English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Efficient computation of the Tate pairing is an important part of pairing-based cryptography. Recently with the introduction of the Duursma-Lee method special attention has been given to the fields of characteristic 3. Especially multiplication in \(\mathbb{F}_{3^{6m}}\), where m is prime, is an important operation in the above method. In this paper we propose a new method to reduce the number of \(\mathbb{F}_{3^{m}}\)-multiplications for multiplication in \(\mathbb{F}_{3^{6m}}\) from 18 in recent implementations to 15. The method is based on the fast Fourier transform and its explicit formulas are given. The execution times of our software implementations for \(\mathbb{F}_{3^{6m}}\) show the efficiency of our results.

Explicit Formulas for Efficient Multiplication in $\mathbb{F}_{3^{6m}}$