arXiv subjects

Oleksandr Kuznetsov

Publications and source records attributed to Oleksandr Kuznetsov.

At least 19 recordsLinked to original sources

arXiv2026

Dimension Rigidity and Projective Geometry of Trace-Product Switchings of the Gold Cube

We completely classify a natural scalar trace-product switching of the Gold almost perfect nonlinear function $x\mapsto x^3$ in every even dimension. Nontrivial switchings occur only for $n=4,6,8$: the admissible coefficients are, respectively, the nonzero trace-zero elements, the six elements of multiplicative order nine, and $\mathbb{F}_4^{*}$. For every even $n\geq10$, no nonzero coefficient is admissible. The infinite range is excluded by additive-character estimates on a Fermat cubic, with exact finite bridges for $n=10,12$. The raw coefficient lists for $n=6,8$ appeared earlier in Arshad's dissertation; our contribution is their intrinsic description, a proof uniform in the dimension, and the resulting dimension-rigidity theorem. We also classify normalized rank-two extensions in dimension eight by $\mathbb{P}^{1}(\mathbb{F}_4)$. A binary trace selector accepts two coefficient values at each non-base projective point, and the eight accepted marked switchings form exactly two extended-affine, hence two CCZ, classes. A centre-independent low-rank derivative criterion reduces each rank-$r$ candidate to $2^r-1$ membership tests in precomputed forbidden sets. The global APN classes reached are known; the results describe their local organization around the Gold centre and rule out this switching mechanism in all larger even dimensions.

cs.IT↗

arXiv2026

Width, Memory, and Delay: A Resource Accounting for the Limits of Flat Multi-Agent Systems

A recurring question in the design of scalable multi-agent systems -- from robot swarms to collectives of large-language-model (LLM) agents -- is whether adding more agents can, on its own, overcome performance limits, or whether a qualitatively \emph{deeper} organization is required. A recent preprint argues that flat, homogeneous multi-agent systems face an irreducible, population-independent ``causal floor'' on achievable error, removable only by hierarchical (nested-loop) organization. Using a controlled disturbance-rejection testbed with an exactly computable optimum, we show this conclusion is too strong and replace it with a quantitative resource model built on three resources: population \emph{width} $N$, per-agent internal-model \emph{memory} $d$, and prediction across the observation \emph{delay} $\tau$. We establish three claims. (i) The achievable floor is governed not by architectural hierarchy but by per-agent internal-model content: a flat, homogeneous swarm whose agents carry a matched internal model of the disturbance matches or beats a designed two-loop hierarchy at equal per-agent memory -- so temporal depth can be dynamical (recurrent memory), not architectural (nesting). (ii) The three resources are \emph{not mutually interchangeable}; we chart the exchange rates and the hard non-exchange boundaries on an explicit width$\times$memory map, including a strict equal-total-state-budget comparison. (iii) A residual floor is set by the observation delay and the environment's unpredictability over that horizon, which we verify against the optimal controller. We quantify the price of replacing oracle knowledge of the disturbance spectrum with online learning, provide a preliminary robustness check against a mild bounded nonlinearity and a spatially-extended plant, and distill four design rules for practitioners.

cs.MA↗

arXiv2026

Structural Kolmogorov-Arnold Convolutions: Learnable Function on the Values or the Filter Shape as Parameter-Efficient Alternative to Per-Edge Convolutional KANs

