A randomized protocol for signing contracts
Communications of the ACM
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
Founding crytpography on oblivious transfer
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
A hard-core predicate for all one-way functions
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Limits on the provable consequences of one-way permutations
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
A general completeness theorem for two party games
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
A zero-one law for Boolean privacy
SIAM Journal on Discrete Mathematics
Journal of the ACM (JACM)
Non-interactive oblivious transfer and applications
CRYPTO '89 Proceedings on Advances in cryptology
Privacy and communication complexity
SIAM Journal on Discrete Mathematics
More general completeness theorems for secure two-party computation
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Reducibility and Completeness in Private Computations
SIAM Journal on Computing
Efficient oblivious transfer protocols
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
Equivalence Between Two Flavours of Oblivious Transfers
CRYPTO '87 A Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology
The relationship between public key encryption and oblivious transfer
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
A personal view of average-case complexity
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
Foundations of Cryptography: Volume 2, Basic Applications
Foundations of Cryptography: Volume 2, Basic Applications
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Oblivious-Transfer Amplification
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
How many oblivious transfers are needed for secure multiparty computation?
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
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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A Secure Function Evaluation (SFE) of a two-variable function f(·,·) is a protocol that allows two parties with inputs x and y to evaluate f(x,y) in a manner where neither party learns "more than is necessary". A rich body of work deals with the study of completeness for secure two-party computation. A function f is complete for SFE if a protocol for securely evaluating f allows the secure evaluation of all (efficiently computable) functions. The questions investigated are which functions are complete for SFE, which functions have SFE protocols unconditionally and whether there are functions that are neither complete nor have efficient SFE protocols.The previous study of these questions was mainly conducted from an Information Theoretic point of view and provided strong answers in the form of combinatorial properties. However, we show that there are major differences between the information theoretic and computational settings. In particular, we show functions that are considered as having SFE unconditionally by the combinatorial criteria but are actually complete in the computational setting. We initiate the fully computational study of these fundamental questions. Somewhat surprisingly, we manage to provide an almost full characterization of the complete functions in this model as well. More precisely, we present a computational criterion (called computational row non-transitivity) for a function f to be complete for the asymmetric case. Furthermore, we show a matching criterion called computational row transitivity for f to have a simple SFE (based on no additional assumptions). This criterion is close to the negation of the computational row non-transitivity and thus we essentially characterize all "nice" functions as either complete or having SFE unconditionally.