Search Results (155)

Orthogonal direct sum masking (ODSM) protects embedded cryptographic implementations against side-channel attacks by splitting the ambient space into a source code C carrying sensitive data and a complementary masking code D carrying fresh randomness; when $D=C^{\perp }$, C must be a linear complementary dual (LCD) code. Much of the literature evaluates the masking code primarily through the minimum distance $d\left(D^{\perp }\right)=d\left(C\right)$ of its dual, treating this parameter as the quantitative summary of leakage resistance under a Hamming-weight leakage model. We show, first computationally and then via a general algebraic theorem, that this one parameter does not determine the variance of the masking code’s Hamming-weight distribution: cyclic codes with identical $d\left(C\right)$ can differ by close to an order of magnitude in this variance. We prove, for an arbitrary cyclic code $C\subseteq \mathrm{GF}{\left(q\right)}^n$ with nonzero dual $D=C^{\perp }$ and defining set T (the LCD property is not required for this algebraic result and is invoked only for the ODSM application), a closed-form theorem expressing ${\mathrm{Var}}_{c\in D}\left[\mathrm{wt}\left(c\right)\right]$ exactly as $(q-1)n^2/\left(q^{2}L\left(T\right)\right)$, where $L\left(T\right)$ is an intrinsically defined, representative-independent arithmetic invariant of T, computable via a single least-common-multiple of greatest-common-divisors and requiring no exponential-sum or Gauss-period evaluation. We verify the formula, with an explicit worked example, reproducible from the displayed defining sets, and zero discrepancies, against 64 independently constructed LCD cyclic codes spanning two finite fields and three code lengths. We are explicit that this variance is a second-order algebraic descriptor of leakage dispersion under an idealized leakage model, not a complete side-channel security metric; the connection to physical Hamming-weight leakage is direct for $q=2$; for $q>2$, the result stands as an exact coding-theoretic characterization whose relevance to physical bit-level leakage depends on an explicit bit-encoding model not developed here. We discuss its role as a design diagnostic for ODSM masking codes. This paper is, at its core, a contribution to the algebraic theory of cyclic codes: the reduction of the variance to a weight-two-codeword count is the classical Pless moment identity, and our closed-form arithmetic characterization of that count via $L\left(T\right)$ is algebraically equivalent, on its domain, to a 2024 result of Coelho and Brochero Martínez; we extend it to arbitrary cyclic length and arbitrary prime-power base fields, and position it as a complement to, not a replacement for, the more operational dual-distance/kissing-number methodology already used in the code-based masking literature. Full article

Palm-vein recognition is an attractive biometric modality for secure access control because its subcutaneous vascular patterns are difficult to observe and reproduce externally. However, existing studies optimize the recognition algorithm and the hardware accelerator in isolation, and rarely satisfy the on-chip memory and energy constraints of edge devices. This paper presents a hardware-aware co-design of a lightweight FPGA accelerator for palm-vein recognition, in which the network is shaped by the cost structure of the target fabric and the inference engine is organized around the resulting layer shapes. On the algorithm side, a hardware-aware neural architecture search with deployment cost terms is combined with divisor-aligned structured pruning and INT8 quantization-aware training. Structured pruning reduces the model parameters to 0.32 M and the MACs to 87.2 M while preserving recognition accuracy. On the hardware side, a task-specific design space exploration selects a $14\times 12$ systolic array and an output-stationary dataflow that keeps all feature maps and weights on chip and reduces the modeled buffer-access count by 34.6% relative to the best alternative stationary dataflow. Implemented on a Xilinx Zynq-7100 at 100 MHz, the deployed INT8 checkpoint attains an accuracy of 99.50%, with a PL inference latency of 33.03 ms and an energy efficiency of 33.27 FPS/W. Full article

