STOC '87 Proceedings of the nineteenth 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
The knowledge complexity of interactive proof systems
SIAM Journal on Computing
SIAM Journal on Computing
Multiple NonInteractive Zero Knowledge Proofs Under General Assumptions
SIAM Journal on Computing
Universally composable two-party and multi-party secure computation
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Identity-Based Encryption from the Weil Pairing
SIAM Journal on Computing
Randomness-Optimal Characterization of Two NP Proof Systems
RANDOM '02 Proceedings of the 6th International Workshop on Randomization and Approximation Techniques
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Non-Malleable Non-Interactive Zero Knowledge and Adaptive Chosen-Ciphertext Security
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Universally Composable Security: A New Paradigm for Cryptographic Protocols
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Universally Composable Protocols with Relaxed Set-Up Assumptions
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Two theorems on random polynomial time
SFCS '78 Proceedings of the 19th Annual Symposium on Foundations of Computer Science
Zero-knowledge proofs of knowledge without interaction
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
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
Simulation-sound NIZK proofs for a practical language and constant size group signatures
ASIACRYPT'06 Proceedings of the 12th international conference on Theory and Application of Cryptology and Information Security
Non-interactive zaps and new techniques for NIZK
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Perfect non-interactive zero knowledge for NP
EUROCRYPT'06 Proceedings of the 24th annual international conference on The Theory and Applications of Cryptographic Techniques
Proceedings of the forty-first annual ACM symposium on Theory of computing
Cryptography in the multi-string model
CRYPTO'07 Proceedings of the 27th annual international cryptology 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
Universally composable multi-party computation with an unreliable common reference string
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Hybrid-secure MPC: trading information-theoretic robustness for computational privacy
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Computational soundness of symbolic zero-knowledge proofs
Journal of Computer Security - 7th International Workshop on Issues in the Theory of Security (WITS'07)
A Survey of Symbolic Methods in Computational Analysis of Cryptographic Systems
Journal of Automated Reasoning
Bringing people of different beliefs together to do UC
TCC'11 Proceedings of the 8th 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
A unified framework for UC from only OT
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
POST'13 Proceedings of the Second international conference on Principles of Security and Trust
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The common random string model introduced by Blum, Feldman and Micali permits the construction of cryptographic protocols that are provably impossible to realize in the standard model. We can think of this model as a trusted party generating a random string and giving it to all parties in the protocol. However, the introduction of such a third party should set alarm bells going off: Who is this trusted party? Why should we trust that the string is random? Even if the string is uniformly random, how do we know it does not leak private information to the trusted party? The very point of doing cryptography in the first place is to prevent us from trusting the wrong people with our secrets. In this paper, we propose the more realistic multi-string model. Instead of having one trusted authority, we have several authorities that generate random strings. We do not trust any single authority; we only assume a majority of them generate the random string honestly. This security model is reasonable, yet at the same time it is very easy to implement. We could for instance imagine random strings being provided on the Internet, and any set of parties that want to execute a protocol just need to agree on which authorities' strings they want to use. We demonstrate the use of the multi-string model in several fundamental cryptographic tasks. We define multi-string non-interactive zero-knowledge proofs and prove that they exist under general cryptographic assumptions. Our multistring NIZK proofs have very strong security properties such as simulation-extractability and extraction zero-knowledge, which makes it possible to compose them with arbitrary other protocols and to reuse the random strings. We also build efficient simulation-sound multi-string NIZK proofs for circuit satisfiability based on groups with a bilinear map. The sizes of these proofs match the best constructions in the single common random string model. We suggest a universally composable commitment scheme in the multistring model. It has been proven that UC commitment does not exist in the plain model without setup assumptions. Prior to this work, constructions were only known in the common reference string model and the registered public key model. One of the applications of the UC commitment scheme is a coin-flipping protocol in the multi-string model. Armed with the coin-flipping protocol, we can securely realize any multi-party computation protocol.