A public key cryptosystem and a signature scheme based on discrete logarithms
Proceedings of CRYPTO 84 on Advances in cryptology
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
Multiparty unconditionally secure protocols
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Verifiable secret sharing and multiparty protocols with honest majority
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Communication complexity of secure computation (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Communications of the ACM
Cryptographic Computation: Secure Faut-Tolerant Protocols and the Public-Key Model
CRYPTO '87 A Conference on the Theory and Applications of Cryptographic Techniques on Advances in Cryptology
Sharing Decryption in the Context of Voting or Lotteries
FC '00 Proceedings of the 4th International Conference on Financial Cryptography
Probabilistic encryption & how to play mental poker keeping secret all partial information
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Oblivious Polynomial Evaluation
SIAM Journal on Computing
Foundations of cryptography: a primer
Foundations and Trends® in Theoretical Computer Science
Secure Distributed Key Generation for Discrete-Log Based Cryptosystems
Journal of Cryptology
Protocols for secure computations
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
How to generate and exchange secrets
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
A practical scheme for non-interactive verifiable secret sharing
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Founding Cryptography on Oblivious Transfer --- Efficiently
CRYPTO 2008 Proceedings of the 28th Annual conference on Cryptology: Advances in Cryptology
Secure Arithmetic Computation with No Honest Majority
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
Fully homomorphic encryption using ideal lattices
Proceedings of the forty-first annual ACM symposium on Theory of computing
Efficient Robust Private Set Intersection
ACNS '09 Proceedings of the 7th International Conference on Applied Cryptography and Network Security
Efficient and secure protocols for privacy-preserving set operations
ACM Transactions on Information and System Security (TISSEC)
Information Theoretically Secure Multi Party Set Intersection Re-visited
Selected Areas in Cryptography
Round Efficient Unconditionally Secure MPC and Multiparty Set Intersection with Optimal Resilience
INDOCRYPT '09 Proceedings of the 10th International Conference on Cryptology in India: Progress in Cryptology
Proving in zero-knowledge that a number is the product of two safe primes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
Public-key cryptosystems based on composite degree residuosity classes
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Black-box construction of a non-malleable encryption scheme from any semantically secure one
TCC'08 Proceedings of the 5th conference on Theory of cryptography
Efficient and secure evaluation of multivariate polynomials and applications
ACNS'10 Proceedings of the 8th international conference on Applied cryptography and network security
Privacy-preserving set operations
CRYPTO'05 Proceedings of the 25th annual international conference on Advances in Cryptology
Fast computation on encrypted polynomials and applications
CANS'11 Proceedings of the 10th international conference on Cryptology and Network Security
Size-hiding in private set intersection: existential results and constructions
AFRICACRYPT'12 Proceedings of the 5th international conference on Cryptology in Africa
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We present a robust secure methodology for computing functions that are represented as multivariate polynomials where parties hold different variables as private inputs. Our generic efficient protocols are fully black-box and employ threshold additive homomorphic encryption; they do not assume honest majority, yet are robust in detecting any misbehavior. We achieve solutions that take advantage of the algebraic structure of the polynomials, and are polynomial-time in all parameters (security parameter, polynomial size, polynomial degree, number of parties). We further exploit a "round table" communication paradigm to reduce the complexity in the number of parties. A large collection of problems are naturally and efficiently represented as multivariate polynomials over a field or a ring: problems from linear algebra, statistics, logic, as well as operations on sets represented as polynomials. In particular, we present a new efficient solution to the multi-party set intersection problem, and a solution to a multiparty variant of the polynomial reconstruction problem.