arXiv subjects

Nastaran Abadi Khooshemehr

Publications and source records attributed to Nastaran Abadi Khooshemehr.

3 recordsLinked to original sources

arXiv2023

Vers: fully distributed Coded Computing System with Distributed Encoding

Coded computing has proved to be useful in distributed computing. We have observed that almost all coded computing systems studied so far consider a setup of one master and some workers. However, recently emerging technologies such as blockchain, internet of things, and federated learning introduce new requirements for coded computing systems. In these systems, data is generated in a distributed manner, so central encoding/decoding by a master is not feasible and scalable. This paper presents a fully distributed coded computing system that consists of $k\in\mathbb{N}$ data owners and $N\in\mathbb{N}$ workers, where data owners employ workers to do some computations on their data, as specified by a target function $f$ of degree $d\in\mathbb{N}$. As there is no central encoder, workers perform encoding themselves, prior to computation phase. The challenge in this system is the presence of adversarial data owners that do not know the data of honest data owners but cause discrepancies by sending different data to different workers, which is detrimental to local encodings in workers. There are at most $β\in\mathbb{N}$ adversarial data owners, and each sends at most $v\in\mathbb{N}$ different versions of data. Since the adversaries and their possibly colluded behavior are not known to workers and honest data owners, workers compute tags of their received data, in addition to their main computational task, and send them to data owners to help them in decoding. We introduce a tag function that allows data owners to partition workers into sets that previously had received the same data from all data owners. Then, we characterize the fundamental limit of the system, $t^*$, which is the minimum number of workers whose work can be used to correctly calculate the desired function of data of honest data owners. We show that $t^*=v^βd(K-1)+1$, and present converse and achievable proofs.

cs.DC↗

arXiv2021

The Discrepancy Attack on Polyshard-ed Blockchains

Sharding, i.e. splitting the miners or validators to form and run several subchains in parallel, is known as one of the main solutions to the scalability problem of blockchains. The drawback is that as the number of miners expanding each subchain becomes small, it becomes vulnerable to security attacks. To solve this problem, a framework, named as \textit{Polyshard}, has been proposed in which each validator verifies a coded combination of the blocks introduced by different subchains, thus helping to protect the security of all subchains. In this paper, we introduce an attack on Polyshard, called \textit{the discrepancy} attack, which is the result of malicious nodes controlling a few subchains and dispersing different blocks to different nodes. We show that this attack undermines the security of Polyshard and is undetectable in its current setting.

cs.CR↗

arXiv2021

Fundamental Limits of Distributed Encoding

In general coding theory, we often assume that error is observed in transferring or storing encoded symbols, while the process of encoding itself is error-free. Motivated by recent applications of coding theory, in this paper, we consider the case where the process of encoding is distributed and prone to error. We introduce the problem of distributed encoding, comprising of $K\in\mathbb{N}$ isolated source nodes and $N\in\mathbb{N}$ encoding nodes. Each source node has one symbol from a finite field and sends it to all encoding nodes. Each encoding node stores an encoded symbol, as a function of the received symbols. However, some of the source nodes are controlled by the adversary and may send different symbols to different encoding nodes. Depending on the number of adversarial nodes, denoted by $β\in\mathbb{N}$, and the number of symbols that each one generates, denoted by $v\in\mathbb{N}$, the process of decoding from the encoded symbols could be impossible. Assume that a decoder connects to an arbitrary subset of $t \in\mathbb{N}$ encoding nodes and wants to decode the symbols of the honest nodes correctly, without necessarily identifying the sets of honest and adversarial nodes. In this paper, we study $t^*\in\mathbb{N}$, the minimum of $t$, which is a function of $K$, $N$, $β$, and $v$. We show that when the encoding nodes use linear coding, $t^*_{\textrm{linear}}=K+2β(v-1)$, if $N\ge K+2β(v-1)$, and $t^*_{\textrm{linear}}=N$, if $N\le K+2β(v-1)$. In order to achieve $t^*_{\textrm{linear}}$, we use random linear coding and show that in any feasible solution that the decoder finds, the messages of the honest nodes are decoded correctly. For the converse of the fundamental limit, we show that when the adversary behaves in a particular way, it can always confuse the decoder between two feasible solutions that differ in the message of at least one honest node.

cs.IT↗