General Framework for Linear Secure Distributed Matrix Multiplication with Byzantine Servers

Okko, Makkonen,; Hollanti, Camilla

doi:10.48550/arxiv.2205.07052

Cited by 2 publications

(6 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Most SDMM schemes in the literature follow some kind of linear structure, where the encoded matrices are obtained as linear combinations of the matrices and some random noise that is added. This structure has been presented as a general framework called linear SDMM in [14]. We shall present our contributions using the help of this framework.…”

Section: Preliminariesmentioning

confidence: 99%

“…In [14] it was shown that a linear SDMM scheme is secure against X-collusion if F >m and G >n generate MDS codes.…”

Section: Preliminariesmentioning

confidence: 99%

“…1 × 1 submatrix of F >p is invertible since α i = 0. By using the result from [14], the scheme is secure for X = 1.…”

Section: Our Proposed Constructionmentioning

confidence: 99%

“…We wish to compare our proposed scheme to regular SDMM schemes in terms of the upload cost, due to the nature of our problem. It is natural to compare our scheme against the secure MatDot scheme, since it is able to achieve the lowest possible recovery threshold and upload cost according to the result in [14]. We will also compare our scheme to the DFT scheme in [4], which also uses the inner product partitioning.…”

Section: E Comparisonmentioning

confidence: 99%

See 3 more Smart Citations

Analog Secure Distributed Matrix Multiplication over Complex Numbers

Okko

Hollanti

2022

2022 IEEE International Symposium on Information Theory (ISIT)

View full text Add to dashboard Cite

This work considers the problem of distributing matrix multiplication over the real or complex numbers to helper servers, such that the information leakage to these servers is close to being information-theoretically secure. These servers are assumed to be honest-but-curious, i.e., they work according to the protocol, but try to deduce information about the data. The problem of secure distributed matrix multiplication (SDMM) has been considered in the context of matrix multiplication over finite fields, which is not always feasible in real world applications. We present two schemes, which allow for variable degree of security based on the use case and allow for colluding and straggling servers. We analyze the security and the numerical accuracy of the schemes and observe a trade-off between accuracy and security.• Encoding phase: The user partitions the matrices to smaller submatrices and draws random matrices of the same size. These smaller matrices are encoded using some code and the encoded pieces ˜︁ A i , ˜︁ B i are sent to server i. This part can be seen as a secret sharing phase, where the secret matrices are shared among the servers.

show abstract

Section: Preliminariesmentioning

confidence: 99%

“…In [14] it was shown that a linear SDMM scheme is secure against X-collusion if F >m and G >n generate MDS codes.…”

Section: Preliminariesmentioning

confidence: 99%

“…1 × 1 submatrix of F >p is invertible since α i = 0. By using the result from [14], the scheme is secure for X = 1.…”

Section: Our Proposed Constructionmentioning

confidence: 99%

Section: E Comparisonmentioning

confidence: 99%

See 2 more Smart Citations

Analog Secure Distributed Matrix Multiplication over Complex Numbers

Okko

Hollanti

2022

2022 IEEE International Symposium on Information Theory (ISIT)

View full text Add to dashboard Cite

show abstract

“…For small numbers of stragglers [20] constructs schemes that outperform the entangled polynomial scheme. Recently, several attempts have been made to design coding schemes to further reduce upload and download rates, the recovery threshold, and computational complexity for both workers and server (see, for example, [21][22][23][24][25][26][27]). For example, in [21], bivariate polynomial codes were used to reduce the recovery threshold in specific cases.…”

Section: Introductionmentioning

confidence: 99%

Straggler- and Adversary-Tolerant Secure Distributed Matrix Multiplication Using Polynomial Codes

Byrne

Gnilke

Kliewer

2023

Entropy

View full text Add to dashboard Cite

Large matrix multiplications commonly take place in large-scale machine-learning applications. Often, the sheer size of these matrices prevent carrying out the multiplication at a single server. Therefore, these operations are typically offloaded to a distributed computing platform with a master server and a large amount of workers in the cloud, operating in parallel. For such distributed platforms, it has been recently shown that coding over the input data matrices can reduce the computational delay by introducing a tolerance against straggling workers, i.e., workers for which execution time significantly lags with respect to the average. In addition to exact recovery, we impose a security constraint on both matrices to be multiplied. Specifically, we assume that workers can collude and eavesdrop on the content of these matrices. For this problem, we introduce a new class of polynomial codes with fewer non-zero coefficients than the degree +1. We provide closed-form expressions for the recovery threshold and show that our construction improves the recovery threshold of existing schemes in the literature, in particular for larger matrix dimensions and a moderate to large number of colluding workers. In the absence of any security constraints, we show that our construction is optimal in terms of recovery threshold.

show abstract

General Framework for Linear Secure Distributed Matrix Multiplication with Byzantine Servers

Cited by 2 publications

References 0 publications

Analog Secure Distributed Matrix Multiplication over Complex Numbers

Analog Secure Distributed Matrix Multiplication over Complex Numbers

Straggler- and Adversary-Tolerant Secure Distributed Matrix Multiplication Using Polynomial Codes

Contact Info

Product

Resources

About