Article
Mathematics, Applied
Ahlem Melakhessou, Karima Chatouh, Kenza Guenda
Summary: This work focuses on studying DNA multi-secret sharing schemes based on codes over the ring Z(4) x R. The authors establish a one-to-one correspondence between the elements of the ring Z(4)xR and 64 codons using a Gray map psi, and obtain DNA simplex codes and DNA first order of Reed-Muller codes over Z(4)xR.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2023)
Article
Multidisciplinary Sciences
Luis Almeida Vieira
Summary: This paper establishes inequalities over the Krein parameters of a symmetric association scheme and of a strongly regular graph in the environment of Euclidean Jordan algebras. It also defines modified Krein parameters of a strongly regular graph and establishes admissibility conditions over these parameters. Furthermore, it introduces relations over the Krein parameters of a strongly regular graph.
Article
Mathematics, Applied
Hadi Kharaghani, Thomas Pender, Sho Suda
Summary: This article presents quasi-balanced weighing matrices, signed strongly regular graphs, and their equivalent association schemes.
FINITE FIELDS AND THEIR APPLICATIONS
(2022)
Article
Computer Science, Information Systems
Rui Xu, Xu Wang, Kirill Morozov, Chi Cheng, Jintai Ding
Summary: This paper revisits and proves that two (t, m, n) group oriented secret sharing schemes cannot provide the so-called group oriented property. Concrete attacks are developed to demonstrate how an unauthenticated adversary can participate in the reconstruction phase and obtain the secret.
INFORMATION SCIENCES
(2022)
Article
Computer Science, Information Systems
Jian Ding, Pinhui Ke, Changlu Lin, Huaxiong Wang
Summary: In this study, we revise previous (t, n)-SSR schemes and propose new secure schemes based on symmetric and asymmetric bivariate polynomials. The share sizes of these schemes are similar to other insecure schemes, but they are easier to construct.
INFORMATION SCIENCES
(2022)
Article
Computer Science, Information Systems
Sara Charoghchi, Samaneh Mashhadi
Summary: This paper introduces three novel secret image sharing schemes based on homogeneous linear recursion, which have merits such as simple sharing and high resolution. The shadow images generated in the schemes can resist attacks based on correlation of adjacent pixels.
INFORMATION SCIENCES
(2021)
Article
Computer Science, Information Systems
Amir Jafari, Shahram Khazaei
Summary: This article introduces and studies an extremely relaxed security notion called partial security for secret sharing schemes (SSSs). The research focuses on the information ratio of linear and non-linear SSSs. The results show that in linear schemes, the partial and perfect information ratios are equal; in non-linear schemes, the partial and statistical information ratios are equal; and in mixed-linear schemes, the partial and almost-perfect information ratios are not equal. The notion of partial secret sharing is also used to strengthen and unify the previous decomposition theorems for constructing SSSs.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2023)
Article
Mathematics
Anuwar Kadir Abdul Gafur, Suhadi Wido Saputro
Summary: The paper investigates the locating-dominating number of k-regular graphs, where k = n - 2 or k = n - 3, meaning each vertex is adjacent to k other vertices in the graph.
JOURNAL OF MATHEMATICS
(2021)
Article
Engineering, Electrical & Electronic
Wang Yaru, Li Fulin, Zhu Shixin
Summary: This work explores constructing two-weight linear codes over finite fields using linear codes over finite rings, specifically focusing on MacDonald codes over F2+vF2+v2F2 and giving torsion codes of MacDonald codes of type alpha and beta. The access structures of secret sharing schemes based on the dual codes of the two-weight codes are also presented.
CHINESE JOURNAL OF ELECTRONICS
(2021)
Article
Computer Science, Information Systems
Sanchita Saha, Arup Kumar Chattopadhyay, Anup Kumar Barman, Amitava Nag, Sukumar Nandi
Summary: The protection of digitized data against unauthorized access and modification has become crucial due to the rapid development of network technology and internet applications. Secret image sharing (SIS) schemes have been developed to safeguard sensitive digital images. These schemes fragment the secret image into multiple shares, designed to prevent any information disclosure to intruders. This paper provides a comprehensive survey of SIS schemes, including their pros and cons, verifiable secret image sharing (VSIS) schemes immune to cheating, and a comparison of various SIS methodologies based on different properties. The paper also highlights applications of SIS and presents open challenges and future directions in this field.
Article
Multidisciplinary Sciences
Danda Prudhvi Krishna, R. Ramaguru, K. Praveen, M. Sethumadhavan, Kattur Soundarapandian Ravichandran, Raghunathan Krishankumar, Amir H. Gandomi
Summary: This paper proposes a distributed authentication and authorization framework using a secret-sharing mechanism, blockchain-based decentralized identifier, and interplanetary file system. Performance analysis shows that secret sharing-based authentication is fast. Security analysis demonstrates that the model is robust, end-to-end secure, and compliant with the Universal Composability Framework.
