Choose Polynomial

asked 2016-12-20 12:11:32 -0600

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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.

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What is your question ?

tmonteil gravatar imagetmonteil ( 2016-12-20 15:35:34 -0600 )edit

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. 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)

ozy gravatar imageozy ( 2016-12-28 01:58:23 -0600 )edit