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Lookup NU author(s): Yousuf Al-Aali, Monir Hamood, Professor Said Boussakta
This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).
© 2023 by the authors. This paper introduces a new derivation of the radix- (Formula presented.) fast algorithm for the forward odd new Mersenne number transform (ONMNT) and the inverse odd new Mersenne number transform (IONMNT). This involves introducing new equations and functions in finite fields, bringing particular challenges unlike those in other fields. The radix- (Formula presented.) algorithm combines the benefits of the reduced number of operations of the radix-4 algorithm and the simple butterfly structure of the radix-2 algorithm, making it suitable for various applications such as lightweight ciphers, authenticated encryption, hash functions, signal processing, and convolution calculations. The multidimensional linear index mapping technique is the conventional method used to derive the radix- (Formula presented.) algorithm. However, this method does not provide clear insights into the underlying structure and flexibility of the radix- (Formula presented.) approach. This paper addresses this limitation and proposes a derivation based on bit-unscrambling techniques, which reverse the ordering of the output sequence, resulting in efficient calculations with fewer operations. Butterfly and signal flow diagrams are also presented to illustrate the structure of the fast algorithm for both ONMNT and IONMNT. The proposed method should pave the way for efficient and flexible implementation of ONMNT and IONMNT in applications such as lightweight ciphers and signal processing. The algorithm has been implemented in C and is validated with an example.
Author(s): Al-Aali Y, Hamood MT, Boussakta S
Publication type: Article
Publication status: Published
Journal: Signals
Year: 2023
Volume: 4
Issue: 4
Pages: 746-767
Online publication date: 23/10/2023
Acceptance date: 19/10/2023
Date deposited: 03/01/2024
ISSN (electronic): 2624-6120
Publisher: MDPI
URL: https://doi.org/10.3390/signals4040041
DOI: 10.3390/signals4040041
Data Access Statement: No new data were created or analyzed in this study. Data sharing is not applicable to this article.
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