Symmetric Balanced Incomplete Block Design Research Articles

Symmetric Balanced Incomplete Block Designs (Sbibd) And Construction of Hadamard Rhotrices

Balanced Incomplete Block Designs (BIBD) are the designs obtained from the arrangement of symbols in blocks following established rules and satisfying relevant necessary conditions. BIBDs have broad applications in many fields.The entries in a Hadamard matrix H are all +1’s or -1’s, satisfying the property HHT = n In [2]. Rhotrix is a new concept in mathematics having applications in cryptography. In this paper, using SBIB designs the Hadamard Rhotrices are constructed. AMS Subject classification: 05B05, 05B20, 62K10.

Optimal key pre‐distribution schemes from affine resolvable and partially affine resolvable designs

AbstractVarious key pre‐distribution schemes (KPSs) for distributed sensor networks (DSNs) were obtained from different combinatorial designs. A block design may be mapped to a KPS where is the number of nodes or network size and is the number of keys (points) per node. A KPS is corresponding to a symmetric balanced incomplete block design has full connectivity where all nodes are connected to each other. But it is desirable that all nodes do not share common keys as the compromise of any node will destroy the whole network (see Lee & Stinson, 2005; Martin, 2009). To meet the situation, Lee and Stinson (2005) introduced μ—common intersection design which has disjoint blocks and these disjoint blocks can establish a secure communication through certain common intersecting blocks. Here we have proposed optimal KPSs from affine resolvable and partially affine resolvable balanced incomplete block designs, group divisible designs and L2—type designs. It is shown that these designs are important classes of μ—common intersection designs. The KPSs obtained here are optimal in the sense of local connectivity. Mathematics Subject Classification (2010): 94C30; 68R05; 05B05; 62K10.

Properties and Construction Method for Symmetric Balanced Incomplete Block Design with λ=1

Symmetric Balanced Incomplete Block Designs with λ=1 is a common class of BIBDs which are mostly used in incomplete experimental block design set up because of their simplicity in set up and also in analysis. Over the years since development of the BIBDs by Yates in the year 1939. A number of research has been done on the design to establish properties of the design and also to determine the construction methods of the design. In terms of properties, the studies have only been able to establish necessary but not sufficient not sufficient conditions for the existence of the design. For the symmetric BIBDs the studies have also determined the non-existence properties for such designs. However, the sufficient existence property for the design have not been established. In terms of construction, the studies have been able to derive several construction methods for BIBDs. However, these methods have been determined not to be adequate in constructing all the BIBDs which still leave the existence of some BIBDs as unknown. For symmetric BIBDs with λ=1 which are also known as projective planes, the studies have not been able to establish the sufficient properties for existence of this class of BIBDs just like the other classes of symmetric BIBDs. Therefore, this give room for investigating other properties of this class of BIBDs. The present study therefore, aimed at deriving the properties of the design from the known properties of BIBDs and also using the properties to determine the construction technique that would be suitable used in constructing this class of BIBDs. The study used the known properties of symmetric BIBDs to derive new properties of symmetric BIBDs, then restricted it to the case of λ=1. Which aided in derivation of new properties of the design and also the construction method. The study was able to derive three new properties for this class of BIBD and it was also able to show that the class of BIBD would be best constructed using PG(2,S).

Efficiency of Sum Constructed Automorphic Symmetric Balanced Incomplete Block Designs

Several construction methods have been introduced to build the elements of balanced incomplete block designs (BIBDs) for specific parameters, with different techniques suggested for testing their existence. There is still no general technique to determine the existence of the designs that have been realized. In this study the efficiencies of some given automorphic symmetric balanced incomplete block designs (AUSBIBD) formed by sum construction method have been presented in details alongside existence and non-existence of such designs. The process involved the application of sum construction method to give new designs of parameters D (v, b, λ1+λ2) and an application of Bruck Ryser Chwola theorem extensively. A test design constructed using the described method was found to be existing with an efficiency of 76.38%. Sum constructed designs are more applicable in agricultural fields as witness in case of KEFRI-Kenya.

