NP is as easy as detecting unique solutions
Theoretical Computer Science
Algebraic methods in the theory of lower bounds for Boolean circuit complexity
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Completeness theorems for non-cryptographic fault-tolerant distributed computation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Small-bias probability spaces: efficient constructions and applications
SIAM Journal on Computing
Efficient search for approximate nearest neighbor in high dimensional spaces
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Simplified VSS and fast-track multiparty computations with applications to threshold cryptography
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
Protecting data privacy in private information retrieval schemes
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
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The round complexity of verifiable secret sharing and secure multicast
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Communication preserving protocols for secure function evaluation
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
Information-Theoretic Private Information Retrieval: A Unified Construction
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Perfect Constant-Round Secure Computation via Perfect Randomizing Polynomials
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
New Algorithms for Subset Query, Partial Match, Orthogonal Range Searching, and Related Problems
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Hiding Instances in Multioracle Queries
STACS '90 Proceedings of the 7th Annual Symposium on Theoretical Aspects of Computer Science
Security with Low Communication Overhead
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
FOCS '00 Proceedings of the 41st 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
A Geometric Approach to Information-Theoretic Private Information Retrieval
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
How to generate and exchange secrets
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
General secure multi-party computation from any linear secret-sharing scheme
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
Keyword search and oblivious pseudorandom functions
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Evaluating 2-DNF formulas on ciphertexts
TCC'05 Proceedings of the Second international conference on Theory of Cryptography
Zero-knowledge from secure multiparty computation
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Communication in the presence of replication
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
How many oblivious transfers are needed for secure multiparty computation?
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Multi-party indirect indexing and applications
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
Scalable secure multiparty computation
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
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Motivated by database search problems such as partial match or nearest neighbor, we present secure multiparty computation protocols for constant-depth circuits. Specifically, for a constant-depth circuit C of size s with an m-bit input x, we obtain the following types of protocols. – In a setting where k≥polylog(s) servers hold C and a client holds x, we obtain a protocol in which the client privately learns C(x) by communicating Õ(m) bits with each server. – In a setting where x is arbitrarily distributed between k≥polylog(s) parties who all know C, we obtain a secure protocol for evaluating C(x) using O(m ·poly(k)) communication. Both types of protocols tolerate t=k/polylog(s) dishonest parties and their computational complexity is nearly linear in s. In particular, the protocols are optimal “up to polylog factors” with respect to communication, local computation, and minimal number of participating parties. We then apply the above results to obtain sublinear-communication secure protocols for natural database search problems. For instance, for the partial match problem on a database of n points in {0,1}m we get a protocol with $k \approx \frac{1}{2} log n$ servers, Õ(m) communication, and nearly linear server computation. Applying previous protocols to this problem would either require Ω(nm) communication, Ω̃(m) servers, or super-polynomial computation.