Applied Cryptography and Network Security

Volume 6715 of the series Lecture Notes in Computer Science pp 130-146

Secure Efficient Multiparty Computing of Multivariate Polynomials and Applications

  • Dana Dachman-SoledAffiliated withColumbia University
  • , Tal MalkinAffiliated withColumbia University
  • , Mariana RaykovaAffiliated withColumbia University
  • , Moti YungAffiliated withGoogle Inc. and Columbia University

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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 multi-party variant of the polynomial reconstruction problem.


secure multiparty computation multivariate polynomial evaluation additive homomorphic encryption threshold cryptosystems secret sharing multiparty set intersection