Year: 2025
Type: conference-paper
Abstract: Fully homomorphic encryption (FHE) and zero-knowledge proofs (ZKPs) are emerging as solutions for data security in distributed environments. However, the widespread adoption of these encryption techniques is hindered by their significant computational overhead, primarily resulting from core cryptographic operations that involve large integer arithmetic. This paper presents a formalization of multi-word modular arithmetic (MoMA), which breaks down large bit-width integer arithmetic into operations on machine words. We further develop a rewrite system that implements MoMA through recursive rewriting of data types, designed for compatibility with compiler infrastructures and code generators. We evaluate MoMA by generating cryptographic kernels, including basic linear algebra subprogram (BLAS) operations and the number theoretic transform (NTT), targeting various GPUs. Our MoMA-based BLAS operations outperform state-of-the-art multi-precision libraries by orders of magnitude, and MoMA-based NTTs achieve near-ASIC performance on commodity GPUs.
Authors: Naifeng Zhang, Franz Franchetti
Institution: Carnegie Mellon University
Language: English
Subfield: Information Systems
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Awards: G1453181110, Molecular and Biochemical Basis for Stable Carbon Isotope Ratios in Marine Autotrophs using Form IA RubisCO, Track 4: Advanced CI Coordination Ecosystem: Monitoring and Measurement Services, G3562386289, Track 1: ACCESS Resource Allocations Marketplace and Platform Services (RAMPS), G4010157413, G4308666867, ACO: An Open CI Ecosystem to Advance Scientific Discovery (OpenCI), Track 3: COre National Ecosystem for CyberinfrasTructure (CONECT), G5367127336, G5464919783, Track 2: Customized Multi-tier Assistance, Training, and Computational Help (MATCH) for End User ACCESS to CI
OpenAlex ID: W4407863044