The Sombor index has recently become a central tool among degree-based graph invariants; however, it does not explicitly isolate degree imbalance along edges. In this work, we introduce the degree-based Contrastive Sombor Index (CSO), which combines endpoint-degree magnitude with local degree imbalance. For a finite simple graph $G=(V,E)$, the index is defined by $\mathrm{CSO}\left(G\right)={\displaystyle \sum _{uv\in E\left(G\right)}}\left(\sqrt{d{\left(u\right)}^2+d{\left(v\right)}^2}-\sqrt{2}\min \{d\left(u\right),d\left(v\right)\}\right).$ Unlike the Sombor index, which primarily reflects the magnitude of the endpoint degrees, the CSO contribution vanishes when the endpoint degrees are equal and responds to degree imbalance while retaining degree-scale information. In particular, it can distinguish certain graphs having the same total edgewise irregularity but different endpoint-degree distributions. In this work, we first show that $CSO\left(G\right)\ge 0$ and prove that $CSO\left(G\right)=0$ if and only if each connected component of G is regular. We also establish general lower and upper bounds for CSO. In addition, we obtain a relation connecting the CSO index with the first Zagreb index and the edgewise degree differences. We also discuss extremal aspects of the index. As an application, we derive an explicit summation formula for CSO on monogenic semigroup graphs. From our computations on $\Gamma \left(S_M\right)$, it follows that the asymptotic growth order of the index satisfies $CSO(\Gamma \left(S_M\right))=\Theta \left(n^3\right).$ These results show that the CSO index combines degree-magnitude information with sensitivity to unequal endpoint degrees and provides an additional perspective on degree heterogeneity in graphs. Full article

Let $\mathcal{P}$ be a finite commutative ring with identity, and let $Z\left(\mathcal{P}\right)$ denote the set of its zero-divisors. The extended zero-divisor graph of $\mathcal{P}$, denoted by $\tilde{\Gamma }\left(\mathcal{P}\right)$, is the undirected simple graph with vertex set $Z{\left(\mathcal{P}\right)}^{*}=Z\left(\mathcal{P}\right)\setminus \left\{0\right\}$, where two distinct vertices $\alpha$ and $\beta$ are adjacent if and only if $\alpha \beta =0$ or $\alpha +\beta \in Z\left(\mathcal{P}\right)$. For a graph G, let $L\left(G\right)$ denote its line graph. In this paper, we first characterize all finite commutative rings $\mathcal{P}$ for which $\tilde{\Gamma }\left(\mathcal{P}\right)$ is a line graph of some graph. We then classify the finite commutative rings $\mathcal{P}$ such that $L\left(\tilde{\Gamma }\left(\mathcal{P}\right)\right)$ is planar, outerplanar, or 2-outerplanar. Finally, we obtain a complete classification of finite commutative rings $\mathcal{P}$ for which $L\left(\tilde{\Gamma }\left(\mathcal{P}\right)\right)$ is toroidal. Full article

Periodic resource reservation underpins vehicular sidelink traffic, yet its compatibility is inherently asymmetric. In New Radio (NR) sidelink Mode 1, two configured grant (CG) streams collide if and only if the greatest common divisor (GCD) of their periods divides their offset difference, so coprime periods cannot be separated by any offset on a single subchannel. Admission opportunity is thus governed by the arithmetic of the period set, not by load alone—a disparity we call schedulability asymmetry. We propose Divisor-Aligned Period Decomposition (DAPD), which fixes a common divisor d and reduces coexistence to a closed-form GCD test: periods that are multiples of d are admitted directly, and incompatible ones are reshaped into a d-aligned substitute within the delay budget rather than rejected. This levels the schedulability asymmetry at its source for any catalog period whose delay budget admits a d-compatible substitute: once every request is represented on a common divisor, no period is structurally disadvantaged, so such a period can be admitted regardless of its arithmetic relationship to the others. Under a collision-only scheduler model that isolates deterministic reservation collisions from physical-layer effects, every admitted CG is collision-free by construction. An extension, DAPD+, salvages the resulting slack with dynamic grants that never overlap an admitted CG. In simulation over 1000 seeds across vehicle densities up to subchannel saturation, DAPD+ attains the highest overall packet delivery ratio among all evaluated schedulers, including an oracle offset optimizer and a recent multi-configuration CG scheduler, while holding admitted-CG delivery at one and keeping far more per-vehicle delivery ratios above target, where the reactive baseline’s per-vehicle reliability collapses with density. DAPD+ thus serves the largest volume of periodic traffic at high reliability without sacrificing aggregate throughput, equalizing admission opportunity across heterogeneous periods. Full article

