Huff’s form for elliptic curves over a local ring

Let Fq be a finite field of order q=pc, where p is a prime number ≥3, c∈N∗. In this paper, we introduce Huff curves denoted Ha,b2 over the local ring R2=Fq[X]/(X2). At first, we recall the arithmetic of the ring R2. After that, we define Huff curves Ha,b2 over this ring and we study the group Ha,b2,...

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Bibliographic Details
Published in:Scientific African
Main Authors: Abdelhakim Chillali, Moha Ben Taleb El Hamam, Abdelâli Grini
Format: Article
Language:English
Published: Elsevier 2025-03-01
Subjects:
Elliptic curve
Huff curve
Finite ring
Cryptography
Online Access:http://www.sciencedirect.com/science/article/pii/S2468227625000675
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Summary:Let Fq be a finite field of order q=pc, where p is a prime number ≥3, c∈N∗. In this paper, we introduce Huff curves denoted Ha,b2 over the local ring R2=Fq[X]/(X2). At first, we recall the arithmetic of the ring R2. After that, we define Huff curves Ha,b2 over this ring and we study the group Ha,b2, its properties and the classification of its elements. Precisely, we give a bijection between the groups Ha,b2 and Ha0,b0×Fq, where Ha0,b0 is the Huff curves over the finite field Fq.
ISSN:2468-2276

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