Sharif Digital Repository

Grobner bases were introduced by Bruno Buchberger in 1965. The terminology acknowledges the influence of Wolfgang Grobner on Buchberger’s work. He introduced a specific generator for ideals in the ring of polynomials over a field and then gave an algorithm for computing of that generator. It leads to solutions to a large number of algorithmic problems that are related to polynomials in several variables. Most notably, algorithms that involve Grobner basis computations allow exact conclusions on the solutions of systems of nonlinear equations, such as the (geometric) dimension of the solution set,the exact number of solutions in case there are finitely many, and their actual computation with... 

The two central topics of information theory are the compression and the transmission of data. Shannon, in his seminal work, formalized both these problems and determined their fundamental limits. Since then the main goal of coding theory has been to find practical schemes that approach these limits.Polar codes, recently invented by Arıkan, are the first practical codes that are known to achieve the capacity for a large class of channels. Their code construction is based on a phenomenon called “channel polarization”.
Since the performance of polar code degrades when the block length is small, several kinds of Reed – Solomon concatenation is considered in order to improve the... 

In the upward trend of advancing technologies in chips manufacturing, utilizing Network on Chip (NOC) solutions is a sensible approach towards overcoming challenges in System on Chip (SOC). The most common form of NOC is the Wired NOC. The continuous physical size reduction of electronic circuits has led to bandwidth deficiency as well as increased temperature in various parts of these circuits. The vast advancement in chips manufacturing industry has made it possible to embed and adapt telecommunication equipment into chips, giving rise to Wireless NOC (WNOC) manufacturing. However, wireless communication increases fault rate; thereby, the system becomes more vulnerable against transient... 

Today Ethernet is the predominant technology for implementing Local Area Networks. Its privileges encourage service providers to extend Ethernet from Local Area Networks to Metropolitan Area Networks or even Wide Area Networks. Ethernet benefits such as low operational costs, well interoperability, plug-n-paly characteristic and rapid provisioning on demand make Ethernet ideal for Metropolitan Area Networks.But Ethernet by itself has some weakness like flat structure that makes it unfit for use in Metropolitan Area Networks. A suitable solution for taking advantages of Ethernet benefits in service provider network is using Ethernet in access network and applying multi-point to multi-point... 

International Data Company (IDC) has reported, at the end of 2020, the total amount of digital data stored in the entire world will reach 40 thousand Exabytes. The idea of accessing this volume of data, anywhere at any time by exploiting commodity hardware, led into the introduction of cloud storage. The abounded rate and variety of failures in the equipment used in cloud storage systems, placed fault tolerance, at top of the challenges in these systems. HDFS layer in Hadoop has provided cloud with reliable storage. Replication is the conventional method to protect data against failures in HDFS. But the storage overhead is a big deal and therefore designers are tending towards erasure codes.... 

By using an encoding scheme based on Algebraic Integers (AIs), we study in this thesis how to map the real numbers needed in the computation of the FFT to integer numbers, in order to prevent error production and propagation throughout the intermediate stages of the FFT computation. To reconstruct encoded data, a decoding stage is to be used at the end of the FFT computation. AI-encoding poses two challenges; how to determine suitable AI bases and an unwanted growth in the number of data passes. This research work, firstly, determines an appropriate FFT architecture, and then, proposes a dedicated architecture based on AI-encoding. The basic and also the proposed dedicated architecture are... 

On-chip caches are regarded as a solution for increasing performance gap between main memory and CPU. In recent years, with the development in the performance of processing cores, the demands for larger on-chip caches are also increased. With the technology scaling trend, SRAM-based on-chip caches suffer from limited scalability, high leakage power consumption and vulnerability to soft errors. Among emerging non-volatile memories, STT-MRAMs are the most promising alternative for SRAMs in large last-level on-chip caches due to their higher density and near zero leakage power. However, the reliability of STT-MRAMs is threatened by soft and hard errors. Soft errors in STT-MRAMs can be... 