On a characterization of symmetric balanced incomplete block designs

On a characterization of symmetric balanced incomplete block designs

Construction of Non-Symmetric Balanced Incomplete Block Design through Combination of Symmetric Disjoint Balanced Incomplete Block Designs

Construction of Non-Symmetric Balanced Incomplete Block Design through Combination of Symmetric Disjoint Balanced Incomplete Block Designs

Development of A Novel Block Design Based Key Agreement Protocol for Cloud Environment to Improve Efficient Performance and Security

Cloud computing is one of the recent emerging technologies. Heavy data sharing among multiple users is an open issue. Data sharing in cloud computing enables multiple participants to freely share the group data, which improves the efficiency of work in cooperative environments and has widespread potential applications. However, how to ensure the security of data sharing within a group and how to efficiently share the outsourced data in a group manner are formidable challenges. In this paper we focused on security issues with the help of key agreement protocols to perform efficient data sharing in cloud environment. We proposed a novel block design based key agreement method in support of symmetric balanced incomplete block design (SBIBD). The main objective of this method is to supports multiple participants, which can flexibly extend the number of participants in a cloud environment according to the structure of the block design. Based on the proposed group data sharing model, we present general formulas for generating the common conference key K for multiple participants. In addition, the fault tolerance property of our protocol enables the group data sharing in cloud computing to withstand different key attacks, which is similar to Yi’s protocol.

Decentralized Self-Auditing Scheme With Errors Localization for Multi-Cloud Storage

With the popularity of cloud storage, increasing users begin to outsource data to the cloud. In order to resist possible data analysis for centralized outsourced data and improve the fault tolerance, users prefer to distribute data to cloud servers of different cloud service providers. However, once the data have been outsourced, it will be out of user’s control and many security issues may occur, such as outsourced data being illegally tamper with, or rarely accessed data being secretly deleted. In this article, we propose a decentralized self-auditing scheme for multi-cloud storage, called DSAS. First, based on the symmetric balanced incomplete block design, DSAS achieves integrity verification for outsourced data via the interactions of cloud servers and the auditing costs are shared by the participating CSs. Second, DSAS can locate misbehavior cloud server with low computation costs, and resist denial of service attack initiated by malicious cloud servers which attempts to destroy the audit. Third, DSAS can recover the corrupted data without fetching data, and support the revocation of cloud servers and batch auditing. Finally, security proof and function evaluation show that DSAS has comprehensive security and functionality, and performance simulations and experiment results show that DSAS is efficient.

Secure Key Management Scheme for Hierarchical Network Using Combinatorial Design

The wireless sensor network (WSN) signifies to a gathering of spatially spread and committed sensors for observing and logging the physical states of the environment and for organizing the information gathered at the central Base station. Many security threats may affect the functioning of these networks. Security of the data in the system depends on the cryptographic procedure and the methods where encryption and decryption keys are developed among the sensors. Symmetric key foundation is one of the best applicable ideal models for safe exchanges in WSNs. The main goal is to improve and evaluate certain issues, such as node attack, to provide better key strength, connectivity, security for node interaction, and throughput. Uniform Balanced Incomplete Block Design (UBIBD) is used to generate the keys allocated by the base station to the cluster head. The cluster head distributes keys to its members using Symmetric Balanced Incomplete Block Design (SBIBD), and the keys are refreshed on a regular basis to avoid out-of-date entries. In wireless sensor networks, compromised nodes can be used to inject false reports. The concept of interacting between sensor nodes using keys and establishing a secure connection aids in ensuring the network's security.

Placement Delivery Arrays Based on Combinatorial Designs

As an effective technique to reduce network congestion during peak-traffic times, coded caching is being widely studied in wireless network. Yan <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> proved that the problem of designing a coded caching scheme can be converted into constructing a placement delivery array (PDA). It is meaningful to design coded caching schemes with low transmission rate and small packet number. In this letter, from the perspective of combinatorial designs, we construct a class of PDA using <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(v,k,2)$ </tex-math></inline-formula> -symmetric balanced incomplete block design which has advantages in transmission rate. Additionally, two classes of PDAs based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$t$ </tex-math></inline-formula> -designs are constructed. Compared with some known schemes, new schemes have advantages in packet number.

