Sharif Digital Repository

The meaning and the nature of space and it’s essential properties seems to be one of the oldest problems which has been continuing to occupy human’s mind during centuries. It can be counted as a common ground between philosophy, mathematics, physics and even art. However this thesis concentrates on the philosophical and mathematical attitudes, neglecting the other aspects of the issue. Prima facie, it appears that the concept of space is essentially mingled with geometry, the science which seems to investigate the essentials of space. Taking it for granted, Kant regarded space, and so Euclidean geometry which dominates it, as an indispensible and necessary structure of the human’s mind.... 

Using interpolation and starting with Bernoulli numbers, posed by Leopold and Kubota, the aspect of adic function was constructed as adic analogues of the Dirichlet functions.Studing Galois module theory of ideal class group and his favorite structure extensions and modules related to them,Iwasawa found a new method for constructing adic functions by using Stickelberger’s elements.These results wich established by Iwasawa are known as Iwasawa Theory and they have many application in Algebriac Number Theory. Iwasawa’s most remarkable disconvry is the facet that at least in some important cases, there is a similar deep algebraic and analytic dichotomy in arithmetic of extensions. A... 

Grothendieck’s theory of dessin d’enfant makes a connection between piecewise flat metrics and conformal structures on a compact surface R on one hand, and the defining equation for R whose coefficients lie in an algebraic number field on the other. This connection is realized by a combinatorial structure (a dessin) on a given surface R.In this thesis we begin by briefly reviewing Grothendieck’s theory of dessin d’enfant and Belyi’s theorem and also the approximation of a Belyi map via Thurston’s theory of circle packings.We then introduce a method for computing the explicit equation of the Riemann surface and Belyi map associated to a dessin. Also we explain how the absolute Galois group... 

In this thesis, zero-divisor ideal graphs and geometric zero-divisor graphs are introduced and are partially studied. We begin by studying the relation between the zero-divisor graph and zero-divisor ideal graph associated to principal ideal rings. We also investigate some of the basic properties of the zero-divisor ideal graphs, including their girth and diameter. Then, we introduce the geometric zero-divisor graphs associated to reduced schemes and study their basic properties to some extent. Finally, we conclude by characterizing all reduced schemes whose associated geometric zero-divisor graph contains a vertex which is... 

Gauss' theory of the arithmetic of quadratic forms appeared in Disquisitiones Arithmeticae (1801) and in particular Gauss presented a composition law for binary quadratic forms and related it to the arithmetic of quadratic extensions of Q. In the series of papers of “Higher Composition Laws” Manjul Bhargava gave a far reaching generalization of Gauss' composition law and extended it to binary cubic, and a number of other cases. He obtained six composition laws one of which the classical one of Gauss. Since the work of Gauss has had deep impact on number theory and in particular on the arithmetic of quadratic fields, one expects that Bhargava’s theory to lead to new insights in... 

This thesis is devoted to study some asymptotic behaviors of Poisson Voronoi tessellation in the Euclidean space as dimension of the space tends to infinity. First we use Blaschke-Petkantschin formula to prove that the variance of volume of the typical cell tends to zero exponentially in dimension. It is also shown that the volume of intersection of the typical cell with the co-centered ball of volume converges in distribution to the constant . Next we consider the linear contact distribution function of the Poisson Voronoi tessellation and compute the limit when dimension goes to infinity. As a byproduct, the chord length distribution and the geometric covariogram of the typical cell are... 

The main purpose of this thesis is to study computational questions related to compact Riemann surfaces (algebraic curves) with main emphasis on the theory of Grothendieck’s dessins d’enfants; where recovering the explicit formula of a Belyi map from the corresponding dessin on a topological surface is important. Some applications such as investigating the modular j-function and also certain classes of modular curves are included in this thesis along with a summary of attempts toward generalizing the Belyi theorem to complex dimension two.First two chapters contain necessary prerequisites on compact Riemann surfaces and a short introduction to the theory of dessins d’enfants and Belyi... 

Hardware Trojans have emerged as a major concern for integrated circuits in recent years. As a result, detecting Trojans has become an important issue in critical applications, such as finance and health. In this work, a trusted platform for detecting Trojans in FPGA bitstreams is presented. The proposed methodology takes advantage of increased Trojan activation, caused by transition aware partitioning of the circuit, while it benefits partial reconfiguration feature of FPGAs to reduce area overhead. Simulation results, performed for the transition probability thresholds of 〖10〗^(-4) and 〖2×10〗^(-5), show that this method increases the ratio of the number of transitions in the Trojan... 

