A randomized protocol for signing contracts
Communications of the ACM
STOC '87 Proceedings of the nineteenth 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
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
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
The All-or-Nothing Nature of Two-Party Secure Computation
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference 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
Foundations of Cryptography: Volume 2, Basic Applications
Foundations of Cryptography: Volume 2, Basic Applications
Completeness in two-party secure computation: a computational view
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Protocols for secure computations
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
How to generate and exchange secrets
SFCS '86 Proceedings of the 27th 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
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
Computational Differential Privacy
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
Limits of random oracles in secure computation
Proceedings of the 5th conference on Innovations in theoretical computer science
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Understanding the minimal assumptions required for carrying out cryptographic tasks is one of the fundamental goals of theoretical cryptography. A rich body of work has been dedicated to understanding the complexity of cryptographic tasks in the context of (semi-honest) secure two-party computation. Much of this work has focused on the characterization of trivial and complete functionalities (resp., functionalities that can be securely implemented unconditionally, and functionalities that can be used to securely compute all functionalities). All previous works define reductions via an ideal implementation of the functionality; i.e., f reduces to g if one can implement f using an ideal box (or oracle) that computes the function g and returns the output to both parties. Such a reduction models the computation of f as an atomic operation. However, in the real-world, protocols proceed in rounds, and the output is not learned by the parties simultaneously. In this paper we show that this distinction is significant. Specifically, we show that there exist symmetric functionalities (where both parties receive the same outcome), that are neither trivial nor complete under "ideal-box reductions", and yet the existence of a constant-round protocol for securely computing such a functionality implies infinitely-often oblivious transfer (meaning that it is secure for infinitely-many n's). In light of the above, we propose an alternative definitional infrastructure for studying the triviality and completeness of functionalities.