Nested block design as key pre-distribution in wireless sensor networks

An accumulation of wireless sensor nodes is combined together to form the Wireless Sensor Networks. The sensor nodes are distributed haphazardly without any decided method into a natural setting, which is generally inhospitable and it is difficult to provide key-chains to each node for security as they are haphazardly distributed. In this paper, we use Nested Block Design (NBD) as Key Pre-distribution Scheme (KPS) and found out that NBD support large networks with fewer keys in each node than Symmetric Balanced Incomplete Block Designs (SBIBD) and Transversal Design (TD[Formula: see text]), provide higher resiliency than SBIBDs and better connectivity than TD[Formula: see text], tradeoff between local connectivity and resiliency ([Formula: see text]) is lower than SBIBD but more than TD[Formula: see text] and key-node ratio ([Formula: see text]) is same for [Formula: see text] but lower than SBIBD.

Lower bounds for the spectral norm of digraphs

Let D be a digraph with n vertices and σ1(D)≥σ2(D)≥⋯≥σn(D) the singular values of the adjacency matrix A of D. The spectral norm of D is σ1(D) and the trace norm of D is ‖D‖⁎=∑i=1nσi(D). In this paper we find lower bounds for the spectral norm of a digraph in terms of the structure of the digraph. Moreover, we introduce the concept of almost regular digraphs (extension of the well known almost regular graphs), and show that the lower bounds are attained precisely in almost regular digraphs. When we apply this theory to graphs, we recover well known lower bounds for the spectral radius of graphs. Also, we give a new upper bound for the trace norm of a digraph. Moreover, we determine the digraphs for which this bound is sharp: sink-source complete bipartite digraphs or symmetric balanced incomplete block designs (BIBD).

The Impossibility of Certain Symmetrical Balanced Incomplete Block Designs

The Impossibility of Certain Symmetrical Balanced Incomplete Block Designs

On improving the construction of balanced incomplete block designs using planar near-rings

The purpose of this paper is to highlight the importance of planar near-rings (PNR) in the construction of balanced incomplete block designs (BIBD), then to give a new precise formula to blocks of this type of BIBD which enables us to generate useful matrices based on the incidence matrix. Moreover, we will improve the efficiency factor and determine the condition to produce a symmetric BIBD from a BIBD.

An efficient resource sharing scheme based on the linear feedback shift register

With the invention of various kinds of electrical equipment, electricity has become an indispensable necessity in human society. The concept of smart grid is proposed in this context. Resource sharing is regarded as one of the important goals in smart grid. However, how to improve communication efficiency has become the bottleneck of resource sharing in smart grid. In this paper, we focus on optimisation of the symmetric balanced incomplete block design (SBIBD) to support efficient communication in smart grid. Note that the linear feedback shift register (LFSR) is employed in the generation of the SBIBD, which is far more efficient than the algorithm implementation. Moreover, the one-step state transition matrix of the LFSR is presented and the s-step state transition matrix is further deduced. Compared with the one-step state transition matrix, the s-step state transition matrix can well support multi-step parallel shift operation thereby increasing efficiency by s times.

On Network Designs with Coding Error Detection and Correction Application

The detection of error and its correction is an important area of mathematics that is vastly constructed in all communication systems. Furthermore, combinatorial design theory has several applications like detecting or correcting errors in communication systems. Network (graph) designs (GDs) are introduced as a generalization of the symmetric balanced incomplete block designs (BIBDs) that are utilized directly in the above mentioned application. The networks (graphs) have been represented by vectors whose entries are the labels of the vertices related to the lengths of edges linked to it. Here, a general method is proposed and applied to construct new networks designs. This method of networks representation has simplified the method of constructing the network designs. In this paper, a novel representation of networks is introduced and used as a technique of constructing the group generated network designs of the complete bipartite networks and certain circulants. A technique of constructing the group generated network designs of the circulants is given with group generated graph designs (GDs) of certain circulants. In addition, the GDs are transformed into an incidence matrices, the rows and the columns of these matrices can be both viewed as a binary nonlinear code. A novel coding error detection and correction application is proposed and examined.

