计算机应用与软件
計算機應用與軟件
계산궤응용여연건
COMPUTER APPLICATIONS AND SOFTWARE
2013年
11期
145-148,194
,共5页
Koblitz曲线%双线性对%基于τ的非相邻表示型( TNAF)%简单功耗分析( SPA)%标量乘
Koblitz麯線%雙線性對%基于τ的非相鄰錶示型( TNAF)%簡單功耗分析( SPA)%標量乘
Koblitz곡선%쌍선성대%기우τ적비상린표시형( TNAF)%간단공모분석( SPA)%표량승
Koblitz curves%Dual pairing%τ-adic non-adjacent form ( TNAF)%Simple power analysis ( SPA)%Scalar multiplication
二元扩域超奇异Koblitz曲线是目前双线性对计算中被广泛采用的曲线。研究二元扩域超奇异Koblitz曲线上标量乘的快速实现算法。由于Koblitz曲线存在特殊的自同态映射τ，使得标量乘算法可以由“double-and-add”算法变成“τ-and-add”算法，因此可以大大提高标量乘的运算效率。基于这个思想，提出了二元扩域超奇异Koblitz曲线上基于τ的非相邻表示型TNAF （τ-adic Non-Adjacent Form）窗口标量乘的实现算法；同时，为了抵御简单功耗分析SPA（Simple Power Analysis）攻击，将TNAF算法进一步改进为规则序列TNAF算法。以窗口取4为例，在同等安全强度下，规则序列TNAF4算法的运算效率比传统的二进制规则序列NAF4标量乘算法提高50％，比传统的Montgomery标量乘算法提高23％。
二元擴域超奇異Koblitz麯線是目前雙線性對計算中被廣汎採用的麯線。研究二元擴域超奇異Koblitz麯線上標量乘的快速實現算法。由于Koblitz麯線存在特殊的自同態映射τ，使得標量乘算法可以由“double-and-add”算法變成“τ-and-add”算法，因此可以大大提高標量乘的運算效率。基于這箇思想，提齣瞭二元擴域超奇異Koblitz麯線上基于τ的非相鄰錶示型TNAF （τ-adic Non-Adjacent Form）窗口標量乘的實現算法；同時，為瞭牴禦簡單功耗分析SPA（Simple Power Analysis）攻擊，將TNAF算法進一步改進為規則序列TNAF算法。以窗口取4為例，在同等安全彊度下，規則序列TNAF4算法的運算效率比傳統的二進製規則序列NAF4標量乘算法提高50％，比傳統的Montgomery標量乘算法提高23％。
이원확역초기이Koblitz곡선시목전쌍선성대계산중피엄범채용적곡선。연구이원확역초기이Koblitz곡선상표량승적쾌속실현산법。유우Koblitz곡선존재특수적자동태영사τ，사득표량승산법가이유“double-and-add”산법변성“τ-and-add”산법，인차가이대대제고표량승적운산효솔。기우저개사상，제출료이원확역초기이Koblitz곡선상기우τ적비상린표시형TNAF （τ-adic Non-Adjacent Form）창구표량승적실현산법；동시，위료저어간단공모분석SPA（Simple Power Analysis）공격，장TNAF산법진일보개진위규칙서렬TNAF산법。이창구취4위례，재동등안전강도하，규칙서렬TNAF4산법적운산효솔비전통적이진제규칙서렬NAF4표량승산법제고50％，비전통적Montgomery표량승산법제고23％。
Supersingular Koblitz curves over binary extension field are the widely used curves in current dual pairings calculation .In this paper we study the fast implementation algorithm of scalar multiplication algorithms on supersingular Koblitz curves over binary extension field.Since on Koblitz curves there are the special endomorphism map τ, this makes it possible to alter the scalar multiplication algorithm from the“double-and-add” algorithm to the “τ-and-add” algorithm, therefore the operation efficiency of scalar multiplication can be improved largely.Based on this thought, in this paper we present the implementation algorithm of τ-adic NAF (TNAF) window scalars multiplication on supersingular Koblitz curves over binary extension field .Meanwhile, in order to resist SPA ( simple power analysis ) attack, we further improve TNAF algorithm to regular sequence TNAF algorithm .Taking ω=4 as the example , the scalar multiplication algorithm based on TNAF4 is 50% faster than the one based on binary NAF 4 and 23% faster than the traditional Montgomery scalar multiplication in same security strength.
