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 September 16th, 2016, 03:06 AM #1 Newbie   Joined: Sep 2016 From: Maharashtra Posts: 8 Thanks: 0 Permutation Polynomials My question is based on permutation polynomials. A polynomial is said to be a 'Permutation Polynomial' of a finite field if it induces a one-to-one map from the field to itself. After searching for methods ,still I am unable to form a proper polynomial as shown in examples from specific paper. I have a doc file which explains the whole construct but the size limit wont let me post it. Is there any way I can post my question? Regards classkid
September 16th, 2016, 03:11 PM   #2
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 Originally Posted by classkid My question is based on permutation polynomials. A polynomial is said to be a 'Permutation Polynomial' of a finite field if it induces a one-to-one map from the field to itself. After searching for methods ,still I am unable to form a proper polynomial as shown in examples from specific paper. I have a doc file which explains the whole construct but the size limit wont let me post it. Is there any way I can post my question? Regards classkid
Doesn't $x^p-1$ work for any field of characteristic $p$? For any $x < p$, $x^{p-1}$ modulo $p$ is 1 so evaluation for each such $x$ results in the values $\{x - 1 \ : x \in \mathbb{Z}_p\}$ which is just a permutation on $\mathbb{Z}_p$.

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