Secret Sharing Schemes for General Access Structures

, M.Sc. Thesis Sharif University of Technology Sefidgaran, Milad (Author) ; Eghlidos, Taraneh (Supervisor)

Abstract

Secret sharing scheme is a method for distributing the secret (secret information) among a set of participants in such a way that only the authorized sets can recover the secret and the unauthorized sets could not. In a perfect secret sharing scheme, unauthorized sets cannot get any additional (i.e. a posteriori) information about the possible value of the secret. In these schemes, to prevent information leakage and increase communication efficiency, the size of the share should be as close to the secret size as possible. In other words, finding the shares with reasonable size which results in an optimal information rate for a given access structure, improves the efficiency of the scheme....

Zero-Sum Flows in Designs and Hypergraphs

, M.Sc. Thesis Sharif University of Technology Bahmani, Asghar (Author) ; Akbari, Saieed (Supervisor)

Abstract

Let X = fx1; : : : ; xng be the set of vertices of a hypergraph H and E = fe1; : : : ; emg be the set of its edges. The incidence matrix of hypergraph H is an n m and (0; 1)-matrix, N, such that nij = 1 if xi 2 ej and nij = 0, otherwise. A zero-sum flow for H is a vector with non-zero entries that is in the null space of N. A zero-sum k-flow is a flow with non-zero integer entries that absolue value of each entry is at
most k 1. In this thesis we study the existence of zero-sum flows for designs and hypergraphs. Also we consider zero-sum 3-flows in 2-Steiner designs

Total Domination Number in Graphs

, M.Sc. Thesis Sharif University of Technology Gorzin, Ali Asghar (Author) ; Akbari, Saeed (Supervisor)

Abstract

In this dissertation we aim to survey the concepts and results concerning Total Domination Set. Consider graph G = (V;E). Let S be a subset of V . S is Total Domination Set in G if every vertex in V is adjacent to at least one vertex in S.Furthermore, we call S a k-Total Domination Set if every vertex in V is adjacent to at least k vertices in S. The size of the smallest Total Domination and k-Total Domination Set in a graph G is respectively called the Total Domination and k-Total Domination Number of G.Now, if there is a sequence of subsets of V like S = V0; V1; V2; : : : ; Vl = V so that for each i, every vertex in Vi is connected to at least k vertices in Vi1, S is a Dynamical k-Total...

Conflict-free Coloring Game

, M.Sc. Thesis Sharif University of Technology Karisani, Helia (Author) ; Abam, Mohammad Ali (Supervisor)

Abstract

Conflict-free coloring problem is one of the computational geometry problems that has been studied in the last two decades. The root of this problem comes from the frequency assignment to cellular networks problem. In that research, we have a cellular network containing several regions in two-dimensional plane and we want to assign a frequency to each of the regions so that if we look at any intersection of them, there is a region with a unique color compared to other regions of that intersection. In other words, a person’s cellular phone in the range of some regions (in the intersection of them) would be able to connect to one antenna with a unique frequency and function properly. This...