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扩展的DBNS椭圆曲线标量乘算法 被引量：1

Extended double-base number system algorithm on elliptic curve scalar multiplication
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摘要 椭圆曲线密码体制的快速实现取决于标量乘算法的运算效率。在传统的(2,3)-双基数标量乘算法的基础上,提出了一种新的(2,5)-双基数标量乘算法。实验数据表明,该算法不仅继承了双基数标量乘算法的优点,同时还改进了传统双基数标量乘算法的不足,如预计算时间长和存储空间要求大等问题,使其应用于存储空间较小的领域如智能卡等成为可能。 The performance of elliptic curve cryptosystems has heavily depended on the efficient computation of scalar multiplication.Based on the traditional double-base chain representation of scalar using bases 2 and 3.This paper develops a new double-base chain scalar multiplication algorithm with power of 2 and 5.Compared with the standard algorithm,the experimental results show the method has greatly relieved the burden of precomputation and saved the space of memory,which makes it possible for its application to the fields with small space of memory requirement such as IP card and IC card etc.
作者 蒲冰 牛荣健
机构地区 重庆工业职业技术学院工商贸易系 重庆工业职业技术学院
出处 《计算机工程与应用》 CSCD 北大核心 2011年第26期98-102,202,共6页 Computer Engineering and Applications
基金 高等职业教育技能鉴定评价体系重点课题(No.09-2-107)
关键词 双基数系统 标量乘 固定基窗口算法 五倍点 double-base number systems scalsar multiplication fixed-base windowing method quintupling
分类号 TP309 [自动化与计算机技术—计算机系统结构]
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参考文献14

  • 1Dimitrov V S, Jullien G A, Miller W C.Theory and applications for a double-base number system[C]//Proceedings of the 13th Symposium on Computer Arithmetic Computer Arithrnetic.Washington D C, USA: IEEE, 1997: 1098-1106.
  • 2Avanzi R, Dimitrov V ,Doche C.Extending scalar multiplication using double bases[C]//Proceedings of Asiacrypt 2006.[S.1.]: Springer, 2006: 130-144.
  • 3Ciet M, Sica F.An analysis of double base number systems and a sublinear scalar multiplication algorithm[C]//Proceedings of Mycrypt in Cryptology Conference.[S.l.] : Springer, 2005 : 171-182.
  • 4Doche C, Imbert L.Extended double-base number system with applications to elliptic curve cryptography[C]//Proceedings of Progress in Cryptology-lNDOCRYPT.[S.l.]:Springer,2006:335-348.
  • 5Mishra P K, Dimilrov V.Efficient quintuple formulas for elliptic curves and efficient scalar multiplication using multibase number representation[C]//Proceedings of the 10th International Conference on Information Securily.[S.1.]:Springer,2007:390-406.
  • 6Avanzi R M, Ciet M, Sica F.Faster scalar multiplication on koblitz curves combining point halving with the Frobenius endomorphism[C]//Proceedings of Public Key Cryptography Conference. [S.1.] : Springer, 2004: 28-40.
  • 7Wong K W,Edward C W,Lee L,et al.Fast elliptic scalar multiplication using new double-base chain and point halving[J]. Mathematics and Computation,2006,183(2) : 1000-1007.
  • 8Dimitrov V S, Imbert L, Mishra P K.Efficient and secure elliptic curve point multiplication using double-base chains[C]//Proceedings of Advances in Cryptology-Asiacrypt.[S.l.] : Springer, 2005 : 59-78.
  • 9Dimitrov V S, Imbert L, Mishra P K.Fast elliptic curve point multiplication using double-base chains[DB/OL].[2010-01].http: //eprint.iacr.org/2005/069.pdf.
  • 10Dimitrov V S,Jarvinen K, Jacobson M J, et al.FPGA implementation of point multiplication on Koblitz curves using Kleinian integers[C]//Proceedings of Conference on Cryptographic Hardware and Embedded Systems.[S.1.] : Springer, 2006: 445-459.

同被引文献14

  • 1Miller V S. Use of elliptic curves in cryptography [ C ]//Proc of CRYPTO~5. [ s. 1. ] : Springer-Verlag, 1986:417-426.
  • 2Koblitz N. Elliptic curve cryptosystems [ J ]. Mathematics of Computation, 1987,48 ( 177 ) :203-209.
  • 3Dimitrov V ,Imbert L,Mishra P K. Efficient and secure elliptic curve point multiplication using double base chain[ C ]//Pmc of Cryptology- ASIACRYPT' 05. [ s. 1. ] : Springer-Yerlag, 2005.
  • 4Mishra P K, Dimitrov V S. Efficient quintuple formulas for el- liptic curves and efficient scalar multiplication using multibase number representation [ C ~//Proe of ISC ' 07. Valparaiso: Springer-Verlag ,2007.
  • 5Purohit G N, Rawat S A, Kumar M. Elliptic curve point multi- plication using MBNR and point halving [ J ]. International Journal of Advanced Networking and Applications, 2012,3 (5) :1329-1337.
  • 6Doche C, Imbert L. Extended double- base number systemwith applications to elliptic curve cryptography [ C ]//Proceed- ings of the 7th international conference on cryptology. Berlin : Springer-Verlag, 2006 : 335 -348.
  • 7Knudsen E W. Elliptic scalar multiplication using point halving [ C ]//Proc of ASIACRYPT' 99. [ s. 1. ] : Springer- Verlag, 1999.
  • 8Liu D G, Ning P. Establishing pairwise keys in distributed sen- sor networks [ C ]//Proceedings of the 10th ACM conference on computer and communication security. New York: ACM Press ,2003:52-61.
  • 9陈辉,鲍皖苏.基于半点运算与多基表示的椭圆曲线标量乘法[J].计算机工程,2008,34(15):153-155. 被引量：8
  • 10郝艳华,李磊,王育民.利用多基链计算椭圆曲线标量乘的高效算法[J].电子科技大学学报,2008,37(6):868-871. 被引量：7

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计算机工程与应用
2011年 第26期

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