with efficient direct user revocation, such as that of Han and colleagues in 2020, impose heavy computation and offer no time-based access control at all. Third, many schemes simply trust the cloud. A malicious or negligent server might hide data breaches caused by mistakes or external attacks to protect its reputation, or quietly delete rarely accessed files to save cost, violating data integrity in ways that are unacceptable for quality of service.

The new scheme tackles all three challenges simultaneously through a construction the authors call a time-release hierarchical access policy tree. Like a traditional access tree, it contains leaf nodes representing attributes and non-leaf nodes representing AND, OR and threshold gates. But it adds two novel ingredients: level nodes that bundle multiple files with their own sub-policies into a single hierarchy, and trapdoor nodes, each bound to a stateful time trapdoor. When the ciphertext is created, every trapdoor is sealed. Only when a central authority publishes a time token at the designated moment can the cloud server unseal it, exposing the missing secret share that completes the access path. Before that instant, even users with perfectly matching attributes cannot decrypt the protected file block.

Dynamic users are handled by a binary tree technique borrowed from group key management. Each user occupies a leaf of a binary tree, and the intersection of a user’s path with the minimum cover set of the revocation list determines whether that user can still derive the necessary key components. Revoking a misbehaving user is direct: the authority updates the revocation list and hands the cloud an update key, and the server rewrites the relevant ciphertext components without touching the encrypted payloads themselves. The authors show that revocation costs grow only sublinearly with the size of the revocation list, a significant improvement over schemes whose costs scale linearly with both the user attribute set and the revocation list.

Integrity is enforced through an identity-based auditing mechanism. The scheme splits each ciphertext into two parts: the encrypted message components, protected by symmetric encryption and accompanied by signatures, and the policy-related components used for access control and verification. A third-party auditor challenges the cloud server with random queries and checks a aggregated proof against a compact verification equation, so a lazy or compromised server that returns incorrect decryption results or tampers with stored data will be caught. Formal security analysis proves the scheme selectively secure against chosen-plaintext attacks in the standard model under the decisional Bilinear Diffie-Hellman assumption, and its auditing security rests on the Computational Diffie-Hellman assumption together with an existentially unforgeable signing algorithm.

The performance story is where the design becomes genuinely striking. Implemented in Java with the JPBC pairing library on a 160-bit elliptic curve, the scheme keeps encryption and decryption time nearly constant as the number of shared file blocks grows, because the hierarchical structure lets the owner encrypt an entire file hierarchy in one pass and lets the cloud perform most of the heavy decryption on behalf of users. Experiments show encryption time roughly 8 percent lower than prior file-hierarchy schemes thanks to an online/offline technique in which the owner precomputes an intermediate ciphertext pool while the device is charging, and decryption time reduced by about 30 percent relative to comparable hierarchical designs. Ciphertext storage on the cloud drops by at least 50 percent, and the time trapdoors add only about 4 percent extra storage overhead. On the user’s side, the locally stored secret key is roughly 70 percent smaller than in competing schemes, because outsourced decryption means the bulky decryption key never needs to be kept on the device.

The team also validated the design in a real-world pilot deployment, using a server to simulate the cloud, auditor and authority, and four laptops to simulate data owners and users. Across 100 repeated runs of key generation, encryption, decryption and revocation, the proposed scheme outperformed the reference FH-CP-ABE and EFH-CP-ABE schemes in encryption and decryption time, key size and communication size, and it was the only one of the three to support user revocation and data auditing at all. For the exploding population of resource-poor IoT devices, that combination of fine-grained, time-aware, revocable and auditable sharing, delivered at a fraction of the usual cost, could mark a turning point in how sensitive data is entrusted to the cloud.

Subject of Research: Revocable and time-based secure file hierarchy sharing in cloud-assisted Internet of Things using ciphertext-policy attribute-based encryption

Article Title: Revocable and time-based secure file hierarchy sharing in cloud-assisted internet of things

Article References: Bai, S., Zhang, J., & Wu, J. (2026). Revocable and time-based secure file hierarchy sharing in cloud-assisted internet of things. Cybersecurity, 9(1), Article 239. https://doi.org/10.1186/s42400-026-00660-w

Image Credits: AI Generated

DOI: 10.1186/s42400-026-00660-w

Keywords: cloud-assisted IoT, ciphertext-policy attribute-based encryption, access control, time-release encryption, user revocation, data integrity auditing, file hierarchy, data privacy, cloud computing, cryptography, outsourced decryption, cybersecurity

The core insight of the new technique is that color medical images carry redundant statistical structure that attackers can exploit. In a typical color image, the red, green, and blue channels are highly correlated with one another, and neighboring pixels within each channel tend to have nearly identical values. Classical encryption that treats an image as an ordinary file often leaves enough of this structure intact for statistical analysis to reconstruct recognizable content. The researchers attack this weakness head-on by first separating each image into its three constituent channels and then deliberately scrambling them with channels drawn from other images in the batch.

This inter-channel mixing serves two purposes at once. First, it drastically lowers the correlation between adjacent pixels, because a pixel in the encrypted red channel may now depend on data that originally lived in the green channel of an entirely different scan. Second, it binds the security of every image in the group to the security of the whole batch, so an adversary who somehow compromises one image still faces an incoherent jumble of fragments from the others. The authors describe the resulting scrambling process as introducing enough uncertainty and diffusion to defeat both statistical and differential attacks, the two workhorses of cryptanalysis against image ciphers.

