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 zero-one law for Boolean privacy
SIAM Journal on Discrete Mathematics
Privacy and communication complexity
SIAM Journal on Discrete Mathematics
A communication-privacy tradeoff for modular addition
Information Processing Letters
The privacy of dense symmetric functions
Computational Complexity
Reducibility and Completeness in Private Computations
SIAM Journal on Computing
On privacy and partition arguments
Information and Computation
Protocols for secure computations
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
MPC vs. SFE: perfect security in a unified corruption model
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Characterizing the cryptographic properties of reactive 2-party functionalities
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
Limits of random oracles in secure computation
Proceedings of the 5th conference on Innovations in theoretical computer science
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There are protocols to privately evaluate any function in the passive (honest-but-curious) setting assuming that the honest nodes are in majority. For some specific functions, protocols are known which remain secure even without an honest majority. The seminal work by Chor and Kushilevitz [7] gave a complete characterization of Boolean functions, showing that each Boolean function either requires an honest majority, or is such that it can be privately evaluated regardless of the number of colluding nodes. The problem of discovering the threshold for secure evaluation of more general functions remains an open problem. Towards a resolution, we provide a complete characterization of the security threshold for functions with three different outputs. Surprisingly, the zero-one law for Boolean functions extends to Z3, meaning that each function with range Z3 either requires honest majority or tolerates up to n colluding nodes.