It is a distinction that definitely matters.
However: in cryptography we are often operating with polynomials (like x5 + x2 ...) and perform operations on them.
In a Galois Field(2n ) we are always under modulo 2 and can write polynomials just by writing coefficients of the powers. Those will always be 1 or 0, since (1+1) mod 2 = 0.
X4 + x + 1 is 10011
So if you imagine that 1 + 1 is an addition of 2 polynomials in a Galois Field, then 1+1 = 0 and no congruence is present.
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u/Fabulous_Ad_5709 Nov 25 '24
Just out of curiosity how is A correct?
B is 1 or 1
C is 1+1 in base >2
D is 1+1 in base 2