WSEAS Transactions on Computer Research
Print ISSN: 1991-8755, E-ISSN: 2415-1521
Volume 10, 2022
Tower Building Technique on Elliptic Curve with Embedding Degree 72
Authors: Ismail Assoujaa, Siham Ezzouak, Hakima Mouanis
Abstract: 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 $$\mathbb{F}_{p^{k}}$$ is more useful and secure with $$k\geq 12$$ the implementation become more important. In
this paper, we will presents cases studies of improving pairing arithmetic calculation on curves with embedding
degree 72. We use the tower building technique, and study the case when using a degree 2 or 3 twist to carry out
most operations in $$\mathbb{F}_{p^{4}}$$, $$\mathbb{F}_{p^{6}}$$, $$\mathbb{F}_{p^{8}}$$, $$\mathbb{F}_{p^{9}}$$, $$\mathbb{F}_{p^{12}}$$, $$\mathbb{F}_{p^{18}}$$, $$\mathbb{F}_{p^{24}}$$, $$\mathbb{F}_{p^{36}}$$, and $$\mathbb{F}_{p^{72}}$$.
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Keywords: Optimal ate pairing, Miller Algorithm, Embedding degree 72, Twist curve
Pages: 126-138
DOI: 10.37394/232018.2022.10.17
WSEAS Transactions on Computer Research, ISSN / E-ISSN: 1991-8755 / 2415-1521, Volume 10, 2022, Art. #17