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I'm new on the topic of finite fields, specifically $GF(2^8)$.

I've come across the information that it's possible to implement multiplication using logarithm and exponential tables. But how are these tables formed exactly? Some answers talk about a generator while others talk about using a primitive polynomial. Are those the same?

What I exactly want to know is how pre-compute the log and exp table using the following primitive polynomial: $$x^8 + x^4 + x^3 + x^2 + 1$$

Maarten Bodewes
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Luxzero
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  • just to clarify , do you mean the Xtime table such as in AES? – hardyrama Nov 22 '18 at 18:36
  • I checked that question before @kelalaka, but they don't use a primitive polynomial to calculate the AES log table, they use a generator. Is it the same? Maybe I'm getting it wrong. – Luxzero Nov 23 '18 at 12:29
  • @Luxzero how do you perform the step where mul denotes multiplication in the AES field. without a primitive polynomial? – kelalaka Nov 23 '18 at 18:57
  • @kelalaka That's it! I missed the relevance of that step I guess. Thanks for pointing me in the right direction. – Luxzero Nov 26 '18 at 13:54

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