Chinese Remainder Theorem Approach to Montgomery-Type Algorithms
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913684151861248 |
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| author | Xu, Guangwu Jia, Yiran Yang, Yanze |
| author_facet | Xu, Guangwu Jia, Yiran Yang, Yanze |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00675 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chinese Remainder Theorem Approach to Montgomery-Type Algorithms Xu, Guangwu Jia, Yiran Yang, Yanze Cryptography and Security 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. |
| title | Chinese Remainder Theorem Approach to Montgomery-Type Algorithms |
| topic | Cryptography and Security |
| url | https://arxiv.org/abs/2402.00675 |