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The knowledge complexity of interactive proof systems
SIAM Journal on Computing
The round complexity of secure protocols
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On the Composition of Zero-Knowledge Proof Systems
SIAM Journal on Computing
An Optimal Probabilistic Protocol for Synchronous Byzantine Agreement
SIAM Journal on Computing
Fully Polynomial Byzantine Agreement for Processors in Rounds
SIAM Journal on Computing
Reaching Agreement in the Presence of Faults
Journal of the ACM (JACM)
Composition and integrity preservation of secure reactive systems
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Efficient oblivious transfer protocols
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
The round complexity of verifiable secret sharing and secure multicast
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Universally composable two-party and multi-party secure computation
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Foundations of Cryptography: Basic Tools
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On 2-Round Secure Multiparty Computation
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Security of Blind Digital Signatures (Extended Abstract)
CRYPTO '97 Proceedings of the 17th Annual International Cryptology Conference on Advances in Cryptology
Non-Interactive CryptoComputing For NC1
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Oblivious signature-based envelope
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Universally Composable Security: A New Paradigm for Cryptographic Protocols
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Foundations of Cryptography: Volume 2, Basic Applications
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Concealing complex policies with hidden credentials
Proceedings of the 11th ACM conference on Computer and communications security
Universally Composable Protocols with Relaxed Set-Up Assumptions
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Policy-based encryption schemes from bilinear pairings
ASIACCS '06 Proceedings of the 2006 ACM Symposium on Information, computer and communications security
Attribute-Based Access Control with Hidden Policies and Hidden Credentials
IEEE Transactions on Computers
Expressiveness of definitions and efficiency of constructions in computational cryptography
Expressiveness of definitions and efficiency of constructions in computational cryptography
How to generate and exchange secrets
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
A Proof of Security of Yao’s Protocol for Two-Party Computation
Journal of Cryptology
Universally composable security with global setup
TCC'07 Proceedings of the 4th conference on Theory of cryptography
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
A construction for general and efficient oblivious commitment based envelope protocols
ICICS'06 Proceedings of the 8th international conference on Information and Communications Security
Smooth projective hashing and two-message oblivious transfer
EUROCRYPT'05 Proceedings of the 24th annual international conference on Theory and Applications of Cryptographic Techniques
Round-optimal composable blind signatures in the common reference string model
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Round-Optimal and efficient verifiable secret sharing
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Security of Blind Signatures under Aborts
Irvine Proceedings of the 12th International Conference on Practice and Theory in Public Key Cryptography: PKC '09
Secure Multi-party Computation Minimizing Online Rounds
ASIACRYPT '09 Proceedings of the 15th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Two-party computing with encrypted data
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
Equivocal blind signatures and adaptive UC-security
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Secure multiparty computation with minimal interaction
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Impossibility of blind signatures from one-way permutations
TCC'11 Proceedings of the 8th conference on Theory of cryptography
Efficient non-interactive secure computation
EUROCRYPT'11 Proceedings of the 30th Annual international conference on Theory and applications of cryptographic techniques: advances in cryptology
Round optimal blind signatures
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
On the impossibility of three-move blind signature schemes
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Security of blind signatures revisited
PKC'12 Proceedings of the 15th international conference on Practice and Theory in Public Key Cryptography
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Round complexity is a central measure of efficiency, and characterizing the round complexity of various cryptographic tasks is of both theoretical and practical importance. We show here a universally-composable (UC) protocol (in the common reference string model) for two-party computation of any functionality, where both parties receive output, using only two rounds. (This assumes honest parties are allowed to transmit messages simultaneously in any given round; we obtain a three-round protocol when parties are required to alternate messages.) Our results match the obvious lower bounds for the round complexity of secure two-party computation under any reasonable definition of security, regardless of what setup is used. Thus, our results establish that secure two-party computation can be obtained under a commonly-used setup assumption with maximal security (i.e., security under general composition) in a minimal number of rounds. To give but one example of the power of our general result, we observe that as an almost immediate corollary we obtain a two-round UC blind signature scheme, matching a result by Fischlin at Crypto 2006 (though, in contrast to Fischlin, we use specific number-theoretic assumptions).