Expand-and-Randomize: An Algebraic Approach to Secure Computation

TL;DR

This paper introduces an algebraic expand-and-randomize coding scheme for secure computation, enabling Alice and Bob to compute functions securely at Carol without revealing extra information, using finite fields and integer rings.

Contribution

It presents a novel algebraic coding scheme combining expansion and randomization steps for secure computation in a minimal model.

Findings

Effective secure computation with algebraic expansion and randomization

Implementation over finite fields and integer rings

Protection against information leakage during computation

Abstract

We consider the secure computation problem in a minimal model, where Alice and Bob each holds an input and wish to securely compute a function of their inputs at Carol without revealing any additional information about the inputs. For this minimal secure computation problem, we propose a novel coding scheme built from two steps. First, the function to be computed is expanded such that it can be recovered while additional information might be leaked. Second, a randomization step is applied to the expanded function such that the leaked information is protected. We implement this expand-and-randomize coding scheme with two algebraic structures - the finite field and the modulo ring of integers, where the expansion step is realized with the addition operation and the randomization step is realized with the multiplication operation over the respective algebraic structures.