| 摘要 |
A method for producing the reciprocal of an arbitrary element in a finite field GF(2n) having a primitive element, the reciprocal of the primitive element and an identity element for multiplying. The method includes the steps of comparing the arbitrary element with the identity element of multiplying; producing the identity element of multiplying as the reciprocal of the arbitrary element, provided that the arbitrary element is the same as the identity element; recursively multiplying it by the primitive element by the identity element so as to produce a first element, and recursively multiplying the identity element by the reciprocal of primitive element so as to produce a second element, until one of the first and second elements equals the arbitrary element, provided that the arbitrary element is different from the identity element; and producing the second element as the reciprocal of the arbitrary element if the first element equals the arbitrary element, and producing the first element as the reciprocal of the arbitrary element if the second element equals the arbitrary element.
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