Efficient pairings on twisted elliptic curve

Yasuyuki Nogami, Yumi Sakemi, Masataka Akane, Yoshitaka Morikawa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

This paper proposes an efficient implementation of Ate pairing on twisted elliptic curve. Suppose that a pairing-friendly elliptic curve E has a twisted elliptic curve E′ of degree d, and let Ψd be an isomorphic map from E′ (double struck F signp e) to the corresponding subgroup of E(double struck F signp k). Then, consider double struck G sign′1 = Ψd -1(double struck G sign1) and double struck G sign′2 = Ψd -1(double struck G sign2) for double struck G sign1, double struck G sign2 at Ate pairing α. Let P ∈ double struck G sign 1, Q ∈ double struck G sign2, P′ ∈ double struck G sign′1 and Q′ ∈ double struck G sign′2, the authors have shown α(Q, P) = f t-1,Q,(P)(pk - 1)/r = ft-1,Q′(P′) (pk - 1)/r. This paper shows that this new Ate pairing, namely cross twisted (Xt) Ate pairing, provides an quite efficient implementation.

Original languageEnglish
Title of host publicationProceedings - 3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008
Pages430-439
Number of pages10
Volume2
DOIs
Publication statusPublished - 2008
Event3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008 - Busan, Korea, Republic of
Duration: Nov 11 2008Nov 13 2008

Other

Other3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008
CountryKorea, Republic of
CityBusan
Period11/11/0811/13/08

ASJC Scopus subject areas

  • Information Systems
  • Software

Cite this

Nogami, Y., Sakemi, Y., Akane, M., & Morikawa, Y. (2008). Efficient pairings on twisted elliptic curve. In Proceedings - 3rd International Conference on Convergence and Hybrid Information Technology, ICCIT 2008 (Vol. 2, pp. 430-439). [4682279] https://doi.org/10.1109/ICCIT.2008.172