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Montgomery Modular Arithmetic over Gaussian Integers

  • The Montgomery multiplication is an efficient method for modular arithmetic. Typically, it is used for modular arithmetic over integer rings to prevent the expensive inversion for the modulo reduction. In this work, we consider modular arithmetic over rings of Gaussian integers. Gaussian integers are subset of the complex numbers such that the real and imaginary parts are integers. In many cases Gaussian integer rings are isomorphic to ordinary integer rings. We demonstrate that the concept of the Montgomery multiplication can be extended to Gaussian integers. Due to independent calculation of the real and imaginary parts, the computation complexity of the multiplication is reduced compared with ordinary integer modular arithmetic. This concept is suitable for coding applications as well as for asymmetric key cryptographic systems, such as elliptic curve cryptography or the Rivest-Shamir-Adleman system.

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Metadaten
Author:Malek Safieh, Jürgen FreudenbergerORCiDGND
URL:https://ieeexplore.ieee.org/document/9070297
DOI:https://doi.org/10.1109/IT48810.2020.9070297
ISBN:978-1-7281-5136-6
Parent Title (English):24th International Conference on Information Technology (IT), 18-22 February 2020, Zabljak, Montenegro
Publisher:IEEE
Document Type:Conference Proceeding
Language:English
Year of Publication:2020
Release Date:2021/01/04
Tag:Computational complexity; Digital arithmetic; Encoding; Public key cryptography
Page Number:4
Note:
Volltextzugriff für Angehörige der Hochschule Konstanz via Datenbank IEEE Xplore möglich
Institutes:Institut für Systemdynamik - ISD
DDC functional group:000 Allgemeines, Informatik, Informationswissenschaft
Relevance:Keine peer reviewed Publikation (Wissenschaftlicher Artikel und Aufsatz, Proceeding, Artikel in Tagungsband)
Open Access?:Nein
Licence (German):License LogoUrheberrechtlich geschützt