One-Round Secure Multiparty Computation of Arithmetic Streams and Functions

Efficient secure multiparty computation (SMPC) schemes over secret shares are presented. We consider scenarios in which the secrets are elements of a finite field, \(\mathbb {F}_{p}\), and are held and shared by a single participant, the user. Evaluation of any function \(f:\mathbb {F}_{p}^n\rightarrow \mathbb {F}_{p}\) is implemented in one round of communication by representing f as a multivariate polynomial. Our schemes are based on partitioning secrets to sums or products of random elements of the field. Secrets are shared using either (multiplicative) shares whose product is the secret or (additive) shares that sum up to the secret. Sequences of additions of secrets are implemented locally by addition of local shares, requiring no communication among participants, and so does sequences of multiplications of secrets. The shift to handle a sequence of additions from the execution of multiplications or vice versa is efficiently handled as well with no need to decrypt the secrets in the course of the computation. On each shift from multiplications to additions or vice versa, the current set of participants is eliminated, and a new set of participants becomes active. Assuming no coalitions among the active participants and the previously eliminated participants are possible, our schemes are information-theoretically secure with a threshold of all active participants. Our schemes can also be used to support SMPC of boolean circuits.