Once the channels are mixed, the scheme applies two further layers of protection: pixel permutation and channel diffusion. Crucially, these operations are not driven by conventional pseudo-random number generators but by three distinct chaotic maps—the logistic map, the Henon map, and the Chebyshev map. Chaotic systems are prized in cryptography because they exhibit extreme sensitivity to initial conditions: a change of even one digit in the starting value produces a completely different sequence. By generating independent encryption keys from three different chaotic systems, the scheme multiplies the difficulty of predicting or reproducing its scrambling behavior.

The division of labor among the three maps is deliberate. The logistic map, a deceptively simple one-dimensional equation famous for producing complex behavior from a single parameter, contributes sequences for one stage of the process. The Henon map, a two-dimensional system introduced in 1976 and known for its strange attractor, adds a second source of pseudo-randomness with richer dynamics. The Chebyshev map rounds out the trio, and each map’s output feeds independent keys for permutation and diffusion stages. This multi-chaotic key architecture means an attacker would need to break three separate dynamical systems simultaneously rather than a single generator.

The numbers reported in the study are the currency in which image-encryption schemes are judged, and they are impressive. The encrypted images achieve an average information entropy of 7.9994 on a scale where the theoretical maximum is 8, meaning the pixel values are distributed almost perfectly uniformly and leak virtually no statistical information. The key space reaches 2 to the power of 512, a number so vast that brute-force search is computationally meaningless with any foreseeable hardware. For context, even a key space of 2 to the power of 100 is generally considered far beyond exhaustive attack.

Two further metrics measure resistance to differential attacks, which test whether changing a single pixel of the original image changes the encrypted output. The number of pixels change rate, or NPCR, came in at 99.61 percent, essentially the ideal value indicating that nearly every encrypted pixel changes when the plaintext is altered by even one bit. The unified average changing intensity, or UACI, measured 33.46 percent, sitting squarely in the optimal range around the theoretical expectation of 33.46 percent for a strong cipher. Together, these figures indicate that the scheme produces avalanche-like sensitivity: the smallest alteration in a medical image cascades into a completely different ciphertext.

The researchers validated their algorithm on publicly available medical datasets, including brain tumor MRI scans, a breast cancer histopathological database, dermatology images, and SARS-CoV-2 CT scans, giving the evaluation a realistic clinical flavor rather than relying on generic test images. Beyond raw security, the team emphasizes efficiency: the method is designed to support the secure transfer of real-time medical information while preserving the integrity and quality of the original images after decryption. That combination matters, because a cipher that garbles diagnostic detail or adds prohibitive latency is useless in an emergency room or a remote consultation.

The work arrives amid a broader surge of interest in medical image security, driven by the growth of the Internet of Medical Things and telemedicine. Recent literature has explored DNA-based operations, hyperchaotic systems, fuzzy logic substitution boxes, and even large language models for plausible-deniability schemes. Hosny and colleagues’ contribution stands out for its focus on encrypting multiple images simultaneously—a practical requirement when hospitals transmit entire imaging sessions—rather than one image at a time, and for the elegance of using the images’ own color channels as raw material for cross-contamination of information.

For clinicians and health IT administrators, the message is that color medical images can be protected with ciphers purpose-built for their statistical quirks rather than adapted from generic file encryption. For cryptographers, the study adds evidence that combining cross-image channel mixing with multiple independent chaotic key generators is a productive design pattern. As healthcare data breaches continue to make headlines, techniques like this one aim to ensure that a stolen stream of encrypted scans reveals nothing more than noise—uniformly distributed, information-theoretically opaque, and mathematically indifferent to the secrets it once carried.

Subject of Research: Chaotic-map-based encryption of multiple color medical images using cross-image channel mixing

Article Title: Efficient encryption of multi-color medical images using channel mixing and multi-chaotic keys

Article References: Hosny, K. M., Ahmed, M. S., & Nada, F. A. (2026). Efficient encryption of multi-color medical images using channel mixing and multi-chaotic keys. Journal of Ambient Intelligence and Humanized Computing. https://doi.org/10.1007/s12652-026-05131-1

Image Credits: AI Generated

DOI: 10.1007/s12652-026-05131-1

Keywords: medical image encryption, chaotic maps, channel mixing, logistic map, Henon map, Chebyshev map, information entropy, differential attacks, telemedicine security, color images, cryptography, Internet of Medical Things

The core insight of the paper is that transaction data in cross-enterprise supply chain collaboration has a fundamentally rational structure. A price of 3.75 units, an exchange rate of 0.917, or a quantity of 12.5 items cannot be faithfully represented as an integer without some loss. Previous approaches to processing rational numbers in secure computing typically multiply every value by the same scaling factor to convert it into an integer, perform the secure computation, and interpret the result afterwards. The authors argue that this practice is risky in two distinct ways. First, any loss of rational number precision can lead to erroneous judgments, for example when two nearly identical prices must be distinguished to detect fraud or verify a contract. Second, simplistic conversion of rational numbers to integers may itself create privacy risks, because the scaling operation can leak structural information about the data if the factor is chosen carelessly.

To avoid these pitfalls, the research team transforms rational numbers into matrices and designs secure protocols for set intersection and set union that operate directly on this matrix representation. The cryptographic engine underneath is the Elgamal homomorphic encryption algorithm, a public key cryptosystem introduced by Taher Elgamal in 1985 and based on the hardness of the discrete logarithm problem. Homomorphic encryption allows mathematical operations to be performed on ciphertexts, so that the encrypted data can be manipulated without decryption. In the setting studied here, the multiplicative homomorphic property of Elgamal enables the participating enterprises to jointly evaluate whether elements appear in both of their sets, which is the intersection, or in at least one of them, which is the union, while each party’s individual inputs remain hidden.

