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Tower building technique on elliptic curve with embedding degree 18

In: Tatra Mountains Mathematical Publications, vol. 83, no. 1
Ismail Assoujaa - Siham Ezzouak - Hakima Mouanis
Detaily:
Rok, strany: 2023, 103 - 118
Jazyk: eng
Kľúčové slová:
optimal ate pairing, Miller algorithm, embedding degree 18, twist curve
Typ článku: Mathematics
Typ dokumentu: Scientific paper, pdf
O článku:
Pairing based cryptography is one of the best security solution that devote a lot of attention. So, to make pairing practical, secure and computationally efficient, we choose to work with extension finite field of the form $\mathbb{F}pk$ 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 $\mathbb{F}p2$, $\mathbb{F}p3$, $\mathbb{F}p6$, $\mathbb{F}p9$ and $\mathbb{F}p18$, thus we speed up the computation in optimal ate pairing.
Ako citovať:
ISO 690:
Assoujaa, I., Ezzouak, S., Mouanis, H. 2023. Tower building technique on elliptic curve with embedding degree 18. In Tatra Mountains Mathematical Publications, vol. 83, no.1, pp. 103-118. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2023-0008

APA:
Assoujaa, I., Ezzouak, S., Mouanis, H. (2023). Tower building technique on elliptic curve with embedding degree 18. Tatra Mountains Mathematical Publications, 83(1), 103-118. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2023-0008
O vydaní:
Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Publikované: 20. 2. 2023
Verejná licencia:
The Creative Commons Attribution-NC-ND 4.0 International Public License