Work

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

Year: 2023

Type: article

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.

Source: PLoS ONE

DOI: 10.1371/journal.pone.0293294

Authors: Ibragim E. Suleimenov, Yelizaveta S. Vitulyova, Dinara K. Matrassulova

Institution: Almaty University of Power Engineering and Telecommunications

Language: English

Topic: Cryptography and Residue Arithmetic

Subfield: Information Systems

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,805

Funder: Uddannelses- og Forskningsministeriet