Convolutional Kolmogorov--Arnold Networks (KANs) replace the fixed weights of a convolutional kernel with learnable univariate functions. The dominant formulation attaches one such function to every kernel entry and lets it act on pixel values, expressive but parameter-heavy and prone to overfitting. We argue that the learnable functions are better placed in the \emph{structure} of the convolution than on each edge, and we organise the design space along a single axis: whether the function acts on the pixel \emph{values} or on the filter \emph{shape}. We study three realisations. SV-KAN applies one shared univariate function to the values and leaves the spatial filter free and static, aa classical convolution with a single learnable shared activation. AG-KAN keeps the shared value function but supplies the spatial structure through a content-adaptive Gaussian gate. RF-KAN instead moves the learnable functions onto the filter shape, building each filter from oriented ridge profiles expanded in a localised oscillatory (Morlet) wavelet basis with content-adaptive amplitudes. Under a matched four-layer protocol with in-run references and three seeds, RF-KAN and SV-KAN reach $88.47\pm0.10\%$ and $88.20\pm0.31\%$ on CIFAR-10 and $64.40\pm0.19\%$ and $64.57\pm0.30\%$ on CIFAR-100, at about $0.4$M parameters. At this matched scale the shape model and the simplest value model meet at the top, both above a plain convolution and every per-edge KAN we tested, including the official Gram variant, at roughly a fifth of the parameters. A controlled study attributes the RF-KAN gain to an intrinsically localised oscillatory basis and to content adaptivity, and an ablation that removes the learned shape entirely, leaving only the shared value function, collapses accuracy by over forty points, identifying the learned shape as the load-bearing ingredient at this scale.

cs.CV↗

arXiv2026

Quadratic APN Functions in Dimension 8 via Gr\"obner Basis Search in a Self-Equivalence Subspace

We describe a computational search for quadratic APN (Almost Perfect Nonlinear) functions over $\mathbb{F}_{2^8}$ within a structured algebraic subspace defined by a self-equivalence constraint. The search space is the 40-dimensional $\mathbb{F}_2$-linear subspace $V_A = \{F : F \circ A = A \circ F\}$ for a specific linear automorphism $A$ of order 5 (class index 22 in the taxonomy of Beierle, Brinkmann, and Leander); this subspace was previously reported to contain no APN functions under their recursive tree search method. We combine two phases: (1) random sampling inside $V_A$ via an explicit RREF parameterization to find APN center functions, and (2) Groebner basis computation in Magma over the Boolean polynomial ring to enumerate all APN functions in a 24-dimensional hyperplane through each center. From 428 hyperplane computations (covering 0.65% of the 65,536 total hyperplanes in $V_A$) we obtained 566 quadratic APN functions falling into six CCZ-equivalence classes under the ortho-derivative invariant. Four of these classes, comprising 500 functions, match no entry in the Beierle et al. 2025 database of 3,775,599 quadratic APN functions and no entry in the pre-2020 compilation of 12,921 instances. Two classes (66 functions) are identified as CCZ-equivalents of the Gold functions x^3 and x^9, confirming pipeline correctness. For quadratic APN functions, a signature mismatch rigorously certifies CCZ-inequivalence, by Yoshiara's theorem (CCZ = EA for quadratic APN) together with the ortho-derivative invariant; the absence of a signature match in the above databases therefore constitutes a rigorous proof of CCZ-inequivalence for the new classes. The complete dataset, source code, and verification scripts are publicly available.

cs.CR↗

arXiv2026

LUT-Compiled Kolmogorov-Arnold Networks for Lightweight DoS Detection on IoT Edge Devices

Denial-of-Service (DoS) attacks pose a critical threat to Internet of Things (IoT) ecosystems, yet deploying effective intrusion detection on resource-constrained edge devices remains challenging. Kolmogorov-Arnold Networks (KANs) offer a compact alternative to Multi-Layer Perceptrons (MLPs) by placing learnable univariate spline functions on edges rather than fixed activations on nodes, achieving competitive accuracy with fewer parameters. However, runtime B-spline evaluation introduces significant computational overhead unsuitable for latency-critical IoT applications. We propose a lookup table (LUT) compilation pipeline that replaces expensive spline computations with precomputed quantized tables and linear interpolation, dramatically reducing inference latency while preserving detection quality. Our lightweight KAN model (50K parameters, 0.19~MB) achieves 99.0\% accuracy on the CICIDS2017 DoS dataset. After LUT compilation with resolution $L=8$, the model maintains 98.96\% accuracy (F1 degradation $<0.0004$) while achieving $\mathbf{68\times}$ speedup at batch size 256 and over $\mathbf{5000\times}$ speedup at batch size 1, with only $2\times$ memory overhead. We provide comprehensive evaluation across LUT resolutions, quantization schemes, and out-of-bounds policies, establishing clear Pareto frontiers for accuracy-latency-memory trade-offs. Our results demonstrate that LUT-compiled KANs enable real-time DoS detection on CPU-only IoT gateways with deterministic inference latency and minimal resource footprint.

