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arXiv · 2402.00675

Chinese Remainder Theorem Approach to Montgomery-Type Algorithms

Guangwu Xu·Yiran Jia·Yanze Yang
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Abstract

This paper explores the ability of the Chinese Remainder Theorem formalism to model Montgomery-type algorithms. A derivation of CRT based on Qin's Identity gives Montgomery reduction algorithm immediately. This establishes a unified framework to treat modular reduction algorithms of Montgomery-type. Several recent notable variants of Montgomery algorithm are analyzed, validation of these methods are performed within the framework. Problems in some erroneous design of reduction algorithms of Montgomery-type in the literature are detected and counter examples are easily generated by using the CRT formulation.

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Guangwu Xu, Yiran Jia, Yanze Yang. 2024-02-01. Chinese Remainder Theorem Approach to Montgomery-Type Algorithms. https://arxiv.org/abs/2402.00675

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