In recent years, in addition to traditional cryptographic blocks, a hardware blocks in this work namely PUF, has been used mostly for chip ID generation, authentication and so on. In this work we study recent proposed PUFs and their implementations on FPGA, and the measurement of quality metrics on them. Some of most important characteristics of PUFs are unpredictability, reliability, number of challenge response pairs and area. According to experiments that have been performed in this study and also according to previous work, one high-quality PUF in term of uniqueness and reliability is Ring Oscillator PUF. However, the disadvantage of this PUF is small number of challenge and response... 

Due to the expansion of digital system threats, trusted computation with a new approach for countering such threats has emerged. This approach is based on using a hardware module for implementing a trusted platform (TPM). TPM includes a chipset and the trusted systems core. Nowadays many of mobile computers do include this technology. This hardware creates trust using a trust chain and expanding this trust to other parts of the system. The starting point in this chain is the computer BIOS. BIOS is the first code that the system usually executes. One of the most powerful recent attacks on computer systems is to infect the BIOS and other firmware. One of such complicated attacks is the rootkit... 

Public key encryption (PKE) cryptography plays a big role in securing communication channels of internet. The security of every PKE scheme is usually based on a hard problem that has no polynomial time solution using any computational structure. However, widely used classic PKE schemes such as RSA or ECC, are based on hard problems that have polynomial solutions using a quantum computer. Therefore, such PKE schemes will not be secure in post-quantum era. Among quantum-resistant schemes, lattice-based cryptography and especially learning with errors (LWE) problem have gained high attention due to their low computational complexity. In this thesis, different LWE-based cryptosystems are... 

Recently, Convolutional neural networks (CNNs) are widely used in many artificial intelligence applications such as image processing, speech processing and robotics. The neural networks superior accuracy comes at the cost of high computational complexity. Recent studies show that these operations can be performed in parallel. Therefore, as graphic processing units (GPUs) offer the best performance in terms of computational power and throughput, they are widely used to implement and accelerate neural networks. Nevertheless, the high price and power consumption of these processors have resulted in drawing more attraction towards Field-Programmable Arrays (FPGAs). In order to improve resource... 

Cloud computing has a significant role in expanding applications of the Internet of Things (IoT). Currently, applications such as virtual reality and augmented reality require low latency, which is not achievable using traditional cloud computing in some scenarios. Edge computing is a new approach in IoT, which solves some of the limitations of the cloud computing by extending and developing its operations. Reducing response time and network traffic are some of the most important achievements of edge computing. Despite of its numerous advantages over cloud computing, edge computing faces serious challenges such as virtualization, implementation infrastructure, resource allocation and task... 

Due to the widespread growth in the use of IoT devices, authors consider these devices as an attractive target platform. Several approaches have been proposed to defend IoT devices against various attacks. However, most of them suffer from some shortcomings such as being computationally expensive, not being general, or not being robust enough.Due to the attacks such as firmware modification and the existence of computational limitations, the use of local approaches is inefficient. Another approach is to use remote attestation techniques, which are divided into two categories, static and dynamic. However, static detection techniques are vulnerable to runtime attacks. Furthermore, existing... 

A distributed ledger is a method of digital data storage and sharing in different places, and the blockchain technology is a way of implementing a distributed ledger. This technology has been employed in many of the cryptocurrencies like Ethereum to store transactions. In addition to storing transactions, Ethereum deploys scripts called smart contracts that are automatically executable. These scripts execute transparently and without preserving the privacy of participants. On the other hand, confidentiality and privacy are among the important components in data, network, and system security. Models such as Hawk and Enigma have been presented to obtain privacy-preserving in smart contracts;... 

Nowadays, with the advancement of internet of things, The number of nodes within the network has increased and there is huge traffic in these networks despite the small volume of data sent and received each node. The current architecture of the Internet network does not have the functionality required for Internet of things, as a result of designing a new architecture for Internet - based Internet of things. Content - based network is a new architecture introduced to the Internet, and its purpose is to change the network from host-centric to content-centric. One of the features of content-based networks is the use of in network caching that helps increase productivity and reduce the traffic... 

Today Internet of Things (IoT) applications are growing rapidly around us and alongside this trend, the topics of security and trust in this field are getting more serious. A big part of this field is composed of embedded systems. Remote attestation is a prominent security option in regards of attesting to the integrity of these type of systems and consequently establishing trust remotely. Remote attestation has been an active field of research to attest different type of systems against various types of threats. A noteworthy security hardware, enabling this type of process, is the Trusted Platform Module (TPM). Incorporating this chip in traditional personal computers for security purposes...