Three-Input Ciphertext Multiplication for Homomorphic Encryption

TL;DR

This paper introduces a novel 3-input ciphertext multiplication scheme for homomorphic encryption, significantly reducing latency, silicon area, and noise compared to traditional 2-input multiplications, thereby enhancing efficiency for complex computations.

Contribution

It presents a new 3-input ciphertext multiplication method with an additional evaluation key and formulas, improving efficiency over consecutive 2-input multiplications in homomorphic encryption.

Findings

Nearly 50% latency reduction

29% smaller silicon area

Lower noise without throughput loss

Abstract

Homomorphic encryption (HE) allows computations to be directly carried out on ciphertexts and is essential to privacy-preserving computing, such as neural network inference, medical diagnosis, and financial data analysis. Only addition and 2-input multiplication are defined over ciphertexts in popular HE schemes. However, many HE applications involve non-linear functions and they need to be approximated using high-order polynomials to maintain precision. To reduce the complexity of these computations, this paper proposes 3-input ciphertext multiplication. One extra evaluation key is introduced to carry out the relinearization step of ciphertext multiplication, and new formulas are proposed to combine computations and share intermediate results. Compared to using two consecutive 2- input multiplications, computing the product of three ciphertexts utilizing the proposed scheme leads to almost a half of the latency, 29% smaller silicon area, and lower noise without scarifying the throughput.