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

An arrangement of $v$ varieties or treatments in $b$ blocks of size $k, (k < v),$ is known as a balanced incomplete block design if every variety occurs in $r$ blocks and any two varieties occur together in $\\lambda$ blocks. These parameters obviously satisfy the equations \\begin{equation*}\\tag{1} bk = vr\\end{equation*}\\begin{equation*}\\tag{2} \\lambda(v - 1) = r(k - 1)\\end{equation*} Fisher [1] has also proved that the inequality \\begin{equation*}\\tag{3} b \\geq v, \\quad r \\geq k\\end{equation*} must hold. If $v, b, r, k$ and $\\lambda$ are positive integers satisfying (1), (2) and (3), then a balanced incomplete block design with these parameters possibly exists, but the actual existence of a combinatorial solution is not ensured. These conditions are thus necessary but not sufficient for the existence of a design. Fisher and Yates in their tables [2] have listed all designs with $r \\leq 10$ and given combinatorial solutions, where known. A balanced incomplete block design in which $b = v$, and hence $r = k$ is called a symmetrical balanced incomplete block design. The impossibility of the symmetrical designs with parameters $v = b = 22, r = k = 7, \\lambda = 2$ and $v = b = 29, r = k = 8, \\lambda = 2$ was first demonstrated by Hussain [3], [4] essentially by the method of enumeration. The object of the present note is to give an alternative simple proof of the impossibility of these designs and to show that the only unknown remaining symmetrical design in Fisher and Yates' tables, viz. $v = b = 46, r = k = 10, \\lambda = 2,$ is definitely impossible. Symmetrical designs with $\\lambda \\leq 5, r, k \\leq 20$, which are impossible combinatorially, are also listed.

The paper discusses the symmetric balanced incomplete block designs (SBIBD’s) and further verifies whether treatment adjustment in SBIBD is necessary using analysis of variance (ANOVA) method. Fortunately, the data collected for the analysis were in the same group of the balanced incomplete-block designs (BIBD’s), that is, symmetric balance incomplete block design (SBIBD).The ANOVA method is applied differently on the two sets of data arising from the symmetric balanced incomplete block designs (SBIBDs). In this work, the basic interest is to verify empirically whether treatment adjustment is necessary in SBIBDs with data from National Root Crop Research Institute (N.R.C.R.I), Umudike, AbiaState. To achieve this, we considered treatment (not adjusted), treatment (adjusted), and block (adjusted) in the ANOVA method. The study discovered that if ANOVA method is applied on the symmetric balanced incomplete block design (SBIBD) when a treatment is not significant, it turns out to be significant when the same treatment is adjusted. It obvious from the experiments that were carried out that the adjustment of the treatment in SBIBD’s is very necessary when the ANOVA method is applied. Apart from the improvement in the level of significance of the result, the error is also greatly reduced when treatment is adjusted.

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.

Motivated by the field experimental designs in agriculture, the theory of block designs has been applied to several areas such as statistics, combinatorics, communication networks, distributed systems, cryptography, etc. An explicit formula and its fast computational algorithm for a class of symmetric balanced incomplete block designs are presented. Based on the formula and the careful investigation of the modulus multiplication table, the algorithm is developed. The computational costs of the algorithm is superior to those of the conventional ones.

The design and analysis of an efficient load balancing algorithm employing the symmetric balanced incomplete block design

: It is shown that among binary and connected block designs with and without equal block sizes and equal replications only a symmetric balanced incomplete block design produces a completely symmetric information matrix for the treatment effects whenever the number of blocks is equal to the number of treatments and the number of experimental units is a multiple of the number of treatments. This result contains a known result as a special case.

BCH codes and Designs

Tables of Parameters of BIBDs with r⩽41 including Existence, Enumeration, and Resolvability Results

Some new construction methods of the optimum chemical balance weighing designs and pairwise efficiency and variance balanced designs are proposed, which are based on the incidence matrices of the known symmetric balanced incomplete block designs. Also the conditions under which the constructed chemical balance weighing designs become A-optimal are also been given.

Symmetric balanced incomplete block designs (SBIBD) and Hadamard matrices

All the symmetric balanced incomplete block (SBIB) designs have been characterized and a new generalized expression on parameters of SBIB designs has been obtained. The parameter b has been formulated in a different way which is denoted by b i , i = 1, 2, 3, associating with the types of the SBIB design D i . The parameters of all the designs obtained through this representation have been tabulated while corresponding them with the suitable formulae for the number of blocks b i and the expression S i for the convenience of practical users for constructional methods of certain designs, which is the main theme of this paper.

A Machine learning approach to predict re-key in wireless sensor network using symmetric balanced incomplete block designs

Abstract This paper illustrates, through a special case, an effect of non-independent numerators on F-test's in an analysis of variance. Symmetrical balanced incomplete block designs are considered with "blocks" a random effect and no interaction. The joint density of the adjusted sums of squares is determined under the null hypothesis of no treatment effect. Given the result of testing for the block effect, the conditional probability of a Type I error when testing the null hypothesis concerning the treatment effect is evaluated for a number of designs.

An identity-based conference key distribution protocol based on SBIBD was proposed by Chung et al. in 2002 [1]. However, this protocol suffers several problems. Consequently, participants cannot correctly authenticate one another and cannot calculate the same conference key. This study investigates these problems and proposes an improved protocol also based on SBIBD.

Sharing Data in cloud allows multiple participants to share the group of data we are gifting a distinctive block design-based key agreement protocol that supports multiple participants, in whatever the way to make the protection of the data more secure while sharing between two users. Secure data sharing is performed using a private key generated and transmitted using secure channels. A key agreement protocol is used for data transfer to make more protection compare to later communication and this protocol is applied in cloud computing to support secure and economical sharing. In addition, an AES algorithm is used to encrypt the data. We have a susceptibility to estimate Block design key for secure data sharing in cloud, based on key agreement protocol with in which TPA verifies the malicious user from the group. To protect the data more secure every time when user as to download the data the TPA generates key to user. Every time the key is generated as, an OTP to secure the data from the attacker the user must use the same key to decrypt the data. In addition to that, the owner file is also generated to user. TPA acknowledge malignant client from group and detract from group we have a tendency to blessing general recipes for creating the normal meeting key for numerous members.