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
An Optimal Probabilistic Protocol for Synchronous Byzantine Agreement
SIAM Journal on Computing
Fair Computation of General Functions in Presence of Immoral Majority
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Foundations of Secure Interactive Computing
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
Protocols for secure computations
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Multiparty computation with faulty majority
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Reducibility and completeness in multi-party private computations
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
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 Adaptive vs. Non-adaptive Security of Multiparty Protocols
EUROCRYPT '01 Proceedings of the International Conference on the Theory and Application of Cryptographic Techniques: Advances in Cryptology
One Round Threshold Discrete-Log Key Generation without Private Channels
PKC '01 Proceedings of the 4th International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Rational Secure Computation and Ideal Mechanism Design
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Founding Cryptography on Oblivious Transfer --- Efficiently
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Sharemind: A Framework for Fast Privacy-Preserving Computations
ESORICS '08 Proceedings of the 13th European Symposium on Research in Computer Security: Computer Security
Realistic Failures in Secure Multi-party Computation
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
Information-Theoretically Secure Protocols and Security under Composition
SIAM Journal on Computing
Perfectly-secure multiplication for any t n/3
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
Universally composable security with local adversaries
SCN'12 Proceedings of the 8th international conference on Security and Cryptography for Networks
Universally composable synchronous computation
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
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Secure Function Evaluation (SFE) protocols are very hard to design, and reducibility has been recognized as a highly desirable property of SFE protocols. Informally speaking, reducibility (sometimes called modular composition) is the automatic ability to break up the design of complex SFE protocols into several simpler, individually secure components. Despite much effort, only the most basic type of reducibility, sequential reducibility (where only a single sub-protocol can be run at a time), has been considered and proven to hold for a specific class of SFE protocols. Unfortunately, sequential reducibility does not allow one to save on the number of rounds (often the most expensive resource in a distributed setting), and achieving more general notions is not easy (indeed, certain SFE notions provably enjoy sequential reducibility, but fail to enjoy more general ones). In this paper, for information-theoretic SFE protocols, we • Formalize the notion of parallel reducibility, where sub-protocols can be run at the same time; • Clarify that there are two distinct forms of parallel reducibility: * Concurrent reducibility, which applies when the order of the sub-protocol calls is not important (and which reduces the round complexity dramatically as compared to sequential reducibility); and * Synchronous reducibility, which applies when the sub-protocols must be executed simultaneously (and which allows modular design in settings where sequential reducibility does not even apply). • Show that a large class of SFE protocols (i.e., those satisfying a slight modification of the original definition of Micali and Rogaway) provably enjoy (both forms of) parallel reducibility.