Let $\mathcal{P}$ be a commutative ring with identity, and denote by $\mathcal{D}\left(\mathcal{P}\right)$ the collection of all zero-divisors of $\mathcal{P}$. An ideal $\mathcal{A}$ of $\mathcal{P}$ is called an essential ideal if its intersection with every nontrivial ideal of $\mathcal{P}$ is nonzero. In such a case, we write $\mathcal{A}{\le }_e\mathcal{P}$. The generalized zero-divisors graph of $\mathcal{P}$, denoted by ${\mathrm{\Gamma }}_g\left(\mathcal{P}\right)$, is defined as the simple undirected graph whose vertex set is $\mathcal{D}{\left(\mathcal{P}\right)}^{\ast }=\mathcal{D}\left(\mathcal{P}\right)\setminus \left\{0\right\}$. For two distinct vertices $\mu$ and $\sigma$, an edge joins them precisely when the sum of their annihilator ideals, namely $Ann\left(\mu \right)+Ann\left(\sigma \right)$, forms an essential ideal of $\mathcal{P}$. This work begins by identifying all finite commutative rings with identity whose generalized zero-divisors graph possesses outerplanarity index equal to 2. Subsequently, we provide a complete classification of finite commutative rings $\mathcal{P}$ for which ${\mathrm{\Gamma }}_g\left(\mathcal{P}\right)$ admits embeddings as a double-toroidal graph, a projective-plane graph, or a Klein-bottle graph. In addition, the book thickness of ${\mathrm{\Gamma }}_g\left(\mathcal{P}\right)$ is established for the class of graphs with genus of at most one. Full article

Existing AISI S100 provisions for cold-formed steel (CFS) screw connections lack codified strength equations for screw shear and net section fracture, and traditional machine learning (ML) models struggle to predict these minority failure modes due to imbalanced experimental datasets. This study proposes a cascaded ML framework that first classifies the failure mode and then predicts strength using mode-specific regressors. Two cascade strategies are evaluated: a Hard Classification Cascade (HC-C) and a novel Probability-Weighted Cascade (PW-C) that weights predictions by class probabilities to mitigate error propagation from misclassification. The predictive performance of the two cascaded models is benchmarked against a single regressor without classification. The superior PW-C model is then compared with AISI S100, and its resistance factor ϕ is subsequently calibrated in accordance with LRFD. Results show that the proposed cascaded models outperform the direct regression model, with PW-C improving the R² for minority-class screw shear from 0.765 to 0.933 and for net section fracture from 0.784 to 0.912. Compared with AISI S100 provisions, PW-C extends coverage to the currently unaddressed failure modes and effectively captures screw group effects on shear strength based on a database of 564 tests. Reliability analysis yields an overall ϕ_c of 0.64 for the PW-C model, with a recommended divisor of 1.15 for direct application within the AISI design framework. This work provides a practical, data-driven pathway for updating design codes to cover failure modes beyond current specification limits. Full article

Let k be a positive integer. A polynomial $A\in {\mathbb{F}}_2\left[x\right]$ is called k-unitary perfectif the sum of the k-th powers of its distinct unitary divisors equals $A^k$. In this paper, we study the case $k=2^n$ and prove that every $2^n$-unitary perfect polynomial over ${\mathbb{F}}_2$ is even. Moreover, we completely classify all even $2^n$-unitary perfect polynomials having at most three distinct irreducible factors. In particular, we characterize all such polynomials of the form $A=x^a{(x+1)}^b{P}^h$, where P is a Mersenne prime over ${\mathbb{F}}_2$ and $a,b,h\in \mathbb{N}$. As a consequence, several explicit infinite families of k-unitary perfect polynomials over ${\mathbb{F}}_2$ are obtained. Full article

