1,378 research outputs found

    Efficient Recovery of a Shared Secret via Cooperation: Applications to SDMM and PIR

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    This work considers the problem of privately outsourcing the computation of a matrix product over a finite field Fq\mathbb{F}_q to NN helper servers. These servers are considered to be honest but curious, i.e., they behave according to the protocol but will try to deduce information about the user's data. Furthermore, any set of up to XX servers is allowed to share their data. Previous works considered this collusion a hindrance and the download cost of the schemes increases with growing XX. We propose to utilize such linkage between servers to the user's advantage by allowing servers to cooperate in the computational task. This leads to a significant gain in the download cost for the proposed schemes. The gain naturally comes at the cost of increased communication load between the servers. Hence, the proposed cooperative scheme can be understood as outsourcing both computational cost and communication cost. While the present work exemplifies the proposed server cooperation in the case of a specific secure distributed matrix multiplication (SDMM) scheme, the same idea applies to many other use cases as well. For instance, other SDMM schemes as well as linear private information retrieval (PIR) as a special case of SDMM are instantly covered.Comment: 10 pages, 2 figure

    Secure distributed matrix computation with discrete fourier transform

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    We consider the problem of secure distributed matrix computation (SDMC), where a user queries a function of data matrices generated at distributed source nodes. We assume the availability of N honest but curious computation servers, which are connected to the sources, the user, and each other through orthogonal and reliable communication links. Our goal is to minimize the amount of data that must be transmitted from the sources to the servers, called the upload cost, while guaranteeing that no T colluding servers can learn any information about the source matrices, and the user cannot learn any information beyond the computation result. We first focus on secure distributed matrix multiplication (SDMM), considering two matrices, and propose a novel polynomial coding scheme using the properties of finite field discrete Fourier transform, which achieves an upload cost significantly lower than the existing results in the literature. We then generalize the proposed scheme to include straggler mitigation, and to the multiplication of multiple matrices while keeping the input matrices, the intermediate computation results, as well as the final result secure against any T colluding servers. We also consider a special case, called computation with own data, where the data matrices used for computation belong to the user. In this case, we drop the security requirement against the user, and show that the proposed scheme achieves the minimal upload cost. We then propose methods for performing other common matrix computations securely on distributed servers, including changing the parameters of secret sharing, matrix transpose, matrix exponentiation, solving a linear system, and matrix inversion, which are then used to show how arbitrary matrix polynomials can be computed securely on distributed servers using the proposed procedur

    Information-Theoretically Private Matrix Multiplication From MDS-Coded Storage

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    We study two problems of private matrix multiplication, over a distributed computing system consisting of a master node, and multiple servers who collectively store a family of public matrices using Maximum-Distance-Separable (MDS) codes. In the first problem of Private and Secure Matrix Multiplication from Colluding servers (MDS-C-PSMM), the master intends to compute the product of its confidential matrix A\mathbf{A} with a target matrix stored on the servers, without revealing any information about A\mathbf{A} and the index of target matrix to some colluding servers. In the second problem of Fully Private Matrix Multiplication from Colluding servers (MDS-C-FPMM), the matrix A\mathbf{A} is also selected from another family of public matrices stored at the servers in MDS form. In this case, the indices of the two target matrices should both be kept private from colluding servers. We develop novel strategies for MDS-C-PSMM and MDS-C-FPMM, which simultaneously guarantee information-theoretic data/index privacy and computation correctness. The key ingredient is a careful design of secret sharings of the matrix A\mathbf{A} and the private indices, which are tailored to matrix multiplication task and MDS storage structure, such that the computation results from the servers can be viewed as evaluations of a polynomial at distinct points, from which the intended result can be obtained through polynomial interpolation. We compare the proposed MDS-C-PSMM strategy with a previous MDS-PSMM strategy with a weaker privacy guarantee (non-colluding servers), and demonstrate substantial improvements over the previous strategy in terms of communication and computation performance