A crucial feature of the new protocols is that they are designed and analyzed under two different adversary models. In the semi-honest model, participants follow the protocol exactly as specified but try to learn extra information from the messages they legitimately observe. This is the classical setting for much of secure multiparty computation, a field that traces back to Andrew Yao’s foundational 1982 work on protocols for secure computation and the famous millionaires’ problem, in which two parties want to know who is richer without disclosing their actual wealth. The malicious model is far more demanding: participants may deviate arbitrarily from the protocol, sending malformed messages, replaying old values, or aborting at strategic moments in order to cheat or extract information. Protocols that are secure against semi-honest adversaries can collapse entirely when faced with active cheating.

The authors prove the security of their protocols under the malicious model using the ideal-practical, or real-ideal, simulation paradigm, which is the standard gold standard for security proofs in modern cryptography. In this framework, one imagines an ideal world in which the parties hand their inputs to a trusted third party who performs the computation and returns only the output. A protocol is deemed secure if whatever an adversary can achieve by attacking the real protocol could also be achieved in that ideal world, meaning the protocol leaks nothing beyond what the ideal functionality itself reveals. By constructing a simulation-based argument for the malicious setting, the researchers demonstrate that even participants who actively misbehave cannot learn the other parties’ rational number inputs or force an incorrect result to be accepted.

The practical motivation comes from the growing dependence of IoT enterprises on automated, cross-organizational data exchange. Modern supply chains are studded with sensors, RFID tags, and connected devices that generate continuous streams of transactional records. Enterprises want to answer questions such as whether a supplier’s price list overlaps with a competitor’s, whether the same batch of goods appears in two different logistics records, or which exchange rates are shared across regional partners. Set intersection and union are the natural mathematical operations for these tasks, but performing them on plaintext data would force companies to expose commercially sensitive information to partners who may be competitors at the same time as they are collaborators. Secure multiparty computation resolves this tension by letting the computation proceed on encrypted inputs, and the paper positions its rational-number-aware protocols as a missing piece for supply chain scenarios where fractional values dominate.

The study situates itself within a rich body of prior work on secure set operations and rational number computation. Earlier research has produced protocols for secure set membership determination, private intersection-sum computation, and the secure computation of the maximum value of the sum of corresponding elements of an intersection set. Other groups have developed secure multiparty computation of rational intervals, secure determination of interval positional relationships, and privacy-preserving two-party rational set computation. Related efforts have extended secure computation to graph intersections and concatenations, and recent surveys have collected efficient protocol families and their applications. Work in adjacent domains, including privacy-preserving authentication for smart cities, secure data analysis in healthcare IoT systems, blockchain-assisted verifiable data computing, and privacy-preserving collaborative routing, illustrates how broadly the demand for secure joint computation has spread across the Internet of Things landscape.

Beyond correctness and security, the paper contributes a comparative efficiency analysis. The authors analyze the efficiency of existing protocols against their proposed construction and argue that the new approach is practical for real deployment. The matrix-based representation of rational numbers plays a double role here: it preserves exact precision, avoiding the rounding errors introduced by uniform scaling, and it provides a uniform structure on which the Elgamal-based operations can be applied systematically. Because Elgamal encryption is well studied and its security rests on a long-standing hardness assumption, the construction inherits a degree of cryptographic maturity that newer, less scrutinized techniques may lack. The authors also report simulation results supporting the practicality claim, and they state that all data generated or analyzed during the study are included in the article itself.

The research was carried out by a team spanning Tianjin Renai College, the Inner Mongolia University of Science and Technology in Baotou, and the North China University of Technology in Beijing, with correspondence to Lanying Liang. The work received support from multiple Chinese funding bodies, including the National Natural Science Foundation of China, the Natural Science Foundation of Inner Mongolia, and several regional talent and technology development programs. The article was received in July 2025, accepted in August 2026, and published on 3 September 2026 in volume 29 of Cluster Computing as article number 722.

For enterprises weighing the trade-off between data utility and data exposure, the message of this research is that precision itself is a security property. A protocol that silently rounds 0.917 to 0.92 does not merely produce a slightly wrong answer; it can produce a confidently wrong answer that propagates through pricing, auditing, and compliance decisions, and it may do so in ways that leak information about the original figures. By keeping rational numbers exact throughout the computation and by hardening the protocols against actively malicious participants, the new work offers IoT-driven supply chains a template for collaboration in which partners can compute exactly the answers they need, and nothing more. As connected devices multiply and supply chains grow more intertwined, techniques of this kind may become a standard layer of the infrastructure that lets rival firms share a market without sharing their secrets.

Subject of Research: Secure multiparty computation protocols for privacy-preserving rational number set operations in IoT supply chain collaboration

Article Title: Secure computational protocols for supply chain security of IoT enterprises based on intersection and union of rational numbers sets under the malicious model

Article References: Liu, X., Wang, Y., Liang, L., Xu, G., Gu, Y., & Zhang, B. (2026). Secure computational protocols for supply chain security of IoT enterprises based on intersection and union of rational numbers sets under the malicious model. Cluster Computing, 29(12), Article 722. https://doi.org/10.1007/s10586-026-06479-x

Image Credits: AI Generated

DOI: 10.1007/s10586-026-06479-x

Keywords: secure multiparty computation, rational numbers, set intersection, set union, Elgamal encryption, homomorphic encryption, malicious model, IoT, supply chain security, privacy-preserving computation, cryptography, Cluster Computing

An S-box is a function that maps an n-bit input to an m-bit output, and in ciphers like the Advanced Encryption Standard it is the primary source of nonlinearity. When analysts model a cipher algebraically, the equations describing the S-box are replicated for every occurrence of the box inside the cipher, so the number and structure of those equations directly shape the size of the full model. The simplest description writes out explicit algebraic normal form equations for each output bit, but that is not always the most efficient formulation. Instead, the researchers work in the Boolean ring, where a relation holds for a given S-box if it evaluates to zero at every valid input-output pair, and a system of relations uniquely describes the box only if it both accepts all valid pairs and rejects every incorrect output.

