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Math Help - Inverse in Galois field

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    Inverse in Galois field

    how can one find the inverse of an element over the Galois field, GF(2^8)?
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    MHF Contributor chisigma's Avatar
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    Quote Originally Posted by pranay View Post
    how can one find the inverse of an element over the Galois field, GF(2^8)?
    The 255 elements of G(256) different from the null element can be written as , where \alpha is a 'primitive root' of the field. A basic property is that the are periodic of period 255 so that the inverse element of is :..

    ... as example we consider the GF(256) generated by the polynomial...

    (1)

    ... one 'primitive root' of which is . We have...

    (2)

    Observing table (2) we can deduce that the inverse of x is , the inverse of is and so one...

    Kind regards

    \chi \sigma
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