Secure Efficient Multiparty Computing of Multivariate Polynomials and Applications
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- 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
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.
Keywordssecure multiparty computation multivariate polynomial evaluation additive homomorphic encryption threshold cryptosystems secret sharing multiparty set intersection
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