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
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
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
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
Telecommunications
Allyson Hineman, Mario Blaum
Summary: The Shamir secret sharing scheme can be simplified and sped up by dropping the MDS condition and using array codes based on XOR operations instead of Reed-Solomon codes.
IEEE COMMUNICATIONS LETTERS
(2022)
Article
Computer Science, Theory & Methods
Angela Aguglia, Michela Ceria, Luca Giuzzi
Summary: Explored the properties of certain algebraic hypersurfaces over finite fields, which have a limited number of intersection values with any hyperplane, resulting in q-divisible linear codes with at most 5 weights. For odd q, these codes are minimal and the access structures of secret sharing schemes can be characterized based on their dual codes.
DESIGNS CODES AND CRYPTOGRAPHY
(2022)
Article
Computer Science, Theory & Methods
Amir Jafari, Shahram Khazaei
Summary: Homomorphic (or abelian) secret sharing is a generalization of ubiquitous linear secret sharing. The study reveals that mixed-linear schemes are more powerful in terms of information ratio, dual access structures have equal information ratios for abelian schemes, and every ideal homomorphic scheme can be transformed into an ideal linear scheme with the same access structure.
JOURNAL OF CRYPTOLOGY
(2021)
Article
Mathematics
Fan Peng, Hao Chen, Chang-An Zhao
Summary: Algebraic geometric secret sharing schemes are proposed for establishing the fundamental theorem in information-theoretically secure multiparty computation. The schemes demonstrate quasithreshold properties and are analyzed in terms of subsets of players' ability to recover the secret or have no knowledge of it. The study explores the asymptotic threshold behavior of these schemes over large finite fields and when the genus approaches infinity with a fixed base field size.
PACIFIC JOURNAL OF MATHEMATICS
(2022)
Article
Computer Science, Theory & Methods
Jian Ding, Changlu Lin, Sihem Mesnager
Summary: This paper discusses secret sharing schemes based on linear codes, proposes two new schemes, and studies their combinatorial properties and democracy. The findings contradict previous research conclusions.
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES
(2021)
Article
Computer Science, Information Systems
Qi Chen, Chunming Tang, Zhiqiang Lin
Summary: This study aims to construct efficient and explicit ideal multipartite secret sharing schemes, which are considered as a useful generalization of threshold secret sharing. Some schemes are classified as hierarchical or compartmented in nature.
IEEE TRANSACTIONS ON INFORMATION THEORY
(2022)
Article
Mathematics, Applied
Alessio Meneghetti, Marco Pellegrini, Massimiliano Sala
Summary: The research proposes a new set of linear relations that must be satisfied by the coefficients of the weight distribution. These relations help derive known identities for interesting cases, such as extremal codes, Hermitian codes, MDS, and NMDS codes, in an easier way. Additionally, the weight distribution of AMDS codes is presented for the first time, along with a discussion on the link between the results and the Pless equations.
FINITE FIELDS AND THEIR APPLICATIONS
(2022)
