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Private Polynomial Computation from Lagrange Encoding

Raviv, Netanel and Karpuk, David A. (2020) Private Polynomial Computation from Lagrange Encoding. IEEE Transactions on Information Forensics and Security, 15 . pp. 553-563. ISSN 1556-6013. https://resolver.caltech.edu/CaltechAUTHORS:20190709-133258792

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Abstract

Private computation is a generalization of private information retrieval, in which a user is able to compute a function on a distributed dataset without revealing the identity of that function to the servers. In this paper, it is shown that Lagrange encoding, a powerful technique for encoding Reed-Solomon codes, enables private computation in many cases of interest. In particular, we present a scheme that enables private computation of polynomials of any degree on Lagrange encoded data, while being robust to Byzantine and straggling servers, and to servers colluding to attempt to deduce the identities of the functions to be evaluated. Moreover, incorporating ideas from the well-known Shamir secret sharing scheme allows the data itself to be concealed from the servers as well. Our results extend private computation to high degree polynomials and to data-privacy, and reveal a tight connection between private computation and coded computation.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/tifs.2019.2925723DOIArticle
ORCID:
AuthorORCID
Raviv, Netanel0000-0002-1686-1994
Karpuk, David A.0000-0003-3621-9752
Additional Information:© 2019 IEEE. Manuscript received December 11, 2018; revised May 9, 2019 and June 18, 2019; accepted June 23, 2019. Date of publication July 3, 2019; date of current version September 24, 2019. This paper was presented in part at the International Symposium on Information Theory (ISIT), Vail, CO, USA, 2018. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Sheng Zhong. The first author would like to thank Prof. Jehoshua Bruck for many helpful discussions. The second author would like to thank Razane Tajeddine and Oliver Gnilke for constructive and helpful conversations regarding the results of the current work.
Subject Keywords:Private computation, private information retrieval (PIR), data privacy, Reed-Solomon codes
Record Number:CaltechAUTHORS:20190709-133258792
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190709-133258792
Official Citation:N. Raviv and D. A. Karpuk, "Private Polynomial Computation From Lagrange Encoding," in IEEE Transactions on Information Forensics and Security, vol. 15, pp. 553-563, 2020. doi: 10.1109/TIFS.2019.2925723
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97003
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:10 Jul 2019 14:32
Last Modified:03 Oct 2019 21:27

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