Proceedings of CRYPTO 84 on Advances in cryptology
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
Verifiable secret sharing and multiparty protocols with honest majority
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Communication complexity of secure computation (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Nonperfect secret sharing schemes and matroids
EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
On the complexity of verifiable secret sharing and multiparty computation
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Communications of the ACM
Introduction to Coding Theory
On the Cost of Reconstructing a Secret, or VSS with Optimal Reconstruction Phase
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Efficient Multiparty Protocols Using Circuit Randomization
CRYPTO '91 Proceedings of the 11th 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 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
On codes, matroids and secure multi-party computation from linear secret sharing schemes
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Algebraic geometric secret sharing schemes and secure multi-party computations over small fields
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Key Predistribution Schemes and One-Time Broadcast Encryption Schemes from Algebraic Geometry Codes
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Efficient and secure evaluation of multivariate polynomials and applications
ACNS'10 Proceedings of the 8th international conference on Applied cryptography and network security
Efficient reductions for non-signaling cryptographic primitives
ICITS'11 Proceedings of the 5th international conference on Information theoretic security
The torsion-limit for algebraic function fields and its application to arithmetic secret sharing
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
On the amortized complexity of zero knowledge protocols for multiplicative relations
ICITS'12 Proceedings of the 6th international conference on Information Theoretic Security
Linear-time encodable codes meeting the gilbert-varshamov bound and their cryptographic applications
Proceedings of the 5th conference on Innovations in theoretical computer science
A simple combinatorial treatment of constructions and threshold gaps of ramp schemes
Cryptography and Communications
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Secure computation consists of protocols for secure arithmetic: secret values are added and multiplied securely by networked processors. The striking feature of secure computation is that security is maintained even in the presence of an adversary who corrupts a quorum of the processors and who exercises full, malicious control over them. One of the fundamental primitives at the heart of secure computation is secret-sharing. Typically, the required secret-sharing techniques build on Shamir's scheme, which can be viewed as a cryptographic twist on the Reed-Solomon error correcting code. In this work we further the connections between secure computation and error correcting codes. We demonstrate that threshold secure computation in the secure channels model can be based on arbitrary codes. For a network of size n, we then show a reduction in communication for secure computation amounting to a multiplicative logarithmic factor (in n) compared to classical methods for small, e.g., constant size fields, while tolerating $t players to be corrupted, where 驴 0 can be arbitrarily small. For large networks this implies considerable savings in communication. Our results hold in the broadcast/negligible error model of Rabin and Ben-Or, and complement results from CRYPTO 2006 for the zero-error model of Ben-Or, Goldwasser and Wigderson (BGW). Our general theory can be extended so as to encompass those results from CRYPTO 2006 as well. We also present a new method for constructing high information rate ramp schemes based on arbitrary codes, and in particular we give a new construction based on algebraic geometry codes.