Isomorphic Mapping for Ate-Based Pairing over KSS Curve of Embedding Degree 18

Khandaker, Md. Al-Amin; Nogami, Yasuyuki

doi:10.1109/candar.2016.0113

Cited by 5 publications

(1 citation statement)

References 15 publications

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“…In [5][6][7]13] Nadia El and others show a study case of working with elliptic curve with embedding degree 5, 9, 15 and 27. Also in [9][10][11][12] researchers show the case of working with curve with embedding degree 18. In [8] they give a study of security level of optimal ate pairing.…”

Section: Introductionmentioning

confidence: 99%

Tower Building Technique on Elliptic Curve with Embedding Degree 18

Assoujaa

Ezzouak

Mouanis

2023

Tatra Mountains Mathematical Publications

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Pairing based cryptography is one of the best security solution that devote a lot of attention. So, to make pairing practical, secure and computationally effcient, we choose to work with extension finite field of the form 𝔽 p k with k ≥ 12. In this paper, we focus on the case of curves with embedding degree 18. We use the tower building technique, and study the case of degree 2 or 3 twist to carry out most arithmetics operations in 𝔽 p 2 , 𝔽 p 3, 𝔽 p 6, 𝔽 p 9 and 𝔽 p 18, thus we speed up the computation in optimal ate pairing.

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Section: Introductionmentioning

confidence: 99%

Tower Building Technique on Elliptic Curve with Embedding Degree 18

Assoujaa

Ezzouak

Mouanis

2023

Tatra Mountains Mathematical Publications

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Tower Building Technique on Elliptic Curve with Embedding Degree 72

Assoujaa¹,

Ezzouak²,

Mouanis³

2022

Wseas Transactions on Computer Research

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Tower Building Technique on Elliptic Curve with Embedding Degree 54

Ismail,

Siham

2024

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Pairing based cryptography is one of the newest security solution that attract a lot of attention, because we can work with efficient and faster pairing to make the security a lot practical, also the working with extension finite field of the form Fpk is more useful and secure with k ≥ 12 the implementation become more important. In this paper, we will presents cases studies of improving pairing arithmetic calculation on curves with embedding degree 54. We use the tower building technique, and study the case when using a degree 3 twist to carry out most operations in Fp3 and Fp6 or Fp9 and Fp18 or Fp27, or when using a degree 2 twist to handle most of the operations in Fp2 and Fp6 and Fp18.

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Isomorphic Mapping for Ate-Based Pairing over KSS Curve of Embedding Degree 18

Cited by 5 publications

References 15 publications

Tower Building Technique on Elliptic Curve with Embedding Degree 18

Tower Building Technique on Elliptic Curve with Embedding Degree 18

Tower Building Technique on Elliptic Curve with Embedding Degree 72

Tower Building Technique on Elliptic Curve with Embedding Degree 54

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