Article
Computer Science, Hardware & Architecture
Kai Song, Wen Li, Boyang Zhang, Liping Yan, Xianchao Wang
Summary: This paper applies the Jacobi iterative algorithm to a ternary optical computer and constructs a parallel design scheme to improve the efficiency of solving large linear equations. The experiment demonstrates that the parallel design has obvious advantages in computing speed, providing a new method for fast solution of large linear equations.
JOURNAL OF SUPERCOMPUTING
(2022)
Article
Computer Science, Software Engineering
Siyu Chen, Qingtang Su, Huanying Wang, Gang Wang
Summary: The algorithm efficiently processes double color images using Walsh Hadamard transform, embedding and extracting digital watermarks by adjusting frequency domain matrix coefficients. It demonstrates superior performance in invisibility, robustness, watermark capacity, and running time based on extensive simulation results.
Article
Computer Science, Theory & Methods
Jinjin Chai, Zilong Wang, Erzhong Xue
Summary: This paper studies the spectrum distribution of binary and quaternary Golay complementary arrays and shows that these arrays can only be constructed from Boolean functions satisfying specific spectral values. Additionally, constructing new binary and quaternary complementary arrays may lead to the discovery of new Boolean functions with specific conditions.
DESIGNS CODES AND CRYPTOGRAPHY
(2021)
Article
Computer Science, Theory & Methods
Marko Djurasevic, Domagoj Jakobovic, Luca Mariot, Stjepan Picek
Summary: Boolean functions are mathematical objects that have been actively researched for several decades and play an important role in cryptography. This survey focuses on metaheuristic approaches to constructing Boolean functions and examines related works from the past 25 years. It provides a new taxonomy of related works and discusses the obtained results. Future research directions in this area are also discussed.
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
(2023)
Article
Mathematics, Applied
Aditi Kar Gangopadhyay, Vikas Kumar, Pantelimon Stanica, Sugata Gangopadhyay
Summary: In this article, we propose a concept of stability for the Walsh-Hadamard spectrum of Boolean functions. We investigate the stability spectrum of bent Boolean functions and derive a bound for it. Additionally, we obtain the formula for the stability transform of Maiorana-McFarland type bent functions. We analyze the stability spectrum of symmetric Boolean functions, characterizing it for symmetric bent Boolean functions and symmetric Boolean functions in an odd number of variables with maximum nonlinearity. Furthermore, we demonstrate that the stability spectrum is not generally invariant under extended affine transformations, and present some non-bent symmetric Boolean functions with flatter stability spectra than that of symmetric bent Boolean functions.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2023)
Article
Mathematics, Applied
Vikas Kumar, Bimal Mandal, Aditi Kar Gangopadhyay
Summary: This article investigates the recursive relation between the Gowers U2 and U3 norms of Boolean functions and their restriction to hyperplanes, which aids in analyzing the second and third-order Gowers norms of Boolean functions in a higher number of variables.
DISCRETE APPLIED MATHEMATICS
(2023)
Article
Computer Science, Theory & Methods
Fei Guo, Zilong Wang, Guang Gong
Summary: In this paper, three secondary methods for constructing bent-negabent functions under different frameworks are presented. The necessary and sufficient conditions for generating these functions are analyzed. Several constructions are proposed based on these frameworks.
DESIGNS CODES AND CRYPTOGRAPHY
(2023)
Article
Computer Science, Hardware & Architecture
Shuang Li, Wenjing Li, Zhehe Wang, Dongdong An
Summary: Researched and implemented a TOC-based artificial fish swarm algorithm that improves the search performance of complex multi-peaked function optimization problems through parallel design and utilization of high-performance processor bits.
MOBILE NETWORKS & APPLICATIONS
(2022)
Article
Computer Science, Theory & Methods
Sampada Tiwari, Deepmala Sharma
Summary: This study determines the lower bound for the higher-order nonlinearity of two classes of Boolean functions, which are crucial in security analysis and coding theory.
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
(2023)
Article
Engineering, Electrical & Electronic
Niu Jiang, Min Zhao, Zhiyao Yang, Zepeng Zhuo, Guolong Chen
Summary: This paper presents a further characterization of bent-negabent functions, providing a necessary and sufficient condition for a class of quadratic Boolean functions to be bent-negabent based on complete mapping polynomial concept. A new characterization of negabent functions is described using the parity of Hamming weight. The paper also extends the classical convolution theorem and calculates the nega-Hadamard transform of the composition of a Boolean function and a vectorial Boolean function.
CHINESE JOURNAL OF ELECTRONICS
(2022)
Article
Computer Science, Information Systems
Zahra Pakdaman, Hossein Nezamabadi-pour, Saeid Saryazdi
Summary: This paper proposes a new reversible watermarking scheme, utilizing Reversible Walsh-Hadamard Transform for image processing and performing Singular Value Decomposition on the transformed image for watermark embedding. Quick Response (QR) code is embedded using a prediction-based method for full recovery.
MULTIMEDIA TOOLS AND APPLICATIONS
(2021)
Article
Computer Science, Artificial Intelligence
Anastasios Kyrillidis, Anshumali Shrivastava, Moshe Y. Vardi, Zhiwei Zhang
Summary: The Boolean SATisfiability problem is crucial in computer science, and recent progress in SAT solvers, particularly in Conflict-Driven Clause Learning (CDCL) and Local Search SAT solvers, has been notable. However, there is still a lack of general approach for handling non-CNF constraints. The designed FouriersAT solver utilizes Fourier Analysis to address systems with different types of constraints, leveraging gradient information for local improvements, demonstrating effectiveness on certain benchmarks.
ARTIFICIAL INTELLIGENCE
(2021)
Article
Computer Science, Information Systems
Shuang Li, Zhehe Wang, Shuxin Wang, Dongdong An
Summary: This paper presents a method for building a programming platform for ternary optical computer (TOC). By analyzing the limitations of existing platforms, the paper proposes a theoretical basis and core technologies to establish the TOC programming platform. The effectiveness of the platform is verified through experiments, showing that it simplifies the application of TOC and bridges the gap between users and TOC.
Article
Optics
Yunfu Shen, Sulan Zhang, Zhehe Wang, Weimin Li
Summary: This paper proposes a parallel carry-free radix-4 MSD iterative division algorithm based on TOP, which can improve the efficiency of multi-bit parallel division. Experimental results show that compared to traditional radix-2 bitwise division, the required clock cycles are reduced by half.
OPTICS COMMUNICATIONS
(2021)
Article
Multidisciplinary Sciences
Andriyan Bayu Suksmono, Yuichiro Minato
Summary: This paper presents new quantum computing methods for finding higher order H-matrices by adopting classical searching techniques, leading to successful discovery of H-matrices of order up to more than one hundred. The proposed method allows for verification of the solutions through an orthogonality test in polynomial time, which is atypical for solving hard optimization problems.
SCIENTIFIC REPORTS
(2022)