To mitigate the structural amplification of random false alarms during multi-pulse repetition frequency (Multi-PRF) ambiguity resolution, this paper proposes a general waveform synthesis optimization framework based on Bezout’s Identity and Genetic Algorithm (Bezout-GA). By leveraging Bezout’s Theorem, the framework establishes an analytical mapping between the Greatest Common Divisor (GCD) topology of transmission parameters and system-level false alarm boundaries. It is mathematically demonstrated that the uncontrolled inflation of the Least Common Multiple (LCM) in traditional coprime-based strategies leads to severe “spatial over-issuance” of false alarms, a phenomenon particularly exacerbated in heavy-tailed K-distributed sea clutter. The proposed two-stage hybrid paradigm employs a genetic algorithm for global multi-objective search, followed by local number-theoretic refinement via the Extended Euclidean Algorithm to strictly satisfy hardware constraints. Simulations across X-band and L-band scenarios confirm the framework’s superior spectral generalizability. Results indicate that the Bezout-GA optimized waveform achieves a 4.1-fold reduction in expected false alarm volume at the cost of a negligible 0.1% clear-region sacrifice. Notably, in extreme K-distributed clutter ($\nu =0.1$), the framework reclaims an equivalent signal-to-clutter-and-noise ratio (SCNR) gain of up to 3 dB in the L-band, significantly outperforming traditional coprime and maximum clear-region benchmarks. Overall, this study provides a number-theoretic perspective for analyzing spatial false alarm mechanisms and serves as a methodological reference for future investigations into robust Multi-PRF waveform optimization. Full article

Assuming the coefficient matrix is a nonzero singular matrix, we demonstrate that the invertible solutions of the Yang–Baxter-like matrix equation must possess at least two elementary divisors. This establishes a necessary condition for an invertible matrix to satisfy the Yang–Baxter-like matrix equation. Building on this finding, we derive several meaningful corollaries. Additionally, we provide some examples to illustrate our results. Full article

Integer factorization plays a foundational role in asymmetric cryptography systems, notably the Rivest, Shamir, and Adleman (RSA) cryptosystem. This paper presents an improvement of the integer factorization from both sequential and parallel computational perspectives. The algorithm is based on polynomial evaluation and the greatest common divisor. The objectives of these improvements are to decrease the execution time and memory consumption associated with the process of finding prime factors. Experimentally, we use different values of parameters (1) the number of bits n, (2) the difference between two factors, and (3) the number of processors in the parallel model. The experimental results indicate that both proposed methods, sequential and parallel, yield significant improvements regarding running time and memory usage when the difference between the two factors is $n^{1/3}$ and $n^{1/4}$. The average improvement observed is $99\%$ in running time, with memory consumption reduced to a constant. This characteristic is important for limited hardware devices. Furthermore, the proposed parallel method demonstrates scalability and achieves sublinear speedup. Full article