cs.LG↗

arXiv2026

LUT-KAN: Segment-wise LUT Quantization for Fast KAN Inference

Kolmogorov--Arnold Networks (KAN) replace scalar weights by learnable univariate functions, often implemented with B-splines. This design can be accurate and interpretable, but it makes inference expensive on CPU because each layer requires many spline evaluations. Standard quantization toolchains are also hard to apply because the main computation is not a matrix multiply but repeated spline basis evaluation. This paper introduces LUT-KAN, a segment-wise lookup-table (LUT) compilation and quantization method for PyKAN-style KAN layers. LUT-KAN converts each edge function into a per-segment LUT with affine int8/uint8 quantization and linear interpolation. The method provides an explicit and reproducible inference contract, including boundary conventions and out-of-bounds (OOB) policies. We propose an ``honest baseline'' methodology for speed evaluation: B-spline evaluation and LUT evaluation are compared under the same backend optimization (NumPy vs NumPy and Numba vs Numba), which separates representation gains from vectorization and JIT effects. Experiments include controlled sweeps over LUT resolution L in 16, 32, 64, 128 and two quantization schemes (symmetric int8 and asymmetric uint8). We report accuracy, speed, and memory metrics with mean and standard deviation across multiple seeds. A two-by-two OOB robustness matrix evaluates behavior under different boundary modes and OOB policies. In a case study, we compile a trained KAN model for DoS attack detection (CICIDS2017 pipeline) into LUT artifacts. The compiled model preserves classification quality (F1 drop below 0.0002) while reducing steady-state CPU inference latency by 12x under NumPy and 10x under Numba backends (honest baseline). The memory overhead is approximately 10x at L=64. All code and artifacts are publicly available with fixed release tags for reproducibility.

cs.LG↗

arXiv2025

A Production-Ready Machine Learning System for Inclusive Employment: Requirements Engineering and Implementation of AI-Driven Disability Job Matching Platform

Employment inclusion of people with disabilities remains critically low in Italy, with only 3.5% employed nationally despite mandatory hiring quotas. Traditional manual matching processes require 30-60 minutes per candidate, creating bottlenecks that limit service capacity. Our goal is to develop and validate a production-ready machine learning system for disability employment matching that integrates social responsibility requirements while maintaining human oversight in decision-making. We employed participatory requirements engineering with Centro per l'Impiego di Villafranca di Verona professionals. The system implements a seven-model ensemble with parallel hyperparameter optimization using Optuna. Multi-dimensional scoring combines semantic compatibility, geographic distance, and employment readiness assessment. The system achieves 90.1% F1-score and sub-100ms response times while processing 500,000 candidate-company combinations in under 10 minutes. Expert validation confirms 60-100% capacity increases for employment centers. The LightGBM ensemble shows optimal performance with 94.6-second training time. Thus, advanced AI systems can successfully integrate social responsibility requirements without compromising technical performance. The participatory design methodology provides a replicable framework for developing ethical AI applications in sensitive social domains. The complete system, including source code, documentation, and deployment guides, is openly available to facilitate replication and adaptation by other regions and countries facing similar challenges.

cs.CY↗

arXiv2025

Deep Learning Models for Robust Facial Liveness Detection

In the rapidly evolving landscape of digital security, biometric authentication systems, particularly facial recognition, have emerged as integral components of various security protocols. However, the reliability of these systems is compromised by sophisticated spoofing attacks, where imposters gain unauthorized access by falsifying biometric traits. Current literature reveals a concerning gap: existing liveness detection methodologies - designed to counteract these breaches - fall short against advanced spoofing tactics employing deepfakes and other artificial intelligence-driven manipulations. This study introduces a robust solution through novel deep learning models addressing the deficiencies in contemporary anti-spoofing techniques. By innovatively integrating texture analysis and reflective properties associated with genuine human traits, our models distinguish authentic presence from replicas with remarkable precision. Extensive evaluations were conducted across five diverse datasets, encompassing a wide range of attack vectors and environmental conditions. Results demonstrate substantial advancement over existing systems, with our best model (AttackNet V2.2) achieving 99.9% average accuracy when trained on combined data. Moreover, our research unveils critical insights into the behavioral patterns of impostor attacks, contributing to a more nuanced understanding of their evolving nature. The implications are profound: our models do not merely fortify the authentication processes but also instill confidence in biometric systems across various sectors reliant on secure access.

