plumsirawit / comp-ec Goto Github PK

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the base polynomial

$$x^3+4x^2+4x+3 \in \mathbb{F}_5[x]$$

is irreducible of degree $3$, however, claiming that

$$\mathbb{F}_{5^3} \cong \mathbb{F}_5[x]/(x^3+4x^2+4x+3),$$

for each $a \in \mathbb{F}_{5^3}$, $a^{5^3-1}$ should have been equal to $1$. It is not true in this case. (I don't know why)

Try editing the final lines of the file debug_extfield.py to see the computation in action.

Note that the problem doesn't exist when the base polynomial is replaced by

$$x^3+2x^2+x+3 \in \mathbb{F}_5[x]$$

as in

(To activate this behavior, uncomment line 9 and comment line 8 to see)