<abstract xmlns="http://www.w3.org/1999/xhtml">

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<italic>pk</italic> with <italic>k</italic> ≥ 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<italic>p</italic>2 , 𝔽<italic>p</italic>3, 𝔽<italic>p</italic>6, 𝔽<italic>p</italic>9 and 𝔽<italic>p</italic>18, thus we speed up the computation in optimal ate pairing.
</abstract>

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 𝔽pk 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 𝔽p2 , 𝔽p3, 𝔽p6, 𝔽p9 and 𝔽p18, thus we speed up the computation in optimal ate pairing.

Tower Building Technique on Elliptic Curve with Embedding Degree 18

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Tower Building Technique on Elliptic Curve with Embedding Degree 18"}

Pairing based cryptography is one of the best security solution that devote a lot of attention. So, to make pairing practical, secure and computationally...

Tower Building Technique on Elliptic Curve with Embedding Degree 18

Published Online: Mar 07, 2023

Page range: 103 - 118

Received: Nov 02, 2022

DOI: https://doi.org/10.2478/tmmp-2023-0008

Keywords
optimal ate pairing, Miller algorithm, embedding degree 18, twist curve

© 2023 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Tower Building Technique on Elliptic Curve with Embedding Degree 18

Published Online: Mar 07, 2023

Page range: 103 - 118

Received: Nov 02, 2022

DOI: https://doi.org/10.2478/tmmp-2023-0008

Keywordsoptimal ate pairing, Miller algorithm, embedding degree 18, twist curve

© 2023 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
optimal ate pairing, Miller algorithm, embedding degree 18, twist curve