Sharif Digital Repository

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... 

Nowadays, we are forced to use distributed computing due to the growth of data, the challenge of storing and processing it, as well as the emergence of new problems in machine learning and the complexity of the models. In distributed computing, the computation is per- formed by a distributed system consisting of several worker nodes such that, the main task is divided into several smaller tasks and assigned to each worker node. Then, different worker nodes will cooperate to accomplish the main task. Although distributed systems are efficient in solving problems and dealing with the mentioned challenges, they are vulnerable to the presence of stragglers, adversarial worker nodes, high... 

Payment channel networks (PCNs) are a promising technology to improve the scalability of cryptocurrencies. Users can send instant and almost free transactions via payment channel networks and, at the same time, enjoy the security guarantees of Blockchains. In order to open a mutual payment channel, two users should send a ``channel creation" transaction to the underlying Blockchain. Through this transaction, two parties deposit some money on the Blockchain. This money, which we call the channel's capacity, can be used to send off-chain transactions between the two users. After the channel creation, the channel-holders can send each other off-chain transactions by forwarding the money back... 

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 consider the problem of distributed computation by many processors.We mainly concentrate on matrix multiplication problem in this thesis because of its importance. A distributed system consists of N worker processors and one master processor. The master processor should distribute the computation between workers and after computation in each of them, collect the results. In this thesis, we are going to mitigate the effect of straggler processors by using coding methods. Straggler processors can cause delays in the computation time.In this thesis, we firstly introduce a method to multiply any number of matrices in each other. The proposed method occurred in one shot without... 

In communications systems, coding is used to combat channel errors. The redundancy introduced by coding enables the detection and/or correction of errors occurring in the channel. In addition to communications systems, coding is also beneficial in various other systems such as distributed storage systems and blockchain systems to cope with node failures, data erasures, and adversarial behaviors attempting to modify information. In existing applications of coding, it is generally assumed that the encoding operation is performed correctly and without errors, and errors are applied to the encoded data. In recent years, applications have emerged where the assumption of error-free encoding is not... 

Lightweight clients are a type of blockchain users who do not store all the blocks in the blockchain due to limited resources. These users store only a small part of each block and when needed, request transactions from full nodes that store the entire blockchain. These users have no role in block validation and only want to receive transactions related to their addresses with proof of the inclusion in the block from full nodes.Since light clients rely on full nodes for receiving transactions, their privacy against full nodes is important. The current implementation of Bitcoin uses Bloom filters for privacy, but this offers very little privacy to the users.In this thesis, we study the... 

This thesis consists of two parts. For the first, we study the identifiability of finite mixtures of finite product measures. This class of mixture models has a large number of applications in real-world data modeling. An important example is the population genetic application of them in modeling of mixed population datasets. The identifiability means that the mapping between the class parameters and the mixture distributions is one to one. In this manuscript, we define some separability metrics inspired by methods used in clustering mixture models and study the fundamental trade off between identifiability and the number of separable variables of the mixture model. For the second part of... 

DNA sequence is the lifetime private information of each individual: it can reveal personal traits, health status, and medical risk of that individual, it can be abused by entities such as insurance companies, it can be used for identity theft, etc. Unfortunately, due to cost, regulations, or some restrictions, we may not be able to complete DNA sequencing in-house and have to outsource it to some unreliable companies in some foreign countries.This would compromise the DNA privacy from the beginning. This would raise the question that how we can guarantee the DNA privacy in the process of sequencing.Here we propose a solution for private DNA sequencing by exploiting the fact that the process... 

In the problem of Distributed Multi¬User Secret Sharing (DMUSS), in which K users are connected through some error¬free links to N distinct storage nodes with the same size M information unit, the users desire to retrieve their corresponding secret message through an arbitrary set of accessible storage nodes. A trusted master node, which knows all of the secret messages transmits correctly and privately, the messages with a means of coding. The capacity of Distributed Multi¬User Secret Sharing is the supremum of all achievable schemes satisfying privacy and correctness conditions. In this thesis we have investigated two notions of privacy namely, individual and joint privacy. Individual... 

