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
A complexity theory of efficient parallel algorithms
Theoretical Computer Science - Special issue: Fifteenth international colloquium on automata, languages and programming, Tampere, Finland, July 1988
Communication complexity of secure computation (extended abstract)
STOC '92 Proceedings of the twenty-fourth 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
Communications of the ACM
The round complexity of verifiable secret sharing and secure multicast
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Robustness for Free in Unconditional Multi-party Computation
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Secure Distributed Linear Algebra in a Constant Number of Rounds
CRYPTO '01 Proceedings of the 21st Annual International Cryptology 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
Secure Computation from Random Error Correcting Codes
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Secure computation, i/o-efficient algorithms and distributed signatures
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
Hi-index | 0.04 |
We consider the standard secure multi-party multiplication protocol due to M. Rabin. This protocol is based on Shamir's secret sharing scheme and it can be viewed as a practical variation on one of the central techniques in the foundational results of Ben-Or, Goldwasser, and Wigderson and Chaum, Crépeau, and Damgaard on secure multi-party computation. Rabin's idea is a key ingredient to virtually all practical protocols in threshold cryptography.Given a passive t-adversary in the secure channels model with synchronous communication, for example, secure multiplication of two secret-shared elements from a finite field Kbased on this idea uses one communication round and has the network exchange O(n2) field elements, if t= 驴(n) and tn/2 and if nis the number of players. This is because each of O(n) players must perform Shamir secret sharing as part of the protocol. This paper demonstrates that under a few restrictions much more efficient protocols are possible; even at the level of a single multiplication.We demonstrate a twist on Rabin's idea that enables one-round secure multiplication with just O(n)bandwidthin certain settings, thus reducing it from quadratic to linear. The ideas involved can additionally be employed in the evaluation of arithmetic circuits, where under appropriate circumstances similar efficiency gains can be obtained.