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Arithmetic in Mathematical Fields (in particular GF(2^8) )

  • Thread starter war485
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  • #1
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Homework Statement



* note that I meant fields in the abstract mathematical sense, notphysical (i.e. electric) fields! *

Finding the determinant of a matrix in GF(28)

I want to know if it is using mod 256 or mod 255 in the field of GF(28)

Homework Equations



Just math

The Attempt at a Solution



I found the determinant of a matrix no problem. Everything in between is all good. What I want to know is that in the field of GF(28), am I taking the number mod 255 or mod 256?

I know that there are a total of 256 elements in the field, but I'm just not sure which mod to take for the final answer, since it is a negative determinant.
 

Answers and Replies

  • #2
33,167
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Modulo 256. The possible moduli are 0, 1, 2, ..., 255, the possible remainders when you divide by 256.
 
  • #3
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thanks Mark
 
  • #4
Hurkyl
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Noooo! You're both wrong. GF(256) is a finite field, an extension field of GF(2). It is not not the same as the ring Z/256 of integers modulo 256.
 
  • #5
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Hurkyl, I agree that GF(256) is a finite field, but if we're both wrong, then how would I handle whole negative numbers?
 
  • #6
1,838
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You are just computing Mod 2 with the numbers. The elements are polynomials, the coefficients are from Z_2 and you're computing Modulo some primitive polynomial over Z_2 of 8th degree.
 

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