Why does this matter for quantum computing? Formulating cryptanalytic problems as quadratic unconstrained binary optimization, or QUBO, remains an active research direction tied to quantum annealing. The computational cost of solving QUBO or Ising problems depends heavily on the number of variables involved. Each quadratic monomial in an equation system must be replaced by a shared auxiliary variable during linearization, and each parity condition needs binary-encoded counter bits. The package therefore evaluates candidate equation systems using a cost measure that sums the counts of linearization variables and parity-counter bits. Minimizing this measure reduces the auxiliary-variable count in the adopted construction, although the authors are careful to note that it does not guarantee lower practical solution difficulty, and their software neither constructs the QUBO matrix nor solves the resulting problem.

The payoff from careful modeling can be dramatic. For the AES S-box, replacing the original 39-equation system with a 13-equation system proposed in earlier work by the same group reduces the number of auxiliary variables from 299 to 106 per S-box, shrinking the AES-128 QUBO model from 68,600 to 30,026 logical variables. Those earlier results, obtained through laborious manual construction for a single cipher, motivated the generalization now embodied in SBoxQUBOSearch. The new package extends the underlying theory of implicit-relation construction and variance-guided basis transformations beyond AES, wrapping the methods in optimized standalone programs, versioned data schemas, reproducible job files, and a partitioning scheme that lets searches run on independent machines without any communication between them.

The software is organized as three command-line programs driven by JSON job files. The first, eqgen, generates equations: explicit ones via an in-place Möbius transform of the truth tables, and implicit relations by building a catalog of all monomials up to a chosen degree, evaluating them at every valid input-output pair, and extracting relations from the left nullspace of the resulting evaluation matrix through packed-row Gaussian elimination. The second program, search-global, then lexicographically enumerates subsets of the generated relations of a specified size, checking each candidate system for exactness using a bit-packed evaluation table in which a bitwise AND with the selected-equation mask vanishes precisely when a pair satisfies all chosen equations. The third, search-local, explores equivalent bases of a chosen system by applying invertible transformations over the two-element field, guided by an LFSR-inspired state machine that uses the variance of equation lengths to steer the traversal.

The exhaustive search is where the tool shows both its power and its limits. For the AES S-box, with 39 quadratic relations available, no exact system of eight, nine, ten, or eleven equations exists; the search confirmed this by testing billions of subsets. Exact twelve-equation systems first appeared among roughly 3.9 billion candidates, and at thirteen equations the search found 611,109 exact systems, the best of which achieved a cost of 109. That unpartitioned run took 13.2 hours on a laptop-class processor, but splitting the enumeration across eight independent partitions reproduced all 611,109 systems and the same eight minimizers, with each partition finishing in roughly 2.5 hours. For the lightweight ciphers ARADI and Ascon, the searches were nearly instant: four equations suffice for ARADI with a cost of just 8, while Ascon yielded 42 exact five-equation systems, the best scoring 19.

The 16-bit MK3 S-box pushed the method to its practical boundary. Exhaustive enumeration of sixteen-equation subsets from 79 relations would require examining roughly 2.16 times ten to the sixteenth power combinations, which is infeasible, and the evaluation table alone occupies 64 gigabytes. The researchers instead used a deletion strategy, removing one equation at a time and verifying with search-global that exactness survived, eventually establishing 28 as an upper bound on the minimum number of equations needed. Verified deletions followed by local optimization reduced the auxiliary-variable count from 1014 to 501. For Ascon, the combination of subset search and local optimization cut the count from 110 to 17, and for ARADI subset search alone reduced it from 71 to 8.

The local optimization stage proved remarkably reliable across hundreds of runs. Fifty sampled AES systems were each evaluated under three configurations, and every one of the 150 runs improved the cost measure, with a median gain of five points and the best system reaching 105. For Ascon, all 42 exact systems were tested under five configurations, improving in 91 percent of the 210 runs with a median gain of two and a best value of 17. For MK3, all 120 runs across two subset sizes improved, with median gains of four. The variance-guided heuristic works because the cost measure includes a logarithmic term, meaning bases that mix very short and very long equations can be advantageous; since an invertible basis change preserves the space spanned by the equations, the linearization-variable count stays fixed and all improvement comes from trimming the counter-bit term.

Beyond the headline numbers, the package is designed as a reproducible, reusable stage in a larger cryptanalytic pipeline. Versioned JSON and JSONL schemas define the persistent interface between stages, streaming output accommodates enormous result collections, and the file holding all 611,109 exact AES systems compresses from 124.7 megabytes to 4.45 megabytes. An 85-test Python suite independently validates equations, metrics, partitioning, and input handling. The authors position the tool as an upstream component rather than a solver: its outputs can feed QUBO models, algebraic attacks, SAT, SMT, and MILP formulations, or Gröbner-basis engines such as PolyBoRi. Current limitations are clearly stated, including support only for relations of degree at most two and memory requirements that scale with the size of the S-box domain. Released under the MIT license with all experimental artifacts, SBoxQUBOSearch turns what was once a bespoke, cipher-specific craft into a systematic search, offering cryptographers a practical head start whenever they need to squeeze a cipher’s innermost component into the variable budget of a quantum annealer.

