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1)  divisor scalar multiplication
除子标量乘
1.
Based on the idea of simple divisor scalar multiplications,Duursma and Sakurai s algorithm for divisor scalar multiplications on a special class of hyperelliptic curves over prime fields has been improved to a larger class of such hyperelliptic curves over prime-extension fields,and two new formulized algorithms for divisor scalar multiplications are proposed.
除子标量乘是超椭圆曲线密码体制中的关键运算。
2)  scalar multiplication
标量乘
1.
Efficient scalar multiplication algorithm against SCA for Koblitz curve cryptosystems;
Koblitz曲线密码体制中一种可抵抗边带信道攻击的标量乘算法
2.
Research of high performance architecture for elliptic curve scalar multiplication over GF(2~m);
GF(2~m)域高效椭圆曲线标量乘结构的研究
3.
Based on the computation of double point, triple point, and quintuple point, it computes scalar multiplication nP by using properoperations.
椭圆曲线密码体制的快速实现依赖于标量乘(nP)的有效计算,该文改进n的二进制和三进制的混合表示方法,并且将其推广到n的二进制、三进制和五进制的混合表示。
3)  scalar multiplication
标量乘法
1.
Re-research on scalar multiplication of Koblitz elliptic curves;
Koblitz椭圆曲线标量乘法的二次研究
2.
A method for the efficient computation of scalar multiplication in Koblitz curve;
Koblitz曲线中标量乘法的快速计算方法
4)  multi-scalar multiplication
多标量乘
1.
The main operations of elliptic curve cryptosystem are scalar multiplication and multi-scalar multiplication for a pair of integers.
椭圆曲线密码体制最主要的运算就是椭圆曲线上的标量乘和多标量乘,在各种密码协议中起到了核心作用。
5)  Multiple scalar multiplication
多标量乘
1.
The scalar multiplication and multiple scalar multiplication dominate the execution time of elliptic curve cryptographic sche-mes.
标量乘及多标量乘算法是实现椭圆曲线密码系统的关键,如何快速高效实现标量乘及多标量乘算法是研究的重点。
2.
Presents a new interleaving multiple scalar multiplication algorithm based on Mutual Opposite Form,which is much faster than basic interleaving method in computing performance.
提出一种基于MOF(Mutual Opposite Form)的interleaving多标量乘算法,该算法在计算速度上明显快于基本inter-leaving方法,在计算速度和预存储方面和基于ωNAF(non-adjacent form)的interleaving方法相当,但MOF编码可从左到右实现,故编码和主计算可以合并,从而节省标量编码的存储空间,因此更适合于内存受限的设备上使用。
3.
Many elliptic curve based cryptographic protocols,such as ECDSA signature verification require computation of multiple scalar multiplications such as kP+IQ.
很多基于椭圆曲线的密码协议如ECDSA签名验证,都需要计算多标量乘法kP+IQ。
6)  scalar product
标量乘积
补充资料:四乘──光宅四乘
【四乘──光宅四乘】
  ﹝出华严经疏﹞
  光宅者,梁光宅寺,云法师也,立四乘教。谓临门三车,为三乘,即权教也;四衢所授大白牛车为第四乘,即实教也。
  [一、羊车],谓声闻之人,以析空观,观于生灭四谛,破见、思烦恼,证真谛理,得离三界生死;如乘羊车,出于火宅。故法华经云:为求羊车,出于火宅。是也。(析空观者,谓于五阴等法,观察分析,离其着心也。四谛者,苦谛、集谛、灭谛、道谛也。三界者,欲界、色界、无色界也。)
  [二、鹿车],谓缘觉之人,以析空观。观十二因缘生灭,破见、思烦恼,觉了真谛之理,得离三界生死;如乘鹿车,出于火宅。故法华经云:为求鹿车,出于火宅。是也。(十二因缘者,一无明、二行、三识、四名色、五六入、六触、七受、八爱、九取、十有、十一生、十二老死也。)
  [三、牛车],谓三藏教菩萨,发四弘誓,修六度行,化导众生,同出三界生死,究竟至于真空涅槃;如乘牛车,出于火宅,故法华经云:为求牛车,出于火宅。是也。(三藏者,经藏、律藏、论藏也。四弘誓者,众生无边誓愿度、烦恼无数誓愿断、法门无量誓愿知、佛道无上誓愿成。六度者,一布施、二持戒、三忍辱、四精进、五禅定、六智慧也。梵语涅槃,华言灭度。)
  [四、大白牛车],谓大乘菩萨,以圆融三观,观于诸法实相之理,顿破无明烦恼,而成一切种智;如乘大白牛车,至于宝所。故经云:有大白牛,肥壮多力,行步平正,其疾如风。是也。(三观者,空观、假观、中观也。一切种智者,佛智也。宝所者,喻实相之理也。)
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