Quantum Fast Implementation of Functional Bootstrapping and Private Information Retrieval

TL;DR

This paper introduces a quantum algorithm that significantly improves the efficiency of privacy-preserving computations like functional bootstrapping and private information retrieval, offering stronger security and polynomial time complexity.

Contribution

It presents the first quantum algorithms for functional bootstrapping and PIR with polynomial and logarithmic complexities, respectively, surpassing classical methods.

Findings

Quantum functional bootstrapping reduces complexity from exponential to polynomial.

Quantum PIR achieves logarithmic query time with enhanced security.

The methods extend classical cryptographic tools to the quantum setting for speedups.

Abstract

Classical privacy-preserving computation techniques safeguard sensitive data in cloud computing, but often suffer from low computational efficiency. In this paper, we show that employing a single quantum server can significantly enhance both the efficiency and security of privacy-preserving computation. We propose an efficient quantum algorithm for functional bootstrapping of large-precision plaintexts, reducing the time complexity from exponential to polynomial in plaintext-size compared to classical algorithms. To support general functional bootstrapping, we design a fast quantum private information retrieval (PIR) protocol with logarithmic query time. The security relies on the learning with errors (LWE) problem with polynomial modulus, providing stronger security than classical ``exponentially fast'' PIR protocol based on ring-LWE with super-polynomial modulus. Technically, we extend a key classical homomorphic operation, known as blind rotation, to the quantum setting through encrypted conditional rotation. Underlying our extension are insights for the quantum extension of polynomial-based cryptographic tools that may gain dramatic speedups.