2
votes
0answers
106 views

Modular Inverse over some given finite field. Which method is more efficient?

I'm trying to do division in some given finite field (let's say mod p). I have 2 Python methods here that are currently doing that, but I'm not sure which is better or if 1 or both is simply wrong. ...
1
vote
2answers
69 views

Find the inverse of $\alpha^{38}$ in $\mathbb F = \mathbb Z_2[x]/\left<x^4+x+1\right>$

Let $\alpha$ be a root of $x^4+x+1$ and we are given some powers of $\alpha$ as linear combinations of $1,\alpha,\alpha^2$ and $\alpha^3$ $\alpha^4=\alpha+1$ $\alpha^5=\alpha^2+\alpha$ ... (the rest ...
0
votes
1answer
445 views

inverse,multiplicative inverse and Congruence of a prime field

I am dealing with ECC in these days which heavily based on finite fields. I want to how to find a inverse of a value in finite field and what is multiplicative inverse and also Congruence F29- ...
1
vote
1answer
549 views

Find multiplicative inverse existense.

I cannot find whether multiplicative inverse of $x^3+x^2+x+1 \pmod{x^5+x^4+x^3-x^2-x+1}$ over $\mathrm{GF}(3)$ exists. This problem must be solved with Extended Euclidean algorithm. I tried to ...