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Scheme for arithmetic operations in finite field and group operations over elliptic curves realizing improved computational speed
Scheme for arithmetic operations in finite field and group operations over elliptic curves realizing improved computational speed
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机译:有限域的算术运算和椭圆曲线上的群运算方案,可提高计算速度
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摘要
A scheme for arithmetic operations in finite field and group operations over elliptic curves capable of realizing a very fast implementation. According to this scheme, by using a normal basis [&agr; &agr;+1], the multiplicative inverse calculation and the multiplication in the finite field GF(22n) can be realized as combinations of multiplications, additions and a multiplicative inverse calculation in the subfield GF(2n). Also, by using a standard basis [1 &agr;], the multiplication, the square calculation, and the multiplicative inverse calculation in the finite field GF(22n) can be realized as combinations of multiplications, additions and a multiplicative inverse calculation in the subfield GF(2n). These arithmetic operations can be utilized for calculating rational expressions expressing group operations over elliptic curves that are used in information security techniques such as elliptic curve cryptosystems.
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机译:一种用于有限域中的算术运算和椭圆曲线上的群运算的方案,能够实现非常快的实现。根据此方案,通过使用正常基础[&agr; &agr;+ 1&rsqb ;,有限域GF(2 2n Sup>)中的乘法逆计算和乘法可以通过子域GF(2)中乘法,加法和乘法逆计算的组合来实现 n Sup>)。而且,通过使用标准基数[ 1&agr;&rsqb ;,可以将有限域GF(2 2n Sup>)中的乘法,平方计算和乘法逆运算实现为乘法的组合子字段GF(2 n Sup>)中的,加法和乘法逆计算。这些算术运算可用于计算在椭圆曲线密码系统等信息安全技术中使用的表示椭圆曲线上的群运算的有理表达式。
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