SCIENTIFIC REPORTS
(2023)
Article
Mathematics
Minjia Shi, Tor Helleseth, Patrick Sole
Summary: For reducible cyclic codes of rank 2 over Z(pm), there are cases where they have exactly two Hamming weights. When these codes are projective, the coset graphs of their dual codes are strongly regular, and their spectra are determined.
JOURNAL OF ALGEBRAIC COMBINATORICS
(2022)
Article
Computer Science, Information Systems
Lein Harn, Chingfang Hsu, Zhe Xia
Summary: In this paper, we propose a dealer-free and non-interactive threshold changeable secret sharing (TCSS) scheme based on a bivariate polynomial. The shares generated by a dealer can serve the purposes of secret reconstruction, secrecy protection, and enabling threshold changeable property simultaneously.
FRONTIERS OF COMPUTER SCIENCE
(2022)
Article
Computer Science, Theory & Methods
Fatemeh Ghasemi, Reza Kaboli, Shahram Khazaei, Maghsoud Parviz, Mohammad-Mahdi Rafiei
Summary: In this paper, a technique is proposed to reduce the secret space of ideal homomorphic secret sharing schemes (IHSSS) and provide an alternative proof for obtaining ideal linear schemes. The concept of decomposition for secret sharing schemes is introduced, along with necessary and sufficient conditions for an IHSSS to be mixed-linear. Further exploration is done on the decomposability of other scheme classes in line with this research.
DESIGNS CODES AND CRYPTOGRAPHY
(2021)
Article
Computer Science, Theory & Methods
Michael Kiermaier, Sascha Kurz, Patrick Sole, Michael Stoll, Alfred Wassermann
Summary: Strongly walk regular graphs (SWRGs or s-SWRGs) are a natural generalization of strongly regular graphs (SRGs) where paths of length 2 are replaced by paths of length s. They can be constructed as coset graphs of the duals of projective three-weight codes whose weights satisfy a certain equation. Feasible parameters of these codes for medium size code lengths are classified in the binary and ternary case. For the binary case, divisibility of the weights of these codes is investigated and general results are shown. It is known that an s-SWRG has at most 4 distinct eigenvalues k > theta(1) > theta(2) > theta(3), and that the triple (theta(1), theta(2), theta(3)) satisfies a certain homogeneous polynomial equation of degree s - 2 (Van Dam, Omidi, 2013). This equation defines a plane algebraic curve; methods from algorithmic arithmetic geometry are used to show that for s = 5 and s = 7, there are only the obvious solutions, and it is conjectured to remain true for all (odd) s >= 9.
DESIGNS CODES AND CRYPTOGRAPHY
(2023)
Article
Computer Science, Information Systems
Chunming Tang, Cunsheng Ding
Summary: This paper resolves the longstanding question by introducing an infinite family of BCH codes and a linear code family holding spherical geometry designs, paving the way for new research directions in searching for t-designs using elementary symmetric polynomials.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2021)
Article
Computer Science, Theory & Methods
Cunsheng Ding, Chunming Tang
Summary: This paper focuses on studying the linear codes of t-designs held in the Reed-Muller and Simplex codes, presenting some general theory for linear codes containing t-designs and introducing several open problems for further research.
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
(2021)
Article
Computer Science, Information Systems
Yang Liu, Cunsheng Ding, Chunming Tang
Summary: The puncturing technique has achieved significant progress over the past 70 years, resulting in many families of linear codes with interesting parameters, while research on the shortening technique remains limited. This paper presents eleven families of optimal shortened codes over finite fields and constructs five infinite families of 2-designs as a byproduct of the study.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2021)
Article
Computer Science, Information Systems
Xiaoqiang Wang, Dabin Zheng, Cunsheng Ding
Summary: Two general constructions of linear codes involving functions over finite fields have been extensively researched. The first construction utilized almost bent functions, quadratic functions, and some monomials on F-2(m) to obtain many families of binary linear codes with few weights. This paper focused on studying punctured codes of these binary codes and obtaining several families of binary linear codes with few weights and new parameters, as well as distance-optimal binary linear codes with new parameters.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2021)
Article
Computer Science, Information Systems
Kanat Abdukhalikov, Cunsheng Ding, Sihem Mesnager, Chunming Tang, Maosheng Xiong
Summary: This paper focuses on cyclic bent functions on F2m-1 xF(2) and their applications, establishing a link between quadratic cyclic bent functions and a special type of prequasifields, and constructing families of optimal sequences using cyclic bent functions. The results show that cyclic bent functions have nice applications in several fields like coding theory, symmetric cryptography, and CDMA communication.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2021)
Article
Computer Science, Information Systems
Hang Chen, Cunsheng Ding, Sihem Mesnager, Chunming Tang