Let $1\ne 0$ be the identity of the commutative ring R. The cozero-divisor graph of a ring R is an undirected simple graph, represented by ${\mathsf{\Gamma }}^{\prime }\left(R\right)$, where two different vertices g and h are adjacent if and only if $g\notin Rh$ and $h\notin Rg$. The vertices of this graph are given by the set of all non-zero and non-unit elements of R. The definition of a graph G’s $A_{\alpha }$ matrix is $A_{\alpha }\left(G\right)=\alpha D\left(G\right)+(1-\alpha )A\left(G\right)$, where $\alpha \in [0,1],D\left(G\right)=diag(deg\left(c_1\right),deg\left(c_2\right),\dots ,deg\left(c_n\right))$ is the diagonal matrix and $A\left(G\right)$ is the adjacency matrix of graph G. In this article, we calculate the sum-connectivity F-index, product-connectivity F-index of ${\mathsf{\Gamma }}^{\prime }\left({\mathbb{Z}}_n\right)$, when $n={\zeta }_1{\zeta }_2,{\zeta }_1^2{\zeta }_2,{\zeta }_1{\zeta }_2{\zeta }_3$, and the $A_{\alpha }$ eigenvalues of ${\mathsf{\Gamma }}^{\prime }\left({\mathbb{Z}}_n\right)$ for $n={{\zeta }_1}^{u_1}{\zeta }_2{\zeta }_3$, where ${\zeta }_1,{\zeta }_2$, ${\zeta }_3$ are distinct primes. Full article

The harmonic structure of a chord C composed of rational frequency ratios is studied from its tonal graph. The graph describes harmoncity/periodicity properties of the chord allowing to characterize the chord from several parameters, which are easily visualized by the chord spheroid. Relevant harmonic structures are analyzed, such as self-symmetric graphs associated with harmonically symmetric chords. Recurrence relationships for the 1cm$\left(C\right)$ in terms of the gcd’s of the powerset of C, and for the $\gcd \left(C\right)$ in terms of the lcm’s, are derived to unveil how the harmonic quotient lcm$\left(C\right)/\gcd \left(C\right)$ depends on the common undertones and overtones. In particular, for any number of tones, the harmonic quotient can be univocally expressed from the chord’s common undertones. Therefore, although undertones and overtones have not been explicitly taken into account in the current model, the harmonic quotient actually incorporates information about them. Full article

This paper establishes a graph-theoretic framework for idealization semigroups arising from Bruck–Reilly extensions. Building on a recent study by Wazzan and Ozalan, we introduce five graph families—${\Gamma }_E$, ${\Gamma }_0$, ${\Gamma }_{\mathrm{Cay}}$, ${\Gamma }_{\mathcal{K}}$, and $\Gamma \left(G_k\right)$—each encoding a distinct algebraic facet of $S{B}_i(\bowtie )B$. We prove explicit correspondences linking combinatorial invariants to algebraic structure: diameter captures generating efficiency and semilattice height; girth signals short relations; chromatic number bounds idempotent cardinalities and $\mathcal{D}$-class counts; clique number measures maximal commuting subsets; and Laplacian spectra encode ideal size and Schützenberger groups. Our central result demonstrates that Green’s relations are combinatorially recoverable from graph pairs. For commutative $S{B}_i(\bowtie )B$, $({\Gamma }_E,{\Gamma }_{\mathcal{K}})$ uniquely determines $\mathcal{J}$-order, $\mathcal{D}$-classes, and $\mathcal{H}$-classes via neighborhood inclusions, bipartite components, and automorphism orbits, yielding the first algorithmic reconstruction of ideal-theoretic structure from graph data. The framework is implemented in SageMath as a reproducible open-source toolkit validated on concrete examples. This work synthesizes algebraic graph theory, semigroup theory, and computational mathematics into a unified algebraic-combinatorial dictionary, providing both new analytical tools and a methodological template for studying algebraic constructions via graph invariants. Full article

Let G be a finite group. The vertex set of the prime-power graph of G is defined as $V\left(G\right)=\left\{p^{e_p\left(G\right)}|p\in \rho \left(G\right)\right\}$, where $\rho \left(G\right)$ is the set of all prime divisors of the degrees of all irreducible characters of G and $p^{e_p\left(G\right)}=max\left\{\psi {\left(1\right)}_p\mid \psi \in Irr\left(G\right)\right\}$. It has been proved that the simple groups $L_3\left(p\right)$ can be characterized by its orders and vertex set of prime-power graphs. In this paper, we continue this topic and prove that $L_3\left(p^2\right)$ can be uniquely characterized by its orders and degree prime-power graphs, where p is a prime. Full article