Communication efficient secure linear algebra

Kobbi Nissim; Enav Weinreb

doi:10.1007/11681878_27

Communication efficient secure linear algebra

Kobbi Nissim
, Enav Weinreb

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

19 Scopus citations

Abstract

We present communication efficient secure protocols for a variety of linear algebra problems. Our main building block is a protocol for computing Gaussian Elimination on encrypted data. As input for this protocol, Bob holds a k × k matrix M, encrypted with Alice's key. At the end of the protocol run, Bob holds an encryption of an upper-triangular matrix M′ such that the number of nonzero elements on the diagonal equals the rank of M. The communication complexity of our protocol is roughly O(k²). Building on Oblivious Gaussian elimination, we present secure protocols for several problems: deciding the intersection of linear and affine subspaces, picking a random vector from the intersection, and obliviously solving a set of linear equations. Our protocols match known (insecure) communication complexity lower bounds, and improve the communication complexity of both Yao's garbled circuits and that of specific previously published protocols.

Original language	English
Title of host publication	Theory of Cryptography
Subtitle of host publication	Third Theory of Cryptography Conference, TCC 2006, Proceedings
Publisher	Springer Verlag
Pages	522-541
Number of pages	20
ISBN (Print)	3540327312, 9783540327318
DOIs	https://doi.org/10.1007/11681878_27
State	Published - 1 Jan 2006
Event	3rd Theory of Cryptography Conference, TCC 2006 - New York, NY, United States Duration: 4 Mar 2006 → 7 Mar 2006

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3876 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd Theory of Cryptography Conference, TCC 2006
Country/Territory	United States
City	New York, NY
Period	4/03/06 → 7/03/06

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

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10.1007/11681878_27

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Nissim, K., & Weinreb, E. (2006). Communication efficient secure linear algebra. In Theory of Cryptography: Third Theory of Cryptography Conference, TCC 2006, Proceedings (pp. 522-541). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3876 LNCS). Springer Verlag. https://doi.org/10.1007/11681878_27

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Nissim, K & Weinreb, E 2006, Communication efficient secure linear algebra. in Theory of Cryptography: Third Theory of Cryptography Conference, TCC 2006, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3876 LNCS, Springer Verlag, pp. 522-541, 3rd Theory of Cryptography Conference, TCC 2006, New York, NY, United States, 4/03/06. https://doi.org/10.1007/11681878_27

Communication efficient secure linear algebra. / Nissim, Kobbi; Weinreb, Enav.
Theory of Cryptography: Third Theory of Cryptography Conference, TCC 2006, Proceedings. Springer Verlag, 2006. p. 522-541 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3876 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Communication efficient secure linear algebra

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