Secure Efficient Multiparty Computing of Multivariate Polynomials and Applications

  • Dana Dachman-Soled
  • Tal Malkin
  • Mariana Raykova
  • Moti Yung
Conference paper

DOI: 10.1007/978-3-642-21554-4_8

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6715)
Cite this paper as:
Dachman-Soled D., Malkin T., Raykova M., Yung M. (2011) Secure Efficient Multiparty Computing of Multivariate Polynomials and Applications. In: Lopez J., Tsudik G. (eds) Applied Cryptography and Network Security. ACNS 2011. Lecture Notes in Computer Science, vol 6715. 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 “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.

Keywords

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

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Dana Dachman-Soled
    • 1
  • Tal Malkin
    • 1
  • Mariana Raykova
    • 1
  • Moti Yung
    • 2
  1. 1.Columbia UniversityUSA
  2. 2.Google Inc. and Columbia UniversityUSA

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