SCC-Cryptosystem on an algebraic closure ring

Chillali, Abdelhakim; Sahmoudi, Mohammed

doi:10.1080/09720529.2019.1624338

Cited by 3 publications

(1 citation statement)

References 3 publications

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“…In [23], Elhassani et al have built an encryption method based on DLP and Lattice. Boulbot et al in [24] have studied elliptic curves on a non-local ring to compare these curves on local and non-local rings, while in [25], Sahmoudi et al have studied these types of curves on a family of finite rings in the authors have introduced a cryptosystem on these types of curves, see [26].…”

Section: Introductionmentioning

confidence: 99%

Elliptic Curve over a Local Finite RingR_n

Chillali¹,

Fadil²

2020

Number Theory and Its Applications

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The goal of this chapter is to study some arithmetic proprieties of an elliptic curve defined by a Weierstrass equation on the local ring R n ¼  q X ½ = X n ðÞ , where n ≥ 1 is an integer. It consists of, an introduction, four sections, and a conclusion. In the first section, we review some fundamental arithmetic proprieties of finite local rings R n , which will be used in the remainder of the chapter. The second section is devoted to a study the above mentioned elliptic curve on these finite local rings for arbitrary characteristics. A restriction to some specific characteristic cases will then be considered in the third section. Using these studies, we give in the fourth section some cryptography applications, and we give in the conclusion some current research perspectives concerning the use of this kind of curves in cryptography. We can see in the conclusion of research in perspectives on these types of curves.

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Section: Introductionmentioning

confidence: 99%

Elliptic Curve over a Local Finite RingR_n

Chillali¹,

Fadil²

2020

Number Theory and Its Applications

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Elliptic curve and k-Fibonacci-like sequence

2023

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New encryption scheme using k-Fibonacci-like sequence

Lagheliel¹,

Chillali

Mokhtar³

2021

Asian-European J. Math.

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In this paper, we present a new encryption scheme using generalization k-Fibonacci-like sequence, we code the points of an elliptic curve with the terms of a sequence of k-Fibonacci-like using of Fibonacci sequence and we call it as k-Fibonacci like sequence [Formula: see text] defined by the recurrence relation: [Formula: see text] and we present some relation among k-Fibonacci like sequence, k-Fibonacci sequence and k-Lucas sequence. After that, we give application of elliptic curves in cryptography using k-Fibonacci like sequence.

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SCC-Cryptosystem on an algebraic closure ring

Cited by 3 publications

References 3 publications

Elliptic Curve over a Local Finite RingR_n

Elliptic Curve over a Local Finite RingR_n

Elliptic curve and k-Fibonacci-like sequence

New encryption scheme using k-Fibonacci-like sequence

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SCC-Cryptosystem on an algebraic closure ring

Cited by 3 publications

References 3 publications

Elliptic Curve over a Local Finite RingRn

Elliptic Curve over a Local Finite RingRn

Elliptic curve and k-Fibonacci-like sequence

New encryption scheme using k-Fibonacci-like sequence

Contact Info

Product

Resources

About

Elliptic Curve over a Local Finite RingR_n

Elliptic Curve over a Local Finite RingR_n