    Coding for Privacy in Distributed Computing

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    I et distribuert datanettverk samarbeider flere enheter for å løse et problem. Slik kan vi oppnå mer enn summen av delene: samarbeid gjør at problemet kan løses mer effektivt, og samtidig blir det mulig å løse problemer som hver enkelt enhet ikke kan løse på egen hånd. På den annen side kan enheter som bruker veldig lang tid på å fullføre sin oppgave øke den totale beregningstiden betydelig. Denne såkalte straggler-effekten kan oppstå som følge av tilfeldige hendelser som minnetilgang og oppgaver som kjører i bakgrunnen på de ulike enhetene. Straggler-problemet blokkerer vanligvis hele beregningen siden alle enhetene må vente på at de treigeste enhetene blir ferdige. Videre kan deling av data og delberegninger mellom de ulike enhetene belaste kommunikasjonsnettverket betydelig. Spesielt i et trådløst nettverk hvor enhetene må dele en enkelt kommunikasjonskanal, for eksempel ved beregninger langs kanten av et nettverk (såkalte kantberegninger) og ved føderert læring, blir kommunikasjonen ofte flaskehalsen. Sist men ikke minst gir deling av data med upålitelige enheter økt bekymring for personvernet. En som ønsker å bruke et distribuert datanettverk kan være skeptisk til å dele personlige data med andre enheter uten å beskytte sensitiv informasjon tilstrekkelig. Denne avhandlingen studerer hvordan ideer fra kodeteori kan dempe straggler-problemet, øke effektiviteten til kommunikasjonen og garantere datavern i distribuert databehandling. Spesielt gir del A en innføring i kantberegning og føderert læring, to populære instanser av distribuert databehandling, lineær regresjon, et vanlig problem som kan løses ved distribuert databehandling, og relevante ideer fra kodeteori. Del B består av forskningsartikler skrevet innenfor rammen av denne avhandlingen. Artiklene presenterer metoder som utnytter ideer fra kodeteori for å redusere beregningstiden samtidig som datavernet ivaretas ved kantberegninger og ved føderert læring. De foreslåtte metodene gir betydelige forbedringer sammenlignet med tidligere metoder i litteraturen. For eksempel oppnår en metode fra artikkel I en 8%-hastighetsforbedring for kantberegninger sammenlignet med en nylig foreslått metode. Samtidig ivaretar vår metode datavernet, mens den metoden som vi sammenligner med ikke gjør det. Artikkel II presenterer en metode som for noen brukstilfeller er opp til 18 ganger raskere for føderert læring sammenlignet med tidligere metoder i litteraturen.In a distributed computing network, multiple devices combine their resources to solve a problem. Thereby the network can achieve more than the sum of its parts: cooperation of the devices can enable the devices to compute more efficiently than each device on its own could and even enable the devices to solve a problem neither of them could solve on its own. However, devices taking exceptionally long to finish their tasks can exacerbate the overall latency of the computation. This so-called straggler effect can arise from random effects such as memory access and tasks running in the background of the devices. The effect typically stalls the whole network because most devices must wait for the stragglers to finish. Furthermore, sharing data and results among devices can severely strain the communication network. Especially in a wireless network where devices have to share a common channel, e.g., in edge computing and federated learning, the communication links often become the bottleneck. Last but not least, offloading data to untrusted devices raises privacy concerns. A participant in the distributed computing network might be weary of sharing personal data with other devices without adequately protecting sensitive information. This thesis analyses how ideas from coding theory can mitigate the straggler effect, reduce the communication load, and guarantee data privacy in distributed computing. In particular, Part A gives background on edge computing and federated learning, two popular instances of distributed computing, linear regression, a common problem to be solved by distributed computing, and the specific ideas from coding theory that are proposed to tackle the problems arising in distributed computing. Part B contains papers on the research performed in the framework of this thesis. The papers propose schemes that combine the introduced coding theory ideas to minimize the overall latency while preserving data privacy in edge computing and federated learning. The proposed schemes significantly outperform state-of-the-art schemes. For example, a scheme from Paper I achieves an 8% speed-up for edge computing compared to a recently proposed non-private scheme while guaranteeing data privacy, whereas the schemes from Paper II achieve a speed-up factor of up to 18 for federated learning compared to current schemes in the literature for considered scenarios.Doktorgradsavhandlin
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