A Somewhat Homomorphic Encryption Scheme based on Multivariate Polynomial Evaluation

TL;DR

This paper introduces a symmetric key homomorphic encryption scheme based on multivariate polynomial evaluation, which supports addition and multiplication, and links its security to a new computational hardness assumption.

Contribution

It presents a novel somewhat homomorphic encryption scheme based on multivariate polynomials and introduces the Hidden Subspace Membership problem for security analysis.

Findings

Scheme is homomorphic for addition and multiplication

Security relies on the hardness of the Hidden Subspace Membership problem

Provides a new approach to symmetric homomorphic encryption

Abstract

We propose a symmetric key homomorphic encryption scheme based on the evaluation of multivariate polynomials over a finite field. The proposed scheme is somewhat homomorphic with respect to addition and multiplication. Further, we define a generalization of the Learning with Errors problem called the Hidden Subspace Membership problem and show that the semantic security of the proposed scheme can be reduced to the hardness of this problem.