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Published in:
2006 | OriginalPaper | Chapter
Communication Efficient Secure Linear Algebra
Authors : Kobbi Nissim, Enav Weinreb
Published in: Theory of Cryptography
Publisher: Springer Berlin Heidelberg
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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
(
k
2
).
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.