计算机应用与软件Issue(11)：145-148,194,5.DOI:10.3969/j.issn.1000-386x.2013.11.041
二元扩域超奇异 Koblitz曲线的标量乘计算
SCALAR MULTIPLICATION ALGORITHM ON SUPERSINGULAR KOBLITZ CURVES OVER BINARY EXTENSION FIELD
摘要
Abstract
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.关键词
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Key words
Koblitz curves/Dual pairing/τ-adic non-adjacent form ( TNAF)/Simple power analysis ( SPA)/Scalar multiplication分类
信息技术与安全科学引用本文复制引用
徐云秀,顾海华,马博..二元扩域超奇异 Koblitz曲线的标量乘计算[J].计算机应用与软件,2013,(11):145-148,194,5.基金项目
2009年上海市科委集成电路设计专项（09706200600）。 （）
