[1] Chudnovsky D V,Chudnovsky G V.Sequences of Numbers Generated by Addition in Formal Groups and New Primality and Factorization Tests[J].Advances in Applied Mathematics,1986,7(4):385-434.
[2] 唐春明,徐茂智,亓延峰.Jacobi交上的配对计算[J].计算机工程与科学,2011,33(10):25-29.
[3] Liardet P Y,Smart N P.Preventing SPA/DPA in ECC Systems Using the Jacobi Form[C]//Proceedings of the 3rd International Workshop on Cryptographic Hardware and Embedded Systems.Berlin,Germany:Springer,2001:391-401.
[4] Bernstein D J,Lange T.Explicit-formulae Database[EB/OL].(2008-03-12).http://www.hyperelliptic.org/EFD.
[5] Hisil H,Carter G,Dawson E.New Formulae for Efficient Elliptic Curve Arithmetic[C]//Proceedings of the 8th International Conference on Cryptology in India.Berlin,Germany:Springer,2007:138-151.
[6] Hisil H,Wong K K H,Carter G,et al.Faster Group Operations on Elliptic Curves[C]//Proceedings of the 7th Australasian Conference on Information Security.[S.l.]:Australian Computer Society Inc.,2009:7-20.
[7] 端木庆峰,张雄伟,王衍波,等.3特征域椭圆曲线群点的快速计算算法[J].解放军理工大学学报:自然科学版,2011,12(1):1-6.
[8] Iijima T,Matsuo K,Chao J,et al.Construction of Frobenius Maps of Twists Elliptic Curves and Its Application to Elliptic Scalar Multiplication[C]//Proceedings of Conference on Small Computer System Interface.Berlin,Germany:Springer,2002:699-702.
[9] Kozaki S,Matsuo K,Shimbara Y.Skew-Frobenius Maps on Hyperelliptic Curves[J].IEICE Transactions on Fundamentals of Electronics,Communications and Computer Sciences,2008,91(7):1839-1843.
[10] Feng Rongquan,Nie Menglong,Wu Hongfeng.Twisted Jacobi Intersections Curves[J].Theoretical Computer Science,2013,494:24-35.
[11] Wang Mingqiang,Wang Xiaoyun,Zhan Tao,et al.Skew-Frobenius Map on Twisted Edwards Curve[C]//Proceedings of the 7th International Conference on Theory and Application of Models of Computation.Prague,Czech:[s.n.],2010:199-210.
[12] Gallant R P,Lambert R J,Vanstone S A.Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms[C]//Advances in Cryptology-CRYPTO’01.Berlin,Germany:Springer,2001:190-200.
[13] Galbraith S D,Lin X,Scott M.Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves[J].Journal of Cryptology,2011,24(3):446-469.
[14] Wu H,Feng R.A Complete Set of Addition Laws for Twisted Jacobi Intersection Curves[J].Wuhan University Journal of Natural Sciences,2011,16(5):435-438.
[15] Silverman J H.The Arithmetic of Elliptic Curves[M].Dordrecht,the Netherlands:Springer,2009.
[16] Solinas J A.Efficient Arithmetic on Koblitz Curves[J].Designs,Codes and Cryptography,2000,19(2/3):195-249.
[17] Solinas J A.An Improved Algorithm for Arithmetic on a Family of Elliptic Curves[C]//Proceedings of CRYPTO’97.Berlin,Germany:Springer,1997:357-371.
[18] Koblitz N.CM-curves with Good Cryptographic Properties[C]//Proceedings of CRYPTO’91.Berlin,Germany:Springer,1992:279-287.
[19] Blake I F,Kumar M V,Xu Guangwu.Efficient Algorithms for Koblitz Curves over Fields of Characteristic Three[J].Journal of Discrete Algorithms,2005,3(1):113-124. |