Faster implementation of ηt pairing over GF(3m) using minimum number of logical instructions for GF(3)-addition

Yuto Kawahara, Kazumaro Aoki, Tsuyoshi Takagi

研究成果: 書籍/レポート タイプへの寄稿会議への寄与

18 被引用数 (Scopus)

抄録

The η T pairing in characteristic three is implemented by arithmetic in GF(3)={0,1,2}. Harrison et al. reported an efficient implementation of the GF(3)-addition by using seven logical instructions (consisting of AND, OR, and XOR) with the two-bit encoding { (0,0) 0, (0,1) 1, (1,0) 2 }. It has not yet been proven whether seven is the minimum number of logical instructions for the GF(3)-addition. In this paper, we show many implementations of the GF(3)-addition using only six logical instructions with different encodings such as { (1,1) 0, (0,1) 1, (1,0) 2 } or { (0,0) 0, (0,1) 1, (1,1) 2 }. We then prove that there is no implementation of the GF(3)-addition using five logical instructions with any encoding of GF(3) by two bits. Moreover, we apply the new GF(3)-additions to an efficient software implementation of the η T pairing. The running time of the η T pairing over GF(3509), that is considered to be realized as 128-bit security, using the new GF(3)-addition with the encoding { (0,0) 0, (0,1) 1, (1,1) 2 } is 16.3 milliseconds on an AMD Opteron 2.2-GHz processor. This is approximately 7% faster than the implementation using the previous GF(3)-addition with seven logical instructions.

本文言語英語
ホスト出版物のタイトルPairing-Based Cryptography - Pairing 2008 - Second International Conference, Proceedings
ページ282-296
ページ数15
DOI
出版ステータス出版済み - 2008
外部発表はい
イベント2nd International Conference on Pairing-Based Cryptography, Pairing 2008 - Egham, 英国
継続期間: 9月 1 20089月 3 2008

出版物シリーズ

名前Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
5209 LNCS
ISSN(印刷版)0302-9743
ISSN(電子版)1611-3349

その他

その他2nd International Conference on Pairing-Based Cryptography, Pairing 2008
国/地域英国
CityEgham
Period9/1/089/3/08

!!!All Science Journal Classification (ASJC) codes

  • 理論的コンピュータサイエンス
  • コンピュータ サイエンス(全般)

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