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Features of digital signal processing algorithms using Galois fields GF(2(n)+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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Detalles Bibliográficos
Autores principales: Suleimenov, Ibragim E., Vitulyova, Yelizaveta S., Matrassulova, Dinara K.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10599577/
https://www.ncbi.nlm.nih.gov/pubmed/37878646
http://dx.doi.org/10.1371/journal.pone.0293294
Descripción
Sumario: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.