Features of digital signal processing algorithms using Galois fields GF(2n+1)

An alternating representation of integers in binary form is proposed, in which the numbers -1 and +1 are used instead of zeros and ones. It is shown that such a representation creates considerable convenience for multiplication numbers modulo p = 2 n +1. For such numbers, it is possible to implement...

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Bibliographic Details
Published in:	PloS one Vol. 18; no. 10; p. e0293294
Main Authors:	Suleimenov, Ibragim E., Vitulyova, Yelizaveta S., Matrassulova, Dinara K.
Format:	Journal Article
Language:	English
Published:	San Francisco, CA USA Public Library of Science 25.10.2023 Public Library of Science (PLoS)
Subjects:	Computer and Information Sciences Engineering and Technology People and Places Physical Sciences Research and Analysis Methods Science Policy
ISSN:	1932-6203, 1932-6203
Online Access:	Get full text
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Summary:	An alternating representation of integers in binary form is proposed, in which the numbers -1 and +1 are used instead of zeros and ones. It is shown that such a representation creates considerable convenience for multiplication numbers modulo p = 2 n +1. For such numbers, it is possible to implement a multiplication algorithm modulo p, similar to the multiplication algorithm modulo the Mersenne number. It is shown that for such numbers a simple algorithm for digital logarithm calculations may be proposed. This algorithm allows, among other things, to reduce the multiplication operation modulo a prime number p = 2 n +1 to an addition operation.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 Competing Interests: The authors have declared that no competing interests exist.
ISSN:	1932-6203 1932-6203
DOI:	10.1371/journal.pone.0293294