@inbook {19643,
title = {Secure Efficient Multiparty Computing of Multivariate Polynomials and Applications},
booktitle = {Applied Cryptography and Network Security},
series = {Lecture Notes in Computer Science},
year = {2011},
month = {2011/01/01/},
pages = {130 - 146},
publisher = {Springer Berlin Heidelberg},
organization = {Springer Berlin Heidelberg},
abstract = {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 {\textquotedblleft}round table{\textquotedblright} 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 multi-party variant of the polynomial reconstruction problem.},
keywords = {additive homomorphic encryption, Algorithm Analysis and Problem Complexity, Computer Communication Networks, Data Encryption, Discrete Mathematics in Computer Science, Management of Computing and Information Systems, multiparty set intersection, multivariate polynomial evaluation, secret sharing, secure multiparty computation, Systems and Data Security, threshold cryptosystems},
isbn = {978-3-642-21553-7, 978-3-642-21554-4},
url = {http://link.springer.com/chapter/10.1007/978-3-642-21554-4_8},
author = {Dana Dachman-Soled and Malkin, Tal and Raykova, Mariana and Yung, Moti},
editor = {Lopez, Javier and Tsudik, Gene}
}