Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Uniform generation of NP - witnesses using an NP -oracle
Information and Computation
Secure Distributed Linear Algebra in a Constant Number of Rounds
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
PKC '01 Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Non-Interactive CryptoComputing For NC1
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Probabilistic encryption & how to play mental poker keeping secret all partial information
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
A complexity theoretic approach to randomness
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Separating the Power of Monotone Span Programs over Different Fields
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Foundations of Cryptography: Volume 2, Basic Applications
Foundations of Cryptography: Volume 2, Basic Applications
Protocols for secure computations
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
A threshold cryptosystem without a trusted party
EUROCRYPT'91 Proceedings of the 10th annual international conference on Theory and application of cryptographic techniques
Public-key cryptosystems based on composite degree residuosity classes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Evaluating 2-DNF formulas on ciphertexts
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Efficient Secure Linear Algebra in the Presence of Covert or Computationally Unbounded Adversaries
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Secure Arithmetic Computation with No Honest Majority
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
Secure linear algebra using linearly recurrent sequences
TCC'07 Proceedings of the 4th conference on Theory of cryptography
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Efficient and secure evaluation of multivariate polynomials and applications
ACNS'10 Proceedings of the 8th international conference on Applied cryptography and network security
Efficient set operations in the presence of malicious adversaries
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Privacy-preserving matrix factorization
Proceedings of the 2013 ACM SIGSAC conference on Computer & communications security
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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(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.