Universally composable two-party and multi-party secure computation
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
The All-or-Nothing Nature of Two-Party Secure Computation
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Parallel Reducibility for Information-Theoretically Secure Computation
CRYPTO '00 Proceedings of the 20th Annual International Cryptology Conference on Advances in Cryptology
Minimal Complete Primitives for Secure Multi-party Computation
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Committed Oblivious Transfer and Private Multi-Party Computation
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Cryptographic Complexity of Multi-Party Computation Problems: Classifications and Separations
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Conditional oblivious transfer and timed-release encryption
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Single database private information retrieval implies oblivious transfer
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Identifying cheaters without an honest majority
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Completeness for symmetric two-party functionalities - revisited
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
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We define the notions of reducibility and completeness in multi-party private computations. Let g be an n-argument function. We say that a function f is reducible to g if n honest-but-curious players can compute the function f n-privately, given a black-box for g (for which they secretly give inputs and get the result of operating g on these inputs). We say that g is complete (for multi-party private computations) if every function f is reducible to g. In this paper, we characterize the complete Boolean functions: we show that a Boolean function g is complete if and only if g itself cannot be computed n-privately (when there is no black-box available). Namely, for Boolean functions, the notions of completeness and n-privacy are complementary. This characterization gives a huge collection of complete functions (any non-private Boolean function!) compared to very few examples given (implicitly) in previous work. On the other hand, for non-Boolean functions, we show that these two notions are not complementary. Our results can be viewed as a generalization (for multi-party protocols and for (n/spl ges/2)-argument functions) of the two-party case, where it was known that Oblivious Transfer protocol (and its variants) are complete.