The All-or-Nothing Nature of Two-Party Secure Computation
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Oblivious Transfer in the Bounded Storage Model
CRYPTO '01 Proceedings of the 21st 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
Efficient Oblivious Transfer in the Bounded-Storage Model
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Completeness in two-party secure computation: a computational view
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Cryptographic Complexity of Multi-Party Computation Problems: Classifications and Separations
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Complete Fairness in Multi-party Computation without an Honest Majority
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
Single database private information retrieval implies oblivious transfer
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
On the limitations of universally composable two-party computation without set-up assumptions
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Round efficiency of multi-party computation with a dishonest majority
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Secret swarm unit: reactive k-secret sharing
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
Almost-everywhere secure computation
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
A zero-one law for cryptographic complexity with respect to computational UC security
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
A zero-one law for secure multi-party computation with ternary outputs
TCC'11 Proceedings of the 8th conference on Theory of cryptography
Non-local box complexity and secure function evaluation
Quantum Information & Computation
On complete primitives for fairness
TCC'10 Proceedings of the 7th international conference on Theory of Cryptography
Identifying cheaters without an honest majority
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
Ad Hoc Networks
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
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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We define the notions of reducibility and completeness in (two-party and multiparty) private computations. Let g be an n-argument function. We say that a function f is reducible to a function 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 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 n-argument boolean functions, the notions of completeness and n-privacy are complementary. This characterization provides a huge collection of complete functions any nonprivate boolean function!) compared to very few examples that were given (implicitly) in previous work. On the other hand, for nonboolean functions, we show that these two notions are not complementary.