Paper 2025/1927

Accelerating LWE-Based Post-Quantum Cryptography with Approximate Computing

Abstract

Conventional cryptographic algorithms rely on hard mathematical problems to ensure an appropriate level of security. However, with the advent of quantum computing, classical cryptographic algorithms are expected to become vulnerable. For this reason, Post-Quantum Cryptography (PQC) algorithms have emerged as a response, being designed to resist quantum attacks. Most PQC algorithms rely on the Learning With Errors (LWE) problem, where generating pseudo-random controlled errors is crucial. A well-known solution is the use of hash functions followed by error samplers, implemented according to specific error distributions, whose implementation is challenging. This paper provides a proof of concept demonstrating how Approximate Computing (AxC) can be exploited in LWE-based cryptographic algorithms to alleviate this implementation bottleneck. The main idea is to use AxC circuits to run some of the algorithm's operations, introducing the required error for free thanks to the approximation. Our key contribution is demonstrating how AxC techniques can be effectively applied to LWE-based algorithms, highlighting a novel approach to generating and introducing the error. This concept has proven effective in an approximate implementation of the FrodoKEM algorithm, where we achieve a 50.3% reduction in the need for Gaussian sampling. Additionally, we observe a performance improvement of 2.19%, which further supports the feasibility of this approach. Overall, this work introduces and validates a new design direction for LWE-based cryptography through AxC, opening the way for further research.