Communication efficient secure linear algebra

Kobbi Nissim, Enav Weinreb

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

18 Scopus citations


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 languageEnglish
Title of host publicationTheory of Cryptography
Subtitle of host publicationThird Theory of Cryptography Conference, TCC 2006, Proceedings
Number of pages20
StatePublished - 7 Jul 2006
Event3rd Theory of Cryptography Conference, TCC 2006 - New York, NY, United States
Duration: 4 Mar 20067 Mar 2006

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3876 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference3rd Theory of Cryptography Conference, TCC 2006
Country/TerritoryUnited States
CityNew York, NY

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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