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

Ibragim E Suleimenov, Yelizaveta S Vitulyova and Dinara K Matrassulova

PLOS ONE, 2023, vol. 18, issue 10, 1-12

Abstract: 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 = 2n+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 = 2n+1 to an addition operation.

Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0293294

DOI: 10.1371/journal.pone.0293294

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