cs.CV↗

arXiv2025

Efficient Denial of Service Attack Detection in IoT using Kolmogorov-Arnold Networks

The proliferation of Internet of Things (IoT) devices has created a pressing need for efficient security solutions, particularly against Denial of Service (DoS) attacks. While existing detection approaches demonstrate high accuracy, they often require substantial computational resources, making them impractical for IoT deployment. This paper introduces a novel lightweight approach to DoS attack detection based on Kolmogorov-Arnold Networks (KANs). By leveraging spline-based transformations instead of traditional weight matrices, our solution achieves state-of-the-art detection performance while maintaining minimal resource requirements. Experimental evaluation on the CICIDS2017 dataset demonstrates 99.0% detection accuracy with only 0.19 MB memory footprint and 2.00 ms inference time per sample. Compared to existing solutions, KAN reduces memory requirements by up to 98% while maintaining competitive detection rates. The model's linear computational complexity ensures efficient scaling with input size, making it particularly suitable for large-scale IoT deployments. We provide comprehensive performance comparisons with recent approaches and demonstrate effectiveness across various DoS attack patterns. Our solution addresses the critical challenge of implementing sophisticated attack detection on resource-constrained devices, offering a practical approach to enhancing IoT security without compromising computational efficiency.

cs.CR↗

arXiv2024

Efficient Zero-Knowledge Proofs for Set Membership in Blockchain-Based Sensor Networks: A Novel OR-Aggregation Approach

Blockchain-based sensor networks offer promising solutions for secure and transparent data management in IoT ecosystems. However, efficient set membership proofs remain a critical challenge, particularly in resource-constrained environments. This paper introduces a novel OR-aggregation approach for zero-knowledge set membership proofs, tailored specifically for blockchain-based sensor networks. We provide a comprehensive theoretical foundation, detailed protocol specification, and rigorous security analysis. Our implementation incorporates optimization techniques for resource-constrained devices and strategies for integration with prominent blockchain platforms. Extensive experimental evaluation demonstrates the superiority of our approach over existing methods, particularly for large-scale deployments. Results show significant improvements in proof size, generation time, and verification efficiency. The proposed OR-aggregation technique offers a scalable and privacy-preserving solution for set membership verification in blockchain-based IoT applications, addressing key limitations of current approaches. Our work contributes to the advancement of efficient and secure data management in large-scale sensor networks, paving the way for wider adoption of blockchain technology in IoT ecosystems.

cs.CR↗

arXiv2024

Unrecognizable Yet Identifiable: Image Distortion with Preserved Embeddings

Biometric authentication systems play a crucial role in modern security systems. However, maintaining the balance of privacy and integrity of stored biometrics derivative data while achieving high recognition accuracy is often challenging. Addressing this issue, we introduce an innovative image transformation technique that effectively renders facial images unrecognizable to the eye while maintaining their identifiability by neural network models, which allows the distorted photo version to be stored for further verification. While initially intended for biometrics systems, the proposed methodology can be used in various artificial intelligence applications to distort the visual data and keep the derived features close. By experimenting with widely used datasets LFW and MNIST, we show that it is possible to build the distortion that changes the image content by more than 70% while maintaining the same recognition accuracy. We compare our method with previously state-of-the-art approaches. We publically release the source code.

cs.CV↗

arXiv2024

Probabilistic Analysis and Empirical Validation of Patricia Tries in Ethereum State Management

