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.
What is your question ?
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)