Fully Homomorphic Encryption based on Multivariate Polynomial Evaluation

TL;DR

This paper introduces a multi-bit leveled fully homomorphic encryption scheme leveraging multivariate polynomial evaluations, which maintains security based on the LWE problem and avoids relinearization during multiplication.

Contribution

It presents a novel FHE scheme that simplifies multiplication by eliminating relinearization and manages noise growth linearly, enhancing efficiency and security.

Findings

Scheme supports multi-bit leveled FHE

Homomorphic multiplication does not require relinearization

Noise increases linearly with each multiplication

Abstract

We propose a multi-bit leveled fully homomorphic encryption scheme using multivariate polynomial evaluations. The security of the scheme depends on the hardness of the Learning with Errors (LWE) problem. For homomorphic multiplication, the scheme uses a polynomial based technique that does not require relinearization (and key switching). The noise associated with the ciphertext increases only linearly with every multiplication.