STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Completeness theorems for non-cryptographic fault-tolerant distributed computation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Multiparty unconditionally secure protocols
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Founding crytpography on oblivious transfer
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Non-cryptographic fault-tolerant computing in constant number of rounds of interaction
Proceedings of the eighth annual ACM Symposium on Principles of distributed computing
Verifiable secret sharing and multiparty protocols with honest majority
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
The round complexity of secure protocols
STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
A minimal model for secure computation (extended abstract)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Robust sharing of secrets when the dealer is honest or cheating
Journal of the ACM (JACM)
Adaptively secure multi-party computation
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Simplified VSS and fast-track multiparty computations with applications to threshold cryptography
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
On arithmetic branching programs
Journal of Computer and System Sciences
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Private Simultaneous Messages Protocols with Applications
ISTCS '97 Proceedings of the Fifth Israel Symposium on the Theory of Computing Systems (ISTCS '97)
Determinant: Combinatorics, Algorithms, and Complexity
Determinant: Combinatorics, Algorithms, and Complexity
Protocols for secure computations
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Efficient multiparty computations secure against an adaptive adversary
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
General secure multi-party computation from any linear secret-sharing scheme
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Minimal-latency secure function evaluation
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Perfect Constant-Round Secure Computation via Perfect Randomizing Polynomials
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
On 2-Round Secure Multiparty Computation
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Atomic Secure Multi-party Multiplication with Low Communication
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Efficient Disjointness Tests for Private Datasets
ACISP '08 Proceedings of the 13th Australasian conference on Information Security and Privacy
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
Anonymous biometric access control
EURASIP Journal on Information Security - Special issue on enhancing privacy protection in multimedia systems
Secure multiparty computation with minimal interaction
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Constant-round multiparty computation using a black-box pseudorandom generator
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Efficient polynomial operations in the shared-coefficients setting
PKC'06 Proceedings of the 9th international conference on Theory and Practice of Public-Key Cryptography
Improved efficiency for private stable matching
CT-RSA'07 Proceedings of the 7th Cryptographers' track at the RSA conference on Topics in Cryptology
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Communication efficient secure linear algebra
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Accelerating multiparty computation by efficient random number bitwise-sharing protocols
WISA'11 Proceedings of the 12th international conference on Information Security Applications
Secure distributed computation of the square root and applications
ISPEC'12 Proceedings of the 8th international conference on Information Security Practice and Experience
Batching multiple protocols to improve efficiency of multi-party computation
Inscrypt'11 Proceedings of the 7th international conference on Information Security and Cryptology
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Consider a network of processors among which elements in a finite field K can be verifiably shared in a constant number of rounds. Assume furthermore constant-round protocols are available for generating random shared values, for secure multiplication and for addition of shared values. These requirements can be met by known techniques in all standard models of communication. In this model we construct protocols allowing the network to securely solve standard computational problems in linear algebra. In particular, we show how the network can securely, efficiently and in constant-round compute determinant, characteristic polynomial, rank, and the solution space of linear systems of equations. Constant round solutions follow for all problems which can be solved by direct application of such linear algebraic methods, such as deciding whether a graph contains a perfect match. If the basic protocols (for shared random values, addition and multiplication) we start from are unconditionally secure, then so are our protocols. Our results offer solutions that are significantly more efficient than previous techniques for secure linear algebra, they work for arbitrary fields and therefore extend the class of functions previously known to be computable in constant round and with unconditional security. In particular, we obtain an unconditionally secure protocol for computing a function f in constant round, where the protocol has complexity polynomial in the span program size of f over an arbitrary finite field.