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Published 2020 | Submitted
Journal Article Open

Private Polynomial Computation from Lagrange Encoding

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.

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.

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August 19, 2023
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