TY - GEN

T1 - Communication efficient secure linear algebra

AU - Nissim, Kobbi

AU - Weinreb, Enav

PY - 2006/7/7

Y1 - 2006/7/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33745558215&partnerID=8YFLogxK

U2 - 10.1007/11681878_27

DO - 10.1007/11681878_27

M3 - Conference contribution

AN - SCOPUS:33745558215

SN - 3540327312

SN - 9783540327318

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 522

EP - 541

BT - Theory of Cryptography

T2 - 3rd Theory of Cryptography Conference, TCC 2006

Y2 - 4 March 2006 through 7 March 2006

ER -