ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 28 Dec 2016 08:58:23 +0100Choose Polynomialhttps://ask.sagemath.org/question/36060/choose-polynomial/ A correction about choosing your polynomial to construct the finite field of 256 elements: (GF(256))
The polynomial should be irreducible (does not need to be primitive) so the list of irreducible polynomials is:
8,4,3,2,0
8,5,3,1,0
8,5,3,2,0
8,6,3,2,0
8,6,4,3,2,1,0
8,6,5,1,0
8,6,5,2,0
8,6,5,3,0
8,6,5,4,0
8,7,2,1,0
8,7,3,2,0
8,7,5,3,0
8,7,6,1,0
8,7,6,3,2,1,0
8,7,6,5,2,1,0
8,7,6,5,4,2,0
# non-primitive:
8,4,3,1,0
8,5,4,3,0
8,5,4,3,2,1,0
8,6,5,4,2,1,0
8,6,5,4,3,1,0
8,7,3,1,0
8,7,4,3,2,1,0
8,7,5,1,0
8,7,5,4,0
8,7,5,4,3,2,0
8,7,6,4,2,1,0
8,7,6,4,3,2,0
8,7,6,5,4,1,0
8,7,6,5,4,3,0
Read the list as follows: 8,7,6,5,4,3,0 ------> x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + 1
The AES polynomial is not primitive and it is in the list.
There are 30 polynomials; some of them are both irreducible and primitive.
Tue, 20 Dec 2016 19:11:32 +0100https://ask.sagemath.org/question/36060/choose-polynomial/Comment by tmonteil for <p>A correction about choosing your polynomial to construct the finite field of 256 elements: (GF(256))</p>
<p>The polynomial should be irreducible (does not need to be primitive) so the list of irreducible polynomials is:</p>
<p>8,4,3,2,0</p>
<p>8,5,3,1,0</p>
<p>8,5,3,2,0</p>
<p>8,6,3,2,0</p>
<p>8,6,4,3,2,1,0</p>
<p>8,6,5,1,0</p>
<p>8,6,5,2,0</p>
<p>8,6,5,3,0</p>
<p>8,6,5,4,0</p>
<p>8,7,2,1,0</p>
<p>8,7,3,2,0</p>
<p>8,7,5,3,0</p>
<p>8,7,6,1,0</p>
<p>8,7,6,3,2,1,0</p>
<p>8,7,6,5,2,1,0</p>
<p>8,7,6,5,4,2,0</p>
<h1>non-primitive:</h1>
<p>8,4,3,1,0</p>
<p>8,5,4,3,0</p>
<p>8,5,4,3,2,1,0</p>
<p>8,6,5,4,2,1,0</p>
<p>8,6,5,4,3,1,0</p>
<p>8,7,3,1,0</p>
<p>8,7,4,3,2,1,0</p>
<p>8,7,5,1,0</p>
<p>8,7,5,4,0</p>
<p>8,7,5,4,3,2,0</p>
<p>8,7,6,4,2,1,0</p>
<p>8,7,6,4,3,2,0</p>
<p>8,7,6,5,4,1,0</p>
<p>8,7,6,5,4,3,0</p>
<p>Read the list as follows: 8,7,6,5,4,3,0 ------> x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + 1
The AES polynomial is not primitive and it is in the list.
There are 30 polynomials; some of them are both irreducible and primitive.</p>
https://ask.sagemath.org/question/36060/choose-polynomial/?comment=36061#post-id-36061What is your question ?Tue, 20 Dec 2016 22:35:34 +0100https://ask.sagemath.org/question/36060/choose-polynomial/?comment=36061#post-id-36061Comment by ozy for <p>A correction about choosing your polynomial to construct the finite field of 256 elements: (GF(256))</p>
<p>The polynomial should be irreducible (does not need to be primitive) so the list of irreducible polynomials is:</p>
<p>8,4,3,2,0</p>
<p>8,5,3,1,0</p>
<p>8,5,3,2,0</p>
<p>8,6,3,2,0</p>
<p>8,6,4,3,2,1,0</p>
<p>8,6,5,1,0</p>
<p>8,6,5,2,0</p>
<p>8,6,5,3,0</p>
<p>8,6,5,4,0</p>
<p>8,7,2,1,0</p>
<p>8,7,3,2,0</p>
<p>8,7,5,3,0</p>
<p>8,7,6,1,0</p>
<p>8,7,6,3,2,1,0</p>
<p>8,7,6,5,2,1,0</p>
<p>8,7,6,5,4,2,0</p>
<h1>non-primitive:</h1>
<p>8,4,3,1,0</p>
<p>8,5,4,3,0</p>
<p>8,5,4,3,2,1,0</p>
<p>8,6,5,4,2,1,0</p>
<p>8,6,5,4,3,1,0</p>
<p>8,7,3,1,0</p>
<p>8,7,4,3,2,1,0</p>
<p>8,7,5,1,0</p>
<p>8,7,5,4,0</p>
<p>8,7,5,4,3,2,0</p>
<p>8,7,6,4,2,1,0</p>
<p>8,7,6,4,3,2,0</p>
<p>8,7,6,5,4,1,0</p>
<p>8,7,6,5,4,3,0</p>
<p>Read the list as follows: 8,7,6,5,4,3,0 ------> x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + 1
The AES polynomial is not primitive and it is in the list.
There are 30 polynomials; some of them are both irreducible and primitive.</p>
https://ask.sagemath.org/question/36060/choose-polynomial/?comment=36110#post-id-36110Read the list as follows: 8,7,6,5,4,3,0 ------> x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + 1
The AES polynomial is not primitive and it is in the list.
There are 30 polynomials; some of them are both irreducible and primitive.
All of you, should choose a polynomial (you can form groups of at most 2),
and send me your polynomial with a screen shot or explanation that verifies that it is irrredudible (you can use SAGE or magma-- online manuals or someother method)Wed, 28 Dec 2016 08:58:23 +0100https://ask.sagemath.org/question/36060/choose-polynomial/?comment=36110#post-id-36110