Subject of Research: Automated search for exact algebraic S-box equation systems to minimize QUBO model size in cryptanalysis

Article Title: SBoxQUBOSearch: Exhaustive subset search and local basis optimization for exact algebraic S-box models

Article References: Burek, E., & Misztal, M. (2026). SBoxQUBOSearch: Exhaustive subset search and local basis optimization for exact algebraic S-box models. SoftwareX, 36, Article 103113. https://doi.org/10.1016/j.softx.2026.103113

Image Credits: AI Generated

DOI: 10.1016/j.softx.2026.103113

Keywords: SBoxQUBOSearch, S-box, cryptography, QUBO, quantum annealing, AES, Ascon, ARADI, MK3, algebraic cryptanalysis, Boolean equations, open-source software

The technique, described in the open-access journal Cybersecurity, is called CL-SCCA, short for Contrastive Learning-based Side-channel Collision Attack. It was developed by Zoushaojie Jiang, An Wang, Annyu Liu, Yaoling Ding, Jingqi Zhang, Jiakun Li, and Liehuang Zhu, most of them affiliated with the Beijing Institute of Technology. Their work targets a family of attacks known as side-channel collision attacks, which were first proposed by Kai Schramm and colleagues back in 2003 as a way of attacking the DES block cipher. The core idea behind collision attacks is elegant: rather than guessing the value of a secret key byte directly, an attacker looks for moments when two different internal operations of a cipher produce the same intermediate value. When two S-box outputs in the Advanced Encryption Standard, for example, collide, the attacker learns that the XOR of the two corresponding key bytes equals the XOR of the two known plaintext bytes. Recover enough of these pairwise relationships, and the entire key space collapses. Instead of searching through an astronomically large key space, the attacker needs only to enumerate a single reference byte, reducing the search to a trivial 256 possibilities.

For two decades, the weak link in collision attacks has been the collision detector itself. Traditional approaches rely on hand-crafted statistical distinguishers, typically correlation coefficients, to measure how similar the power traces of two different byte operations look. The trouble is that real hardware is messy. Noise floods the measurements, leakage signals are nonlinear, and the leakage from one byte position may be shifted in time or distorted in shape compared with another. Under these conditions, simple statistical similarity measures struggle to uncover the hidden shared features that would reveal a genuine collision, and the recovered key relationships become unstable. The result is that collision attacks, despite their theoretical power, have often underperformed in practice.

Deep learning promised to change that. In 2023, Moritz Staib and Amir Moradi introduced DL-SCCA, the first deep learning-based side-channel collision attack. Their insight exploited a structural property of fixed-key encryption: under a fixed key, there is a one-to-one mapping between each plaintext byte and the intermediate S-box value it produces. A neural network can therefore be trained on the traces of one byte position, using plaintext values as labels, and then transferred to the traces of other bytes to infer key differences. This worked, but only up to a point. Because different key bytes are generally different, the same plaintext label can correspond to entirely different intermediate values at different byte positions. Training jointly on multiple bytes using plaintext labels would confuse the model, forcing it to pull together leakage features that actually belong to different secrets. DL-SCCA was therefore confined to learning from a single byte at a time, leaving the richer, multi-byte leakage distribution largely untapped.

This is where contrastive learning enters the picture. Contrastive learning is a self-supervised technique that rose to fame in image recognition, most famously through frameworks like SimCLR. Its central trick is to learn representations without labels: two randomly augmented views of the same input are pulled together in the model’s representation space, while views of different inputs are pushed apart. Applied to power traces, this means the network can learn what makes a trace distinctive without ever being told which plaintext or key produced it. The researchers behind CL-SCCA realized this was exactly the missing ingredient. By pretraining an encoder on unlabeled traces drawn from multiple byte positions simultaneously, the model learns leakage features that are shared across bytes, precisely the transferable, collision-relevant structure that a single-byte supervised model cannot capture.

The technical pipeline is straightforward to describe but carefully engineered. After segmenting full traces into byte-specific leakage windows using sensitivity analysis, the method proceeds in three stages. First comes unsupervised pretraining: each trace is augmented twice using random shifting, random cropping, and random denoising, producing a positive pair, while augmented samples from other traces serve as negatives. A simple multilayer perceptron with four fully connected layers encodes these samples, and a projection head maps them into a 128-dimensional contrastive space where a normalized temperature-scaled cross-entropy loss does the pulling and pushing. Second, the projection head is discarded and a classification head is attached; the model is fine-tuned with plaintext labels from one chosen byte. Third, the fine-tuned model is applied to traces of target bytes, and candidate key differences are ranked by accumulating log-probabilities across attack traces. Notably, the researchers found that this simple MLP architecture outperformed a convolutional network variant, suggesting the gains come from the learning strategy rather than model size.

One subtlety threatened to undermine the whole approach. In a mini-batch mixing traces from several bytes, cross-byte negative samples vastly outnumber same-byte negatives. Because traces from different bytes differ in position, amplitude, and morphology, the model can separate them cheaply using these superficial byte-source cues rather than the fine-grained leakage features that actually matter for collision detection. The team’s solution is a byte-weighted contrastive loss, which assigns a reduced weight, controlled by a coefficient alpha, to cross-byte negative pairs. Gradient analysis shows this scales down the backpropagation contribution of cross-byte pairs, discouraging the model from wasting capacity on byte-identity discrimination. Ablation experiments on the ASCAD_F dataset showed that lowering alpha consistently reduced average key-rank and raised success rates, and t-SNE visualizations confirmed that the learned representations from different bytes overlapped far more when cross-byte repulsion was weakened.

