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ARITHMETIC UNIT DEVICE ON FINITE FIELD AND GROUP COMPUTING DEVICE ON ELLIPTIC CURVE
ARITHMETIC UNIT DEVICE ON FINITE FIELD AND GROUP COMPUTING DEVICE ON ELLIPTIC CURVE
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机译：有限域上的算术单元装置和椭圆曲线上的群计算装置
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摘要
PROBLEM TO BE SOLVED: To increase the computing speed on a finite field by computing multiplications based on specific equations in the device which performs the arithmetic computations employing α, that satisfies specific equations, on the finite field. ;SOLUTION: The device performs the arithmetic computations on a finite field employing α that satisfies an equation I i.e., GF(22n) =GF(2n)(α) on a finite field GF (22n). The device has the multiplication means which computes multiplications based on an equation II i.e., (x1+y1α)×(x2+y2α)=(x1x2+ay1y2)+ ((x1+y1)(x2+y2)+x1x2) α(x1, x2, y1, y2εGF(2n)). Moreover, the device has a squaring means, which computes squaring operations based on an equation III, i.e., (x1+y1α)2=(x12+ay12)+y12α(x1, x2εGF (2n)). Furthermore, the device is provided with an inverse elements computing means which computes an inverse elements based on an equation IV, i.e., (x1+y1α)-1=(x1(x1+y1)+ay12)-1 ((x1+y1)+y1α)(x1, y1 E GF(2n)).;COPYRIGHT: (C)1999,JPO
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机译：要解决的问题：通过在设备上基于特定方程计算乘法来提高有限域上的计算速度，该设备在有限域上使用满足特定方程的α进行算术运算。 ;解决方案：设备使用满足方程式I的α在有限域上执行算术运算，即GF（2 2n ）= GF（2 n ）（α）在有限域GF（2 2n ）上。该设备具有乘法装置，该乘法装置基于等式II，即（x 1 + y 1 α）×（x 2 + y 2 α）=（x 1 x 2 + ay 1 y 2 ）+（（x 1 + y 1 ）（x 2 + y 2 ）+ x 1 x 2 ）α（x 1 ，x 2 ，y 1 ，y 2 ＆epsi; GF（2 n ））。此外，该设备具有平方装置，其基于等式III，即，（x 1 + y 1 α） 2 =（x 1 2 + ay 1 2 ）+ y 1 < Sup> 2 α（x 1 ，x 2 ＆epsi; GF（2 n ））。此外，该设备设置有逆元素计算装置，该逆元素计算装置基于等式IV，即，（x 1 + y 1 α），计算逆元素。 -1 =（x 1 （x 1 + y 1 ）+ ay 1 2 ） -1 （（x 1 + y 1 ）+ y 1 α） （x 1 ，y 1 E GF（2 n ））.;版权：（C）1999，JPO
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