This study presents a comprehensive theoretical and empirical analysis of Patricia tries, the fundamental data structure underlying Ethereum's state management system. We develop a probabilistic model characterizing the distribution of path lengths in Patricia tries containing random Ethereum addresses and validate this model through extensive computational experiments. Our findings reveal the logarithmic scaling of average path lengths with respect to the number of addresses, confirming a crucial property for Ethereum's scalability. The study demonstrates high precision in predicting average path lengths, with discrepancies between theoretical and experimental results not exceeding 0.01 across tested scales from 100 to 100,000 addresses. We identify and verify the right-skewed nature of path length distributions, providing insights into worst-case scenarios and informing optimization strategies. Statistical analysis, including chi-square goodness-of-fit tests, strongly supports the model's accuracy. The research offers structural insights into node concentration at specific trie levels, suggesting avenues for optimizing storage and retrieval mechanisms. These findings contribute to a deeper understanding of Ethereum's fundamental data structures and provide a solid foundation for future optimizations. The study concludes by outlining potential directions for future research, including investigations into extreme-scale behavior, dynamic trie performance, and the applicability of the model to non-uniform address distributions and other blockchain systems.

cs.CR↗

arXiv2024

Evolutionary Approach to S-box Generation: Optimizing Nonlinear Substitutions in Symmetric Ciphers

This study explores the application of genetic algorithms in generating highly nonlinear substitution boxes (S-boxes) for symmetric key cryptography. We present a novel implementation that combines a genetic algorithm with the Walsh-Hadamard Spectrum (WHS) cost function to produce 8x8 S-boxes with a nonlinearity of 104. Our approach achieves performance parity with the best-known methods, requiring an average of 49,399 iterations with a 100% success rate. The study demonstrates significant improvements over earlier genetic algorithm implementations in this field, reducing iteration counts by orders of magnitude. By achieving equivalent performance through a different algorithmic approach, our work expands the toolkit available to cryptographers and highlights the potential of genetic methods in cryptographic primitive generation. The adaptability and parallelization potential of genetic algorithms suggest promising avenues for future research in S-box generation, potentially leading to more robust, efficient, and innovative cryptographic systems. Our findings contribute to the ongoing evolution of symmetric key cryptography, offering new perspectives on optimizing critical components of secure communication systems.

cs.CR↗

arXiv2024

Scalable Zero-Knowledge Proofs for Verifying Cryptographic Hashing in Blockchain Applications

Zero-knowledge proofs (ZKPs) have emerged as a promising solution to address the scalability challenges in modern blockchain systems. This study proposes a methodology for generating and verifying ZKPs to ensure the computational integrity of cryptographic hashing, specifically focusing on the SHA-256 algorithm. By leveraging the Plonky2 framework, which implements the PLONK protocol with FRI commitment scheme, we demonstrate the efficiency and scalability of our approach for both random data and real data blocks from the NEAR blockchain. The experimental results show consistent performance across different data sizes and types, with the time required for proof generation and verification remaining within acceptable limits. The generated circuits and proofs maintain manageable sizes, even for real-world data blocks with a large number of transactions. The proposed methodology contributes to the development of secure and trustworthy blockchain systems, where the integrity of computations can be verified without revealing the underlying data. Further research is needed to assess the applicability of the approach to other cryptographic primitives and to evaluate its performance in more complex real-world scenarios.

cs.CR↗

arXiv2024

Efficient and Universal Merkle Tree Inclusion Proofs via OR Aggregation

Zero-knowledge proofs have emerged as a powerful tool for enhancing privacy and security in blockchain applications. However, the efficiency and scalability of proof systems remain a significant challenge, particularly in the context of Merkle tree inclusion proofs. Traditional proof aggregation techniques based on AND logic suffer from high verification complexity and data communication overhead, limiting their practicality for large-scale applications. In this paper, we propose a novel proof aggregation approach based on OR logic, which enables the generation of compact and universally verifiable proofs for Merkle tree inclusion. By aggregating proofs using OR logic, we achieve a proof size that is independent of the number of leaves in the tree, and verification can be performed using any single valid leaf hash. This represents a significant improvement over AND aggregation, which requires the verifier to process all leaf hashes. We formally define the OR aggregation logic, describe the process of generating universal proofs, and provide a comparative analysis demonstrating the advantages of our approach in terms of proof size, verification data, and universality. Furthermore, we discuss the potential of combining OR and AND aggregation logics to create complex acceptance functions, enabling the development of expressive and efficient proof systems for various blockchain applications. The proposed techniques have the potential to significantly enhance the scalability, efficiency, and flexibility of zero-knowledge proof systems, paving the way for more practical and adaptive solutions in the blockchain ecosystem.