The experimental results are striking. Across three public benchmark datasets, CL-SCCA achieved relative improvements in key-difference recovery success rate of approximately 14.88 percent on ASCAD_F, 77.73 percent on ASCAD_R, and 65.20 percent on DPA Contest v4 compared with the previous state of the art. On both ASCAD variants, the method drove the key-rank of the correct difference to zero for every target byte, meaning the right answer always surfaced at the top of the ranking. The method was not limited to AES: the team collected their own datasets for the Chinese national cipher SM4 on a 16-bit smart card and for the lightweight cipher PRESENT-128 on a 32-bit microcontroller, and in both cases the contrastive approach substantially outperformed DL-SCCA, demonstrating generality across different S-box sizes, cipher structures, and hardware platforms. Comparisons against other self-supervised baselines were equally decisive: an autoencoder-based method managed a recovery success rate below one percent, a Siamese network reached only about fifteen percent, while the byte-weighted variant of CL-SCCA exceeded eighty percent on ASCAD_F.

The study is candid about limits. On DPA Contest v4, which uses rotating S-box masking, cross-byte transfer proved harder: recovery results clustered into groups, and Pearson correlation analysis of group-averaged traces showed that leakage similarity between bytes within a group was high while similarity across groups was near zero. No loss function can erase such inherent leakage differences. The researchers also found that leakage window size matters in a non-monotonic way, with a 700-sample window on ASCAD_F outperforming both smaller and larger choices, because extra trace regions inject irrelevant information. Robustness tests against desynchronization and random delay countermeasures showed the contrastive approach still held the advantage, though the byte-weighted refinement lost its edge when perturbations made same-byte traces differ as much as cross-byte ones.

For defenders, the message is sobering. Masking countermeasures, long considered a robust shield, did not stop these attacks on any of the masked datasets tested. The work signals a broader trend in hardware security: self-supervised learning, which thrives on unlabeled data, is a natural fit for realistic attack scenarios where adversaries cannot easily obtain labeled profiling traces from a clone device. The authors point toward future end-to-end frameworks that would jointly localize leakage, align cross-byte features, and recover keys directly from raw traces. As machine learning continues to lower the expertise and data barriers of side-channel attacks, the race between leakage and countermeasure design is entering a new, faster phase, and the chips guarding our keys will need every advantage physics and mathematics can offer.

Subject of Research: Contrastive learning-based side-channel collision attacks for recovering cryptographic key differences from power traces

Article Title: CL-SCCA: multi-byte contrastive learning for side-channel collision attacks on cryptosystems

Article References: Jiang, Z., Wang, A., Liu, A., Ding, Y., Zhang, J., Li, J., & Zhu, L. (2026). CL-SCCA: multi-byte contrastive learning for side-channel collision attacks on cryptosystems. Cybersecurity, 9(1), Article 232. https://doi.org/10.1186/s42400-026-00658-4

Image Credits: AI Generated

DOI: 10.1186/s42400-026-00658-4

Keywords: side-channel analysis, collision attack, contrastive learning, deep learning, cryptography, AES, SM4, PRESENT, power traces, masking countermeasures, key recovery, self-supervised learning

The research, led by Yong Wang of Wannan Medical University together with colleagues at Anhui Normal University, Bengbu University and Zhejiang University, introduces a scheme called UDSQ, short for user-defined dynamic skyline secure query. At its heart lies a classic problem from multi-criteria database theory known as the skyline query. Given a collection of data points, each described by several attributes, a skyline query returns the set of points that are not dominated by any other point. A point dominates another if it is at least as good in every attribute and strictly better in at least one. In a medical context, imagine searching a database of patient cases for records that minimize both treatment cost and symptom severity while maximizing treatment success. The skyline consists of all cases that no other case beats across that entire combination of criteria, giving clinicians a shortlist of genuinely compelling matches rather than an arbitrary ranking.

What makes the new work distinctive is the word dynamic in its title. In conventional skyline systems, the attributes used for comparison are fixed in advance by the database designer. A patient consulting an online diagnosis service, however, may care about very different things: one might prioritize the experience level of the treating physician, another the proximity of the clinic, a third the cost of medication. UDSQ allows the user to define the region of interest, the set of dimensions and the thresholds that matter to them at query time. The system then restricts the skyline computation to that user-defined region, which has a welcome side effect: by shrinking the search space, it reduces the computational burden and the amount of data that must travel back and forth between the server and the client.

The central obstacle, of course, is that the medical records on the server are supposed to be encrypted. A skyline query appears to require exactly what encryption forbids: comparing values to determine which point dominates which. The authors resolve this tension by combining two cryptographic primitives. The first is order-revealing encryption, a technique that allows a server to compare the relative order of two ciphertexts without being able to decrypt either one. With order-revealing encryption, the server can evaluate dominance relationships among encrypted records, determining whether one encrypted case is better than another across the user’s chosen attributes, while learning nothing about the actual values of cost, severity or success rate.

The second primitive is proxy re-encryption, which addresses a different problem: how a single untrusted server can process queries from many users without each user having to share a secret key with the server. In a proxy re-encryption scheme, a data owner can generate a special transformation key that lets the server convert ciphertexts encrypted under one key into ciphertexts readable under another, without the server ever seeing the plaintext or the original key. In UDSQ, this mechanism allows the diagnosis platform to re-encrypt results so that only the querying patient can read them. Crucially, the authors show that combining proxy re-encryption with a single-server model defends against collusion attacks, scenarios in which a malicious server and a compromised user pool their information in an attempt to reconstruct other patients’ data. Because the transformation keys are structured to prevent any coalition from inverting the encryption, the scheme maintains its privacy guarantees even under this stronger adversary model.