Despite its extraordinary empirical achievements, the theoretical foundation of modern Machine Learning, and in particular deep neural networks (DNN), is still a mystery. In this thesis, we have studied the effect of optimization algorithms on the generalization properties for shallow neural networks. Particularly, we have focused on the implicit biases these optimization procedures, specifically dropout, deal with. As an example for this implicit bias, classical results had shown that for linear regression, in the interpolation regime, gradient descent, among all the possible solutions, converges to the minimum L2-norm interpolation. Due to the complex nature of the neural networks... 

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... 

Nowadays we are witnessing the emergence of machine learning in various applications. One of the key problems in data science and machine learning is the problem of dimensionality reduction, which deals with finding a mapping that embeds samples to a lower-dimensional space such that, the relationships between the samples and their properties are preserved in the secondary space as much as possible. Obtaining such mapping is essential in today's high-dimensional settings. Moreover, due to the large volume of data and high-dimensional samples, it is infeasible or insecure to process and store all data in a single machine. As a result, we need to process data in a distributed manner.In this... 

Nowadays, with the development of machine learning and deep learning on one hand, and the dramatic increase in the amount of information available and the complexity of models on the other hand, it is practically impossible to implement learning algorithms on a single node. Thus it is inevitable to distribute learning algorithms on several machines. In a distributed system, the main operations are divided into smaller tasks and performed by different nodes. The final result is then calculated by exchanging messages among the existing nodes.In this thesis, a method is introduced to compute the gradient of a massive data set in a distributed system. In this problem, there are a number of... 

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... 

The emerging applications of machine learning algorithms on mobile devices motivate us to offload the computation tasks of training a model or deploying a trained one to the cloud or at the edge of the network. One of the major challenges in this setup is to guarantee the privacy of the client data. Various methods have been proposed to protect privacy in the literature. Those include (i) adding noise to the client data, which reduces the accuracy of the result, (ii) using secure multiparty computation (MPC), which requires significant communication among the computing nodes or with the client, (iii) relying on homomorphic encryption (HE) methods, which significantly increases computation... 

In this thesis, we consider multiple-antenna K-user interference channels with backhaul collaboration in one side (among the transmitters or among the receivers) and investigate the trade-off between the rate in the channel versus the communication load in the backhaul. In this investigation, we focus on a first order approximation result, where the rate of the wireless channel is measured by the degrees of freedom (DoF) per user, and the load of the backhaul is measured by the entropy of backhaul messages per user normalized by log of transmit power, at high power regimes. This trade-off is fully characterized for the case of even values of K, and approximately characterized for the case of... 

Blockchain technology presents a decentralized management structure designed to cater to various needs, such as decentralization and the elimination of single points of failure. With the evolution of blockchain technology, smart contracts have emerged as a remarkable platform for facilitating financial activities in a decentralized manner. Among the different types of smart contracts, decentralized exchanges stand out by their absence of a central authority overseeing user transactions. This lack of a central oversight exposes users of such exchanges to potential attacks from malicious entities. A key challenge faced by these exchanges is the concept of Miner Extractable Value. Miner... 

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... 

A biocompatible ferrofluid containing ?Fe?_3 O_4 nanoparticles was produced using co precipitation of ?FeCl?_2.?4H?_(2 )O and ?FeCl?_3 ?6H?_2 O under ultrasonic irradiation power with NaOH being the alkaline. Two variables studied in this research were concentration and molecular weight of PEG, as the coating agent. The impact of these variables were carefully monitored on shape, size distribution and magnetic behavior of nanoparticles through SEM, DLS, XRD and VSM characterization techniques. Moreover, MRI relaxation times,T_1and T_2, were calculated using synthesized nanoparticles as contrast agents. Accordingly these nanoparticles were biologically evaluated by MTT assay. Results...