Summary: This paper introduces two methodologies for constructing minimal binary codes from sets, Boolean functions, and vectorial Boolean functions with high algebraic immunity. It presents a general construction of new minimal codes using minimal codes contained in Reed-Muller codes as well as sets without nonzero low degree annihilators. Another construction allows minimal codes to be derived from certain subcodes of Reed-Muller codes and vectorial Boolean functions with high algebraic immunity. Additionally, a lower bound on the minimum distance of the proposed minimal linear codes is established.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2021)
Article
Computer Science, Information Systems
Binkai Gong, Cunsheng Ding, Chengju Li
Summary: This paper investigates the symmetry problem of BCH codes, provides the symmetry conditions for primitive narrow-sense BCH codes and projective narrow-sense ternary BCH codes, and studies their dual codes. For binary primitive narrow-sense BCH codes, improved bounds on the minimum distances of the dual codes are obtained, and the question of which subclasses of cyclic codes are BCH codes is answered to some extent.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2022)
Article
Computer Science, Information Systems
Can Xiang, Chunming Tang, Cunsheng Ding
Summary: This paper investigates two families of linear codes from APN functions and some p-ary shortened codes associated with PN functions, and determines the weight distributions of these shortened codes and the parameters of their duals. The results indicate that the shortening technique has great potential for constructing good codes.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2022)
Article
Computer Science, Information Systems
Ziling Heng, Cunsheng Ding
Summary: This paper studies the subfield codes of geometric codes with dimension 3 and 4 over large finite fields and obtains distance-optimal subfield codes. The key idea is to choose good linear codes over extension fields with small dimensions. The results include two families of dimension-optimal codes and several families of nearly optimal codes. Additionally, several open problems are proposed in this paper.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2022)
Article
Computer Science, Information Systems
Qi Liu, Cunsheng Ding, Sihem Mesnager, Chunming Tang, Vladimir D. Tonchev
Summary: This paper studies some q-ary BCH codes with length q + 1, focusing on narrow-sense antiprimitive BCH codes. By using tools from algebraic coding theory, combinatorial designs, and group theory, the dimension, minimum distance, and dual codes of these BCH codes are determined.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2022)
Article
Computer Science, Information Systems
Chunming Tang, Qi Wang, Cunsheng Ding
Summary: This paper studies the quaternary subfield subcodes and quaternary subfield codes of a subfamily of MDS codes for even m. A family of quaternary cyclic codes is obtained, which are distance-optimal in some cases and generally very good. Furthermore, two infinite families of 3-designs from these quaternary codes and their duals are presented.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2022)
Article
Computer Science, Information Systems
Chunming Tang, Cunsheng Ding
Summary: This paper introduces the binary quadratic-residue codes and the punctured Reed-Muller codes R.2((ru-1)/2, m)), two families of binary cyclic codes with special parameters and minimum distance bounds. The objective of the paper is to construct two families of binary cyclic codes with length 2^m-1 and dimension near 2m-1.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2022)
Article
Computer Science, Information Systems
Xiaoqiang Wang, Chunming Tang, Cunsheng Ding
Summary: The interplay between coding theory and combinatorial t-designs has been a popular topic of research among combinatorialists and coding theorists for many years. While infinite families of cyclic codes supporting 3-designs have been constructed, no infinite family of negacyclic codes supporting 3-designs has been reported. This paper aims to present an infinite family of cyclic codes and two infinite families of negacyclic codes that support 3-designs. The parameters and weight distributions of these codes are determined, and the subfield subcodes of the negacyclic codes over GF(q) are studied. Three infinite families of almost MDS codes and a constacyclic code supporting a 4-design are also presented.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2023)
Article
Computer Science, Information Systems
Mengyuan Fan, Chengju Li, Cunsheng Ding
Summary: As a special subclass of cyclic codes, BCH codes are among the best cyclic codes and are widely used in communication, storage systems, and consumer electronics. This paper aims to derive a necessary and sufficient condition for two classes of narrow-sense BCH codes to be Hermitian dually-BCH codes and improve the lower bounds on the minimum distances of their Hermitian dual codes.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2023)
Proceedings Paper
Computer Science, Interdisciplinary Applications
Cunsheng Ding, Zhonghua Sun, Xiaoqiang Wang
Summary: Constacyclic codes are a family of linear codes that include cyclic codes as a subclass. They are of theoretical importance and outperform cyclic codes in several aspects. In practice, constacyclic codes are important due to their rich algebraic structures and potential for efficient decoding algorithms. This extended abstract presents the construction of two classes of constacyclic codes using a general construction with cyclic codes, analyzes their parameters, and discusses some open problems.
ARITHMETIC OF FINITE FIELDS, WAIFI 2022
(2023)
