Vectorized SQIsign Implementation Using AVX-512

2026-08-14

AI Summary

This study addresses the computational intensity and deployment limitations of SQIsign by proposing the first full-stack vectorized implementation leveraging the AVX-512 IFMA instruction set. By optimizing core modules—including finite field arithmetic, batched scalar multiplication, cubic arithmetic, and two-dimensional isogeny evaluation—the proposed approach significantly enhances execution efficiency. Experimental results demonstrate that under NIST Level I security parameters, signing and verification speeds are accelerated by factors of 2.69× and 3.18×, respectively. This work not only substantially improves the practicality of SQIsign but also validates the critical value of SIMD technologies in optimizing post-quantum isogeny-based cryptography.

Abstract

SQIsign is the sole isogeny-based digital signature scheme submitted to the NIST Post-Quantum Cryptography standardization process, distinguished by its foundation on the hardness of the endomorphism ring problem for supersingular elliptic curves. While offering compact key and signature sizes, SQIsign's practical deployment is hindered by computationally intensive signing procedures. This paper presents the first comprehensive vectorized implementation of SQIsign utilizing the AVX-512 Integer Fused Multiply-Add (IFMA) instruction set architecture. By systematically redesigning the computational stack---encompassing prime-field and extension-field arithmetic, elliptic curve operations including batched point doubling and scalar multiplication, as well as pairing computations via cubical arithmetic and two-dimensional isogeny evaluations---we achieve substantial performance improvements over the reference implementation. When combined with Qlapoti technology, our implementation attains a $2.69\times$ speedup for signing and a $3.18\times$ improvement for verification at NIST security level I. Contrary to misconceptions regarding the obsolescence of AVX-512, we emphasize that Intel's AVX10 instruction set architecture (revision 10.2, scheduled for widespread deployment in late 2026) will standardize AVX-512 capabilities---including IFMA instructions---across both performance and efficiency cores, ensuring long-term viability of these optimization techniques. Furthermore, our vectorization strategies are architecture-agnostic and provide a methodological foundation applicable to broader isogeny-based cryptographic constructions. This work demonstrates that SIMD vectorization represents a critical yet underexplored optimization dimension for post-quantum isogeny-based schemes, independent of recent algorithmic advances.

Problem

• SQIsign
• Post-Quantum Cryptography
• Performance Optimization
• Isogeny-based Cryptography

Innovation

• SQIsign
• AVX-512 IFMA
• SIMD vectorization
• isogeny-based cryptography
• performance optimization