Secure and Efficient Data Sharing in Dynamic Vehicular Networks

With the development of wireless communication and the pervasive Internet of Things, vehicular ad hoc networks (VANETs) have attracted much attention in recent years. As a platform for vehicular communication and management, VANETs require the guarantee of security and efficiency for the resources constrained and unreliable networks. In this article, a data-sharing scheme is proposed for VANETs where both efficient key updating and dynamic property of VANETs are supported. In particular, the symmetric balanced incomplete block design (SBIBD) in combinatorics is introduced to ensure secure and efficient VANETs while the concept of indistinguishability obfuscation is employed to support efficient key updating. In order to simultaneously satisfy the resources constrained and real-time requirements of VANETs, both serial and parallel construction of the SBIBD is implemented by the shift register. Taking advantage of this efficient sequential logical circuit, we eliminate the complicated construction of the SBIBD, thereby, making it effective for the resource-constrained environment. Theoretical and experimental analyses indicate that the proposed scheme is practical for VANETs with high security and efficiency.

Energy adaptive block design based neighbor discovery for asynchronous wireless sensor networks

Background: The need for an efficient neighbor discovery model is tremendously essential with the development of Wireless Sensor Networks (WSNs).The neighbor discovery model has growingly been significant in enhancing the performance of WSNs. Methods: In this study, adaptive energy duty-cycle, energy-efficient Balanced Incomplete Block Design (BIBD) hybrid scheme is proposed for WSNs that controls collisions, and overhearing obstacle by maintaining energy over WSNs. Energy adaptive BIBD leverages the features of symmetric BIBD. Evaluation of the proposed model is demonstrated using the TOSSIM tool, and the performance parameters are compared with other wellknown neighbor discovery process, including Disco, U-Connect, and Searchlight, Hedis, and Todis algorithms. Findings: The outputs of our simulation study illustrates that the proposed model significantly outperforms other neighbor discovery algorithms with reference to energy-efficiency and discovery latency.Keywords: Wireless sensor networks; energy efficiency; neighbor discovery; block design; collisions

On the Construction of Trend Free Run Order of the Two-Level Factorial Design Using BIBD

Randomization is one of the powerful tools to analyze, construct and draw valid and unbiased conclusions about the factorial design. But in some experimental situations, the technique may not perform equally well to draw valid inferences. These situations may arise due to an influence of external variations like the ageing of catalyst, known as Time-trend or Trend, on the response. Thus, instead of randomizing the run order of the factorial design, systematically arranging the order of treatments that is free of variations, neutralizes the adverse effect of Trend. Such systematic designs are known as Trend Free designs. The design gives not only higher importance to the treatments but also ensures the independence of treatments for further analysis. Methods for constructing trend-free run order of two-level designs have been studied and developed by many authors. The proposed run order for 2k and 2k-p design that are linear and quadratic trend free. Systematic run order has been constructed not only to eliminate the effect of the linear and quadratic trend but also to improve design performance in the presence of a trend. This article provides another technique to develop trend free run order of two-level factorial design using Symmetric Balanced Incomplete Block Design.

Security and Confidentiality of the Data using Block Level in Health Care System

Nowadays rapid development of cloud computing in smart healthcare system has significantly improved the quality of health. However, data security and user privacy are a major concern for smart healthcare systems. These days any kind of data can be used for malicious purposes. Many harmful entities constantly try to gain access to the personal data of internet users. This data includes sensitive information that doctors store of patients and is often stored using some kind of third party cloud providing service that is not very secure. To take care of this issue, in this paper, Symmetric Balanced Incomplete Block Design (SBIBD) is utilized for key Security so that unauthorized client can’t get access to the data easily. It also allows the patients immediate and easy access to the data using unique user ID. This system makes use of double encryption using Blowfish algorithm to ensure maximum security of data and the concept of block level is used where data is stored using multiple blocks.