Elliptic curve over ring A_4=F_{2^d}[\epsilon]; \epsilon^4=0

Tadmori, Abdelhamid; Chillali, Abdelhakim; Ziane, M'hammed

doi:10.12988/ams.2015.5147

Cited by 8 publications

(2 citation statements)

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“…• Z invertible: then, [X : Y : Z] = [XZ −1 : Y Z −1 : 1] hence, we take just [X : Y : 1]. • Z non invertible: so, Z = z 1 ε see [3], in this case we have two cases for Y.…”

Section: Notationsmentioning

confidence: 99%

ECC over the ring F_{s^d}[X]/(X^2) by using a password

Tadmori¹,

Chillali²,

Zaine³

2018

GJOM

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In this work, we will present an example of encryption and decryption, by using the elliptic curve defined over the ring A2 = F2d[ε], where d is a positive integer and ε2 = 0. The motivation for this work came from the observation that communications, industrial automation and many more. For majority of these applications, security is a vital issue. Cryptography plays an important role in providing data security. In a first time, we describe these curves defined over this ring. Then, we study the algorithmic properties by proposing effective implementations for representing the elements and the group law. In other we give an example of encrypted message with a secret key.

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“…• Z invertible: then, [X : Y : Z] = [XZ −1 : Y Z −1 : 1] hence, we take just [X : Y : 1]. • Z non invertible: so, Z = z 1 ε see [3], in this case we have two cases for Y.…”

Section: Notationsmentioning

confidence: 99%

ECC over the ring F_{s^d}[X]/(X^2) by using a password

Tadmori¹,

Chillali²,

Zaine³

2018

GJOM

Self Cite

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“…For the characteristic 2, the study is done by Tadmori et al in [27]. Also, he studied in [25,26] such curves over a non-local ring. In the same context of a nonlocal ring, Boulbot et al have studied this kind of curve over F q [e], e 3 = e 2 [4], and over F q [e], e 2 = e [5].…”

Section: Introductionmentioning

confidence: 99%

Elliptic curves over a finite ring

Zakariae,

Abdelhakim,

Ali

2023

AUCMCS

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Let Fq be a finite field, where q is a power of a prime p such that p>5. Let \alpha be a root of a monic polynomial of a minimal degree over Fq. In this paper, we will study elliptic curves over (Fq[\alpha],+,*), where + is the usual addition and * represent a non-standard product law over Fq[\alpha]. Elliptic curves over this ring can be used to create a new type of cryptography. The method is fast, simple, and secure.

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