Automatic Generation of Vectorized Montgomery Algorithm
Lingchuan Meng
TL;DR
This paper introduces a vectorized Montgomery algorithm optimized for SIMD instructions, enabling faster modular multiplication, and demonstrates its automatic generation via the { exttt{SPIRAL}} system for cryptographic and symbolic computation applications.
Contribution
It presents a novel vectorized Montgomery algorithm and its automatic generation method using the { exttt{SPIRAL}} system, advancing efficient modular arithmetic implementations.
Findings
Achieved significant speedup in modular multiplication.
Successfully integrated the algorithm into the { exttt{SPIRAL}} system.
Demonstrated applicability in cryptography and symbolic computation.
Abstract
Modular arithmetic is widely used in crytography and symbolic computation. This paper presents a vectorized Montgomery algorithm for modular multiplication, the key to fast modular arithmetic, that fully utilizes the SIMD instructions. We further show how the vectorized algorithm can be automatically generated by the {\SPIRAL} system, as part of the effort for automatic generation of a modular polynomial multiplication library.
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Taxonomy
TopicsCryptography and Residue Arithmetic · Polynomial and algebraic computation · Coding theory and cryptography