In this thesis, we introduce limited-sharing multi-party computation; in which there is a network of workers (processors) and a set of sources, each having access to a massive matrix as a private input. These sources aim to offload the task of computing a polynomial function of the matrices to the workers, while preserving the privacy of data. We also assume that the load of the link between each source and each worker is upper bounded by a fraction of each input. The objective is to minimize the number of workers needed to perform the computation, such that even if an arbitrary subset of t 1 workers, for some t 2 N, collude, they cannot gain any information about the input matrices. This... 

In this thesis, we argue that in many basic algorithms for machine learning, including support vector machine (SVM) for classification, principal component analysis (PCA) for dimensionality reduction, and regression for dependency estimation, we need the inner products of the data samples, rather than the data samples themselves. Motivated by the above observation, we introduce the problem of private inner product retrieval for distributed machine learning, where we have a system including a database of some files, duplicated across some non-colluding servers. A user intends to retrieve a subset of specific size of the inner products of the data files with minimum communication load, without... 

Blockchains are not scalable by design, and it is known to be the most important barrier in the way of development of these systems. One of the main approaches to this problem is sharding, that is under development in industry and academia. Sharding scales the system up by reducing redundancy, that makes blockchains vulnerable in terms of security. In this paper, we will study the effect of sharding on availability of these systems, and will show that sharding can magnify the unavailability of the service, and introduce an adversary threat model that takes real concerns of availability in today’s Internet like DoS attacks into account. We also introduce a basic unavailability-resistant... 

In this work, we consider the problem of secure multi-party computation (MPC). This system includes Γ sources, N processing nodes or workers and one data collector or master. Each node has a constraint on its storage,such that it can store 1/m fraction of size of each input matrices from each node. In addition, up to t of these workers are adversary and may collude to gain information about the private inputs or can do malicious actions to make the final result incorrect. The objective is to calculate an arbitrary polynomial of some massive private matrices as inputs while the privacy is preserved. The main concern in these kind of systems is to reduce the minimum number of workers needed... 

Zero knowledge proofs allow a person (prover) to convince another person (verifier) that he has performed a specific computation on a secret data correctly, and has obtained a true answer, without having to disclose the secret data. QAP (Quadratic Arithmetic Program) based zkSNARKs (zero knowledge Succinct Non-interactive Argument of Knowledge) are a type of zero knowledge proof. They have several properties that make them attractive in practice, e.g. verifier's work is very easy. So they are used in many areas such as Blockchain and cloud computing. But yet prover's work in QAP based zkSNARKs is heavy, therefore, it may not be possible for a prover with limited processing resource to run... 

The representation concept links the information processed by the brain back to the world and enables us to understand what the brain does at a functional level.Representational models specify how activity patterns in the population of neurons relate to sensory stimuli, motor responses, or cognitive processes. In an experimental context, representational models can be defined as hypotheses about the distribution of activity profiles across experimental conditions. Three different methods are currently being used to test such hypotheses: encoding analysis, pattern component modeling (PCM), and representational similarity analysis (RSA). All three evaluate the second moment of the distribution... 

In this contemporary era, distributed computing is a vital solution for many applications. The traditional computing scheme based on allocating one complete computation to only one server is not efficient anymore. Delay has a very important role in computation’s performance especially for the computation at the edge of the network. To alleviate the effect of big data and complex algorithms, distributed computing is a very promising solution. In this structure, all computations are divided into some small tasks or coded, based on the system's status and will be executed in parallel. In fully parallelized distributed computing, a task is broken into N smaller tasks and whenever all N subtasks... 

The classification of biological sequences is an open issue for a variety of data sets, such as viral and metagenomics sequences. Therefore, many studies utilize neural network tools, as the well-known methods in this field, and focus on designing customized network structures. However, a few works focus on more effective factors, such as input encoding method or implementation technology, to address accuracy and efficiency issues in this area. Therefore, in this work, we propose an image-based encoding method, called as WalkIm, whose adoption, even in a simple neural network, provides competitive accuracy and superior efficiency, compared to the existing classification methods (e.g. VGDC,...