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Method and apparatus for basis conversion in finite field
Method and apparatus for basis conversion in finite field
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机译:有限域中基数转换的方法和装置
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摘要
There are provided efficient basis conversion matrices Dsd and Dds and a basis conversion method in a finite field GF(2n) using the basis conversion matrices for a case where a defining polynomial is a pentanomial, xn+xk(3)+xk(2)+xk(1)+1, and the exponents n, k(3), k(2), and (k1) satisfy the condition, n−k(3)k(3)−k(1). In addition, an apparatus for the basis conversion in the finite field GF(2n) is provided. Since a pentanomial having a general form in an arbitrary degree is used as the defining polynomial, basis conversion between a standard representation and a dual representation is efficiently performed. Consequently, a dual basis multiplier can be efficiently implemented.
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机译:提供了有效的基本转换矩阵D sd Sub>和D ds Sub>,以及在有限域GF(2 n Sup>)中使用该基的转换方法定义多项式为五项式的情况下的转换矩阵x n Sup> + x k(3) Sup> + x k(2) Sup> + x k(1) Sup> +1,并且指数n,k(3),k(2)和(k1)满足条件n-k(3)> k(3)-k (1)。另外,提供了一种用于在有限域GF(2 n Sup>)中进行基转换的设备。因为具有任意程度的一般形式的五项式被用作定义多项式,所以有效地执行了标准表示和对偶表示之间的基数转换。因此,可以有效地实现对偶乘法。
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