cs.CR↗

arXiv2024

Evaluating the Security of Merkle Trees in the Internet of Things: An Analysis of Data Falsification Probabilities

Addressing the critical challenge of ensuring data integrity in decentralized systems, this paper delves into the underexplored area of data falsification probabilities within Merkle Trees, which are pivotal in blockchain and Internet of Things (IoT) technologies. Despite their widespread use, a comprehensive understanding of the probabilistic aspects of data security in these structures remains a gap in current research. Our study aims to bridge this gap by developing a theoretical framework to calculate the probability of data falsification, taking into account various scenarios based on the length of the Merkle path and hash length. The research progresses from the derivation of an exact formula for falsification probability to an approximation suitable for cases with significantly large hash lengths. Empirical experiments validate the theoretical models, exploring simulations with diverse hash lengths and Merkle path lengths. The findings reveal a decrease in falsification probability with increasing hash length and an inverse relationship with longer Merkle paths. A numerical analysis quantifies the discrepancy between exact and approximate probabilities, underscoring the conditions for the effective application of the approximation. This work offers crucial insights into optimizing Merkle Tree structures for bolstering security in blockchain and IoT systems, achieving a balance between computational efficiency and data integrity.

cs.CR↗

arXiv2024

AttackNet: Enhancing Biometric Security via Tailored Convolutional Neural Network Architectures for Liveness Detection

Biometric security is the cornerstone of modern identity verification and authentication systems, where the integrity and reliability of biometric samples is of paramount importance. This paper introduces AttackNet, a bespoke Convolutional Neural Network architecture, meticulously designed to combat spoofing threats in biometric systems. Rooted in deep learning methodologies, this model offers a layered defense mechanism, seamlessly transitioning from low-level feature extraction to high-level pattern discernment. Three distinctive architectural phases form the crux of the model, each underpinned by judiciously chosen activation functions, normalization techniques, and dropout layers to ensure robustness and resilience against adversarial attacks. Benchmarking our model across diverse datasets affirms its prowess, showcasing superior performance metrics in comparison to contemporary models. Furthermore, a detailed comparative analysis accentuates the model's efficacy, drawing parallels with prevailing state-of-the-art methodologies. Through iterative refinement and an informed architectural strategy, AttackNet underscores the potential of deep learning in safeguarding the future of biometric security.

cs.CV↗

arXiv2024

Adaptive Restructuring of Merkle and Verkle Trees for Enhanced Blockchain Scalability

The scalability of blockchain technology remains a pivotal challenge, impeding its widespread adoption across various sectors. This study introduces an innovative approach to address this challenge by proposing the adaptive restructuring of Merkle and Verkle trees, fundamental components of blockchain architecture responsible for ensuring data integrity and facilitating efficient verification processes. Unlike traditional static tree structures, our adaptive model dynamically adjusts the configuration of these trees based on usage patterns, significantly reducing the average path length required for verification and, consequently, the computational overhead associated with these processes. Through a comprehensive conceptual framework, we delineate the methodology for adaptive restructuring, encompassing both binary and non-binary tree configurations. This framework is validated through a series of detailed examples, demonstrating the practical feasibility and the efficiency gains achievable with our approach. Moreover, we present a comparative analysis with existing scalability solutions, highlighting the unique advantages of adaptive restructuring in terms of simplicity, security, and efficiency enhancement without introducing additional complexities or dependencies. This study's implications extend beyond theoretical advancements, offering a scalable, secure, and efficient method for blockchain data verification that could facilitate broader adoption of blockchain technology in finance, supply chain management, and beyond. As the blockchain ecosystem continues to evolve, the principles and methodologies outlined herein are poised to contribute significantly to its growth and maturity.

cs.CR↗