SAFE ETERNAL 1-SECURE SETS IN GRAPHS

An eternal $1$-secure set, in a graph $G = (V, E)$ is a set $D \subset V$ having the property that for any finite sequence of vertices $r_1, r_2, \ldots, r_k$ there exists a sequence of vertices $v_1, v_2, \ldots, v_k$ and a sequence $ D = D_0, D_1, D_2, \ldots, D_k$ of dominating sets of $G$, such that for each $i$, $1 \leq i \leq k$, $D_{i} = (D_{i-1} - \{v_i\}) \cup \{r_i\}$, where $v_i \in D_{i-1}$ and $r_i \in N[v_i]$. Here $r_i = v_i$ is possible. The cardinality of the smallest eternal $1$-secure set in a graph $G$ is called the eternal $1$-security number of $G$. In this paper we study a variations of eternal $1$-secure sets named safe eternal $1$-secure sets. A vertex $v$ is safe with respect to an eternal $1$-secure set $S$ if $N[v] \bigcap S =1$. An eternal 1 secure set $S$ is a safe eternal 1 secure set if at least one vertex in $G$ is safe with respect to the set $S$. We characterize the class of graphs having safe eternal $1$-secure sets for which all vertices - excluding those in the safe $1$-secure sets - are safe. Also we introduce a new kind of directed graphs which represent the transformation from one safe 1 - secure set to another safe 1-secure set of a given graph and study its properties.

Co-Secure Set Domination in Graphs

Throughout this paper, consider G = (V,E) as a connected graph. A subset D of V(G) is a set dominating set of G if for every M  V / D there exists a non-empty set N of D such that the induced sub graph <MUN> is connected. A subset D of the vertex set of a graph G is called a co-secure dominating set of a graph if D is a dominating set, and for each u' D there exists a vertex v'V / D such that u'v' is an edge and D \u'v' is a dominating set. A co-secure dominating set D is a co-secure set dominating set of G if D is also a set dominating set of G. The co-secure set domination number G s cs γ is the minimum cardinality of a co-secure set dominating set. In this paper we initiate the study of this new parameter & also determine the co-secure set domination number of some standard graphs and obtain its bounds.

JSSecure: A Secured Encryption Strategy for Payment Gateways in E-Commerce

JSSecure is a framework for online payment systems over e-commerce websites. Payments made online using debit/credit cards have become familiar, and the users are shifting to a higher comfort level with this method of payment. Nowadays for any online transactions, a payment gateway is used which is a service that is provided by an e-commerce or by any bank that authorizes the details of the user for the secure transaction. This paper presents a frame format of JSSecure. For any transaction, there has to be a way in which the user details needs to be protected. Cryptography is one of the methods which is used for converting the information from its standard form to encrypted form or unreadable for the attackers. Using JSSecure, each user detail is encrypted individually to provide extra security against attackers. There are umpteen number of payment gateway methods like 3D Secure, SET, and MSET Protocols. Various algorithms help user securely enter his/her card details, some of them are Jumbling Salting (JS), Data Encryption Standard (DES), Advanced Encryption Standard (AES), etc. which are used for the encrypting the details securely. All these algorithms are symmetric key. JSSecure uses double encryption strategy for more security. We will be providing a fair comparison of Data Encryption Standard (DES), Advanced Encryption Standard (AES) and Jumbling Salting (JS) algorithms. Since our major concern here is the performance of algorithms under different conditions, we will be comparing on the basis of speed, block size, and key size on the encryption time, decryption time, throughput and size of cipher text. This analysis will help in implementing the best-suited algorithm for the proposed payment gateway. It will be open source and hence it will be more cost efficient.

Linking Health Records for Federated Query Processing

A federated query portal in an electronic health record infrastructure enables large epidemiology studies by combining data from geographically dispersed medical institutions. However, an individual’s health record has been found to be distributed across multiple carrier databases in local settings. Privacy regulations may prohibit a data source from revealing clear text identifiers, thereby making it non-trivial for a query aggregator to determine which records correspond to the same underlying individual. In this paper, we explore this problem of privately detecting and tracking the health records of an individual in a distributed infrastructure. We begin with a secure set intersection protocol based on commutative encryption, and show how to make it practical on comparison spaces as large as 1010 pairs. Using bigram matching, precomputed tables, and data parallelism, we successfully reduced the execution time to a matter of minutes, while retaining a high degree of accuracy even in records with data entry errors. We also propose techniques to prevent the inference of identifier information when knowledge of underlying data distributions is known to an adversary. Finally, we discuss how records can be tracked utilizing the detection results during query processing.

Secure sets and their expansion in cubic graphs

Consider a graph whose vertices play the role of members of the opposing groups. The edge between two vertices means that these vertices may defend or attack each other. At one time, any attacker may attack only one vertex. Similarly, any defender fights for itself or helps exactly one of its neighbours. If we have a set of defenders that can repel any attack, then we say that the set is secure. Moreover, it is strong if it is also prepared for a raid of one additional foe who can strike anywhere. We show that almost any cubic graph of order n has a minimum strong secure set of cardinality less or equal to n/2 + 1. Moreover, we examine the possibility of an expansion of secure sets and strong secure sets.