Completeness theorems for non-cryptographic fault-tolerant distributed computation
STOC '88 Proceedings of the twentieth 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
Universally Composable Commitments
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Bounded-concurrent secure two-party computation without setup assumptions
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Universally Composable Security: A New Paradigm for Cryptographic Protocols
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Bounded-Concurrent Secure Two-Party Computation in a Constant Number of Rounds
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Bounded-concurrent secure multi-party computation with a dishonest majority
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Universally Composable Protocols with Relaxed Set-Up Assumptions
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Information-theoretically secure protocols and security under composition
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Concurrent Non-Malleable Zero Knowledge
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Cryptography from Sunspots: How to Use an Imperfect Reference String
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Universally Composable Multi-party Computation Using Tamper-Proof Hardware
EUROCRYPT '07 Proceedings of the 26th annual international conference on Advances in Cryptology
Proceedings of the forty-first annual ACM symposium on Theory of computing
Universally composable security with global setup
TCC'07 Proceedings of the 4th conference on Theory of cryptography
Cryptography in the multi-string model
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Isolated proofs of knowledge and isolated zero knowledge
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
David and Goliath commitments: UC computation for asymmetric parties using tamper-proof hardware
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
New constructions for UC secure computation using tamper-proof hardware
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Universally composable multi-party computation with an unreliable common reference string
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Concurrently secure computation in constant rounds
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Non-black-box simulation in the fully concurrent setting
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Known constructions of UC secure protocols are based on the premise that different parties collectively agree on some trusted setup. In this paper, we consider the following two intriguing questions: Is it possible to achieve UC if the parties do not want to put all their trust in one entity (or more generally, in one setup)? What if the parties have a difference of opinion about what they are willing to trust? The first question has been studied in only a limited way, while the second has never been considered before. In this paper, we initiate a systematic study to answer the above questions. We consider a scenario with multiple setup instances where each party in the system has some individual belief (setup assumption in terms of the given setups). The belief of a party corresponds to what it is willing to trust and its security is guaranteed given that its belief "holds." The question considered is: "Given some setups and the (possibly) different beliefs of all the parties, when can UC security be achieved?" We present a general condition on the setups and the beliefs of all the parties under which UC security is possible. Surprisingly, we show that when parties have different beliefs, UC security can be achieved with a more limited "trust" than what is necessary in the traditional setting (where all parties have a common belief).