To make the encrypted skyline computation efficient, the researchers designed two dedicated algorithms. The Rectangles Intersection Determination Algorithm, or RIDA, represents the user-defined query region geometrically and determines which candidate data points fall within its boundaries by computing intersections between rectangular regions in the attribute space. Rather than testing every record against every dimension individually, RIDA prunes the candidate set using rectangle intersection tests performed directly on encrypted representations. The Skyline Point Determination Algorithm, or SPDA, then takes the surviving candidates and establishes their dominance relationships in ciphertext, identifying which points belong to the final skyline. The division of labor matters: by separating spatial pruning from dominance testing, the pipeline avoids the quadratic comparisons that plague naive skyline implementations, and the authors report that the combination yields measurable advantages in both communication and computation overhead compared with existing approaches.

The experimental evaluation, conducted on publicly available benchmark datasets rather than real patient records, supports the efficiency claims. Because the study did not involve human participants or new human subject data, the authors note that ethics approval was not applicable, and the use of public benchmarks means the performance figures reflect the algorithms themselves rather than any particular clinical deployment. The reported results indicate that UDSQ reduces the communication cost between client and server, a critical factor for patients in areas with limited bandwidth, while also lowering the computational load on the server. In encrypted-query research, where cryptographic operations typically impose orders-of-magnitude slowdowns, achieving both security and competitive overhead is the benchmark of a practical design.

The implications extend beyond medicine. Skyline queries arise wherever users must choose among multi-attribute alternatives: hotel bookings balancing price, location and rating; investment portfolios balancing risk and return; sensor networks balancing energy consumption and data fidelity. Any of these domains could adopt the user-defined, encrypted paradigm that UDSQ demonstrates. But medicine is the most urgent case, because the stakes of disclosure are highest. A patient’s diagnostic history, once leaked, cannot be changed the way a compromised password can. Regulatory frameworks around the world increasingly demand that health data be protected not only in transit but also during computation, and techniques like order-revealing encryption represent one of the few viable paths to computing on data that remains sealed throughout the process.

Still, the scheme is not a panacea, and honest reporting requires acknowledging the boundaries of what the study demonstrates. Order-revealing encryption, while powerful, leaks the ordering of values by design, and the cryptographic community continues to study what auxiliary information an adversarial server might infer from such leakage when combined with background knowledge. The single-server model simplifies deployment but concentrates trust in one infrastructure provider, even if that provider cannot read the data. And the user-defined nature of the query, while empowering, means that the privacy profile can shift with each new query configuration, a dynamic that future work will need to characterize formally. The authors’ contribution is best understood as a well-engineered point in the design space, one that balances these tensions more favorably than prior schemes while leaving open questions that the field is actively pursuing.

What the study ultimately signals is a maturing of privacy-preserving computation from theoretical curiosity toward deployable infrastructure. The researchers, funded by the doctoral research foundation of Wannan Medical College and the Anhui Province Intelligent Robot Information Fusion and Control Engineering Research Center, have published their work open access, allowing clinicians, cryptographers and system builders to scrutinize and extend it. As online diagnosis platforms expand into regions where they can do the most good, the demand for systems that never force patients to choose between accurate answers and protected data will only grow. UDSQ offers a concrete demonstration that this choice is not inevitable: with the right combination of user control, geometric pruning and modern encryption, the skyline of the best possible medical matches can be computed entirely in the dark, and delivered intact to the one person who holds the key.

Subject of Research: Secure user-defined dynamic skyline queries for privacy-preserving online medical diagnosis

Article Title: UDSQ: a secure and efficient user-defined dynamic skyline query in online medical diagnosis

Article References: Wang, Y., Xu, X., Nie, X., & Peng, G. (2026). UDSQ: a secure and efficient user-defined dynamic skyline query in online medical diagnosis. Journal of Big Data. https://doi.org/10.1186/s40537-026-01581-8

Image Credits: AI Generated

DOI: 10.1186/s40537-026-01581-8

Keywords: skyline query, data security, privacy protection, online medical diagnosis, order-revealing encryption, proxy re-encryption, encrypted queries, cloud computing, database management, collusion attacks, health informatics, cryptography

The research, led by Xinrong Sun of Shandong University together with Yunting Tao of Fudan University and Binzhou Polytechnic, Fanyu Kong and Guoyan Zhang of Shandong University, tackles a dilemma that has grown sharper as machine learning has colonized remote sensing. The state-of-the-art method for segmenting hyper-spectral images, known as joint sparse coding-based clustering, or JSCC, produces remarkably accurate maps of ground targets. But its core phases, dictionary construction and joint sparse recovery, are dominated by large-scale matrix multiplications and matrix pseudo-inversions, operations whose cost explodes as image size and spectral band count grow. For a resource-constrained client, outsourcing those computations to a powerful cloud server is the obvious move, and it is also a dangerous one.

The danger is straightforward: hyper-spectral imagery of a military installation, a disaster zone, or a commercially sensitive mining site is not public data. Handing raw matrices to an untrusted cloud server exposes them to curious operators, lazy servers that might return fabricated results to save money, and outright malicious adversaries who try to reconstruct the original imagery from whatever they observe. Existing cryptographic defenses each carry their own burdens. Secure multi-party computation requires elaborate interactive protocols and numerous secure multiplications. Fully homomorphic encryption inflates data into ciphertexts many times larger than the plaintext and relies on depth-consuming iterative approximations even for something as basic as matrix inversion. For high-dimensional matrix workloads, both approaches can cost more than they save.

