О схемной реализации арифметики в конечных полях характеристики 7 для вычисления спариваний
Автор: Бурцев А.А., Гашков С.Б.
Журнал: Труды Московского физико-технического института @trudy-mipt
Статья в выпуске: 1 (9) т.3, 2011 года.
Бесплатный доступ
Короткий адрес: https://sciup.org/142185723
IDR: 142185723
Список литературы О схемной реализации арифметики в конечных полях характеристики 7 для вычисления спариваний
- Blake I., Seroussi G., Smart N. Elliptic curves in cryptography. { Cambridge: Cambridge University Press, 1999.
- Blake I.,Seroussi G., Smart N. Advances in elliptic curve cryptograhy. { Cambridge: Cambridge University Press, 2005. 3. ®«®â®¢ €.€.,. 誮¢...,.஫®¢ €..,. á®¢áª¨å €.€. «¥¬¥â ஥ ¢¢¥¤¥¨¥ ¢ í««¨¯-â¨ç¥áªãî ªà¨¯â®£à ä¨î. €«£¥¡à ¨ç¥áª¨¥ ¨ «£®-à¨â¬¨ç¥áª¨¥ ®á®¢ë. {..:.®¬.¨£, 2006. 4. ®«®â®¢ €.€.,. 誮¢...,.஫®¢ €..,. á®¢áª¨å €.€. «¥¬¥â ஥ ¢¢¥¤¥¨¥ ¢ í««¨¯â¨-ç¥áªãî ªà¨¯â®£à ä¨î. à®â®ª®«ë ªà¨¯â®£à 䨨 í««¨¯â¨ç¥áª¨å ªà¨¢ëå. {..:.®¬.¨£, 2006.
- Barreto P.S.L.M., Kim H.Y., Lynn B.,
- Scott M. E cient algorithms for pairing-based cryptosystems//Crypto-2002, LNCS 2442, 2002. {. 354{368.
- Scott M. and Barreto P.S.M.L. Compressed pairing//CRYPTO-2004, LNCS 3152(2004), P. 140{ 156.
- Barreto P.S.M.L., Galbraith S.,
- O hEigeartaigh C. and Scott M. E cient pairing computation on supersingular abelian varieties//Cryptology ePrint Archive, Report 2004/375. http://eprint.iacr.org/2004/375
- Kerins T., Marname W.P., Popovici E.M., and
- Barreto P.S.L.M. E cient hardware for Tate pairing calculation in characteristic three//CHES-2005.
- Page D., Smart N.P. Hardware implementation of nite elds of characteristic three//CHES-2002, LNCS, 2002.
- Granger R., Page D., Stam M. Hardware and software normal basis arithmetic for pairing based cryptography in characteristic three//IEEE Trans. on Comp. { 2005. { V. 54, N 7. {. 852{860.
- Bailey D.V., Paar C. E cient arithmetic in nite eld extensions with application in elliptic curve cryptography//J. of Cryptology. { 2001. { 14:3. {. 156{173.
- Duursma I. and Lee H.-S. Tate pairing implementation for hyperelliptic curves y2 = xp ¡x+d//Asiacrypt-2003, LNCS 2894, 2003. {. 111{123.
- Duursma I. and Lee H.-S. Tate pairing implementation for tripartite key agreement//Cryptology ePrint Archive, Report 2003/053. http://eprint.iacr.org/2003/053
- Kwon S. E cient Tate pairing computation for supersingular elliptic curves over binary elds//Cryptology ePrint Archive, Report 2004/303. http://eprint.iacr.org/2004/303 15. Beuchat J-L., Shiraze M., Takagi T. and
- Okamoto E. An algorithm for the ´T -pairing calculation in characteristic three and its hardwareimplementation//Cryptology ePrint Archive, Report 2006/327. http://eprint.iacr.org/2006/327
- Shiraze M., Takagi T. and Okamoto E. Some e cient algorithms for the nal exponentiation ofn ´T¡ pairing // Cryptology ePrint Archive, Report 2006/. http://eprint.iacr.org/2006/ 17. Eunjeong Lee, Huang-Sook Lee and Yoonjin Lee. Fast computation of Tate pairing on general divisors for hyperelliptic curves of genus 3 // Cryptology ePrint Archive, Report 2006/125. http://eprint.iacr.org/2006/125 18. . à æã¡ €.€., .ä¬ ... .¬®¦¥¨¥ ¬®£®§ çëå ç¨á¥« ¢â®¬ â å // .®ª« ¤ë € ..., 1962, { .. 145(2). { .. 293{294. 19. .®®¬ €... . á«®¦®á⨠áå¥¬ë ¨§ äãªæ¨- ® «ìëå í«¥¬¥â®¢, ॠ«¨§ãî饩 㬮¦¥¨¥ æ¥- «ëå ç¨á¥« // .®ª« ¤ë € ..., 1963. { .. 150. { .. 496{498. 20. ®¤¥ ., .¨â⥠.. €«£¥¡à ¨ç¥áª ï «£®- à¨â¬¨ª . { ..: .¨à, 1999. 21. ®«®â®¢ €.€., . 誮¢ ..., .஫®¢ €.., . á®¢áª¨å €.€. à®£à ¬¬ë¥ ¨ áå¥¬ë¥ ¬¥â®¤ë 㬮¦¥¨ï ¬®£®ç«¥®¢ ¤«ï í««¨¯â¨ç¥áª®© ªà¨¯- ⮣à 䨨 // .§¢¥áâ¨ï €. .¥®à¨ï ¨ á¨á⥬ë ã¯à ¢«¥¨ï. { 2000, ü 5. { .. 66{75. 22. .® «ì¤ . .ãâ. .áªãáá⢮ ¯à®£à ¬¬¨à®- ¢ ¨ï. .®¬ 2. ®«ãç¨á«¥ë¥ «£®à¨â¬ë. .à¥âì¥ ¨§¤ ¨¥. { .§¤. .¨«ìï¬á. 2000. 23. .㯠®¢ ... €á¨¬¯â®â¨ç¥áª¨¥ ®æ¥ª¨ á«®¦®á⨠ã¯à ¢«ïîé¨å á¨á⥬. { ..: .§¤-¢® .®áª®¢áª®£® 㨢¥àá¨â¥â . 1984.
Статья