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 multi-party variant of the polynomial reconstruction problem. © 2011 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Dachman-Soled, D., Malkin, T., Raykova, M., & Yung, M. (2011). Secure efficient multiparty computing of multivariate polynomials and applications. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6715 LNCS, pp. 130–146). https://doi.org/10.1007/978-3-642-21554-4_8
Mendeley helps you to discover research relevant for your work.