That is why the field has long favored a lighter technique called matrix blinding, in which the client disguises its data with secret transformation matrices before sending them out. The trouble with previous blinding schemes, the authors argue, is the secret key itself. To encrypt a data matrix, earlier methods needed at least two large sparse key matrices, one for each dimension, and storing them consumed significant client-side resources. Those storage demands limited how widely the techniques could be deployed and, ultimately, how well the underlying analysis performed. The new work replaces those bulky key matrices with something far leaner: compact index sets that behave like matrices without ever being stored as matrices.

The heart of the scheme is a novel matrix encryption method built from three index sets. Each set contains a random permutation index, its inverse, and a value index of coefficients drawn from randomly generated two-by-two orthogonal transformations. Together these indices let the client perform elementary transformations on the rows and columns of a sensitive matrix, permuting them, scaling them, and mixing adjacent rows or columns, entirely through element-wise arithmetic. Because the orthogonal coefficients satisfy a normalization condition, the transformations are perfectly invertible: applying the corresponding inverse encryption restores the original matrix exactly. Crucially, the index sets are single-use, generated fresh for each encryption task, so no adversary can ever observe two different matrices scrambled by the same key.

The elegance of the design lies in a set of algebraic properties the authors prove formally. Encrypting the columns of one matrix and multiplying it by another is equivalent to multiplying the original matrix by a row-encrypted version of its partner. Encrypting a product is equivalent to encrypting one of its factors. Transposing an encrypted matrix equals encrypting the transposed matrix, and inverting an encrypted matrix equals encrypting the inverse. These associativity, transposition, and inversion properties mean the cloud server can perform ordinary matrix multiplication and pseudo-inversion on the blinded inputs, and the client can decrypt the blinded output to recover exactly the result it would have obtained by computing in the clear. The server learns nothing, because the blinded matrices are computationally indistinguishable from random matrices filled with uniformly distributed noise, a property the authors establish through a formal indistinguishability proof.

Security against cheating is handled by a sampling-based verification method. A lazy or malicious server might return a plausible-looking but incorrect matrix, so the client checks randomly selected columns of the returned result against the encrypted inputs using lightweight element-wise computations, with fresh random weights generated for every verification round. The authors show that any incorrect result slips past a single round of checks with probability at most one half, so after twenty rounds, the setting used in their experiments, the chance of a forged result being accepted falls below one in a million. Verification, like encryption and decryption, never requires the client to touch a full matrix operation.

The performance numbers are striking. Across simulated matrix datasets ranging from modest to very large scales, the new scheme outperformed the leading matrix-blinding competitors by 4.15 to 10.79 percent on average, and beat homomorphic-encryption and multi-party-computation baselines by wider margins on multiplication tasks. Theoretically, the scheme cuts the cost of a matrix multiplication from cubic complexity to a quadratic form, and slashes matrix pseudo-inversion from cubic to linear in the matrix dimensions. When the full JSCC segmentation pipeline was run on five real hyper-spectral datasets, including the well-known Indian Pines, Salinas, Botswana, and Pavia scenes, the outsourced version completed the analysis 73.49 to 80.45 percent faster than the original algorithm, while producing segmentation maps indistinguishable in quality from those computed locally. Numerical errors introduced by the encryption and decryption round-trips were below ten to the minus fourteenth, negligible against the precision of the underlying data.

The team also stress-tested the blinding method itself by building a neural network inversion attacker, a two-stream convolutional and up-convolutional model trained on pairs of original and blinded super-pixel matrices, inspired by techniques for inverting visual representations. Because every matrix is scrambled with independently generated index sets, the attacker could never learn a general inverse mapping. On held-out images the reconstructed outputs showed mean squared errors of roughly 0.026 to 0.052, peak signal-to-noise ratios of only about 13 to 16 decibels, and spectral angle deviations of 23 to 34 degrees, meaning the recovered data lost both fine spatial texture and the spectral direction of the original pixels. In plain terms, the neural network produced blurry, spectrally distorted ghosts rather than usable imagery.

The implications reach beyond satellite imagery. Matrix multiplication and pseudo-inversion sit at the core of many machine learning algorithms, and the authors note that their blinding method applies to any workload dominated by those operations, from K-means clustering to dimensionality reduction, and could support the linear layers of deep networks when combined with secure protocols for non-linear operations. As hyper-spectral sensors proliferate on drones, small satellites, and ground platforms, and as privacy regulation tightens around geospatial data, the ability to rent cloud-scale computation without surrendering cloud-scale secrets may determine who gets to turn raw spectral light into actionable knowledge. This study suggests the key to that future may be nothing more than a handful of cleverly shuffled indices.

Subject of Research: Privacy-preserving cloud outsourcing of hyper-spectral remote sensing image analysis using matrix blinding with index-set keys

Article Title: A privacy-preserving hyper-spectral remote sensing image analysis framework based on matrix outsourcing computation

Article References: Sun, X., Tao, Y., Kong, F., & Zhang, G. (2026). A privacy-preserving hyper-spectral remote sensing image analysis framework based on matrix outsourcing computation. Cybersecurity, 9(1), Article 225. https://doi.org/10.1186/s42400-026-00667-3

Image Credits: AI Generated

DOI: 10.1186/s42400-026-00667-3

Keywords: hyper-spectral imaging, remote sensing, cloud computing, privacy-preserving computation, matrix blinding, matrix outsourcing, secure outsourcing, joint sparse coding, image segmentation, data privacy, cryptography, machine learning