Limits on the security of coin flips when half the processors are faulty
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Non-interactive zero-knowledge and its applications
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
A zero-one law for Boolean privacy
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
More general completeness theorems for secure two-party computation
STOC '00 Proceedings of the thirty-second 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
Precomputing Oblivious Transfer
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Universally Composable Security: A New Paradigm for Cryptographic Protocols
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Protocols for secure computations
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
One-way functions are essential for complexity based cryptography
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Privacy and communication complexity
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Cryptographic Complexity of Multi-Party Computation Problems: Classifications and Separations
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
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
TCC '09 Proceedings of the 6th Theory of Cryptography Conference on Theory of Cryptography
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
Exploring the limits of common coins using frontier analysis of protocols
TCC'11 Proceedings of the 8th conference on Theory of cryptography
Exploring the limits of common coins using frontier analysis of protocols
TCC'11 Proceedings of the 8th conference on Theory of cryptography
The limits of common coins: further results
INDOCRYPT'11 Proceedings of the 12th international conference on Cryptology in India
Limits of random oracles in secure computation
Proceedings of the 5th conference on Innovations in theoretical computer science
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In 2-party secure computation, access to common, trusted randomness is a fundamental primitive. It is widely employed in the setting of computationally bounded players (under various complexity assumptions) to great advantage. In this work we seek to understand the power of trusted randomness, primarily in the computationally unbounded (or information theoretic) setting. We show that a source of common randomness does not add any additional power for secure evaluation of deterministic functions, even when one of the parties has arbitrary influence over the distribution of the common randomness. Further, common randomness helps only in a trivial sense for realizing randomized functions too (namely, it only allows for sampling from publicly fixed distributions), if UC security is required. To obtain these impossibility results, we employ a recently developed protocol analysis technique, which we call the frontier analysis. This involves analyzing carefully defined "frontiers" in a weighted tree induced by the protocol's execution (or executions, with various inputs), and establishing various properties regarding one or more such frontiers. We demonstrate the versatility of this technique by employing carefully chosen frontiers to derive the different results. To analyze randomized functionalities we introduce a frontier argument that involves a geometric analysis of the space of probability distributions. Finally, we relate our results to computational intractability questions. We give an equivalent formulation of the "cryptomania assumption" (that there is a semi-honest or standalone secure oblivious transfer protocol) in terms of UC-secure reduction among randomized functionalities. Also, we provide an unconditional result on the uselessness of common randomness, even in the computationally bounded setting. Our results make significant progress towards understanding the exact power of shared randomness in cryptography. To the best of our knowledge, our results are the first to comprehensively characterize the power of large classes of randomized functionalities.