雙線性對快速計算中的多項式選取

蘇志圖，李 暉，馬建峰

(西安電子科技大學計算機網絡與信息安全教育部重點實驗室 西安 710071)

如何高效地實現密碼算法是公鑰密碼體制中的重要問題。在基于身份的密碼體制中，雙線性對的計算效率是影響整個密碼算法性能的關鍵[1-4]。目前，所有的雙線性對快速計算方法都建立在M iller算法[5]的基礎上。因此優化M iller算法一直是基于身份的密碼體制中的重要研究課題[6-7]。雙線性對快速計算的當前研究就如何減少M iller算法中的循環次數以提高計算效率，提出了一些新的雙線性對，如eta對[1]、ate對[2]、 Atei對[8]。

1 一些背景知識

2 多項式選取

3 結 論

[1] BARRETO P, GALBRAITH S, HIGEARTAIGH C, et al.Efficient pairing computation on supersingular abelian varieties[J]. Designs, Codes and Cryptography, 2007, 42:239-271.

[2] HESS F, SMART N, VERCAUTEREN F. The eta pairing revisited[J]. IEEE Transactions on Information Theory,2006, 52: 4595-4602.

[3] MATSUDA S, KANAYAMA N, HESS F, et al. Optimised versions of the ate and tw isted ate pairings[C]//Cryptography and Coding 2007: Lecture Notes in Computer Science 4887. Berlin: Springer-verlag, 2007:302-312.

[4] DUURSMA I, LEE H S. Tate pairing implementation for hyperelliptic curves[C]//Advances in Cryptology-ASIACRYPT 2003: Lecture Notes in Computer Science 2894. Berlin: Springer-verlag, 2003: 111-123.

[5] M ILLER V. The Weil pairing and its efficient calculation[J]. Journal of Cryptology, 2004, 17: 235-261.

[6] 趙昌安，張方國. 雙線性對有效計算研究進展[J]. 軟件學報, 2009, 20(11): 3001-3009.

ZHAO Chang-an, ZHANG Fang-guo. Research and development on efficient pairing computations[J]. Journal of Software, 2009, 20(11): 3001-3009.

[7] 胡磊. 橢圓曲線Tate對的壓縮[J]. 軟件學報, 2007, 18(7):1799-1805.

HU Lei. Compression of tate pairings on elliptic curves[J].Journal of Software, 2007, 18(7): 1799-1805.

[8] ZHAO C A, ZHANG F G, HUANG J W. A note on the ate pairing[J]. International Journal of Information Security,2008, 7: 379-382.

[9] BLAKE I, SEROUSSI G, SMART N. Advances in elliptic curve cryptography[M]. New York: Cambridge University Press, 2005: 183-213.

[10] FREEMAN D. Constructing abelian varieties for pairing-based cryptography[D]. Berkeley: University of California, 2008.

[11] BARRETO P, KIM H, LYNN B, et al. Efficient algorithms for pairing-based cryptosystems[C]//Advances in Cryptology CRYPTO 2002: Lecture Notes in Computer Science 2442. Berlin: Springer-verlag, 2002: 354-369.

[12] SILVERMAN J. The arithmetic of elliptic curves[M]. New York : Springer-Verlag, 2009: 137-157.

編 輯 張 俊