蘇志圖，李 暉，馬建峰

(西安電子科技大學(xué)計(jì)算機(jī)網(wǎng)絡(luò)與信息安全教育部重點(diǎn)實(shí)驗(yàn)室 西安 710071)

如何高效地實(shí)現(xiàn)密碼算法是公鑰密碼體制中的重要問(wèn)題。在基于身份的密碼體制中，雙線性對(duì)的計(jì)算效率是影響整個(gè)密碼算法性能的關(guān)鍵[1-4]。目前，所有的雙線性對(duì)快速計(jì)算方法都建立在M iller算法[5]的基礎(chǔ)上。因此優(yōu)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(duì)快速計(jì)算的當(dāng)前研究就如何減少M(fèi) iller算法中的循環(huán)次數(shù)以提高計(jì)算效率，提出了一些新的雙線性對(duì)，如eta對(duì)[1]、ate對(duì)[2]、 Atei對(duì)[8]。

1 一些背景知識(shí)

2 多項(xiàng)式選取

3 結(jié) 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(guó). 雙線性對(duì)有效計(jì)算研究進(jìn)展[J]. 軟件學(xué)報(bào), 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(duì)的壓縮[J]. 軟件學(xué)報(bào), 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