How to calculate Trace function for a point on an elliptic curve I encountered trouble with calculating Tr (trace function) for points on an elliptic curve in polynomial basis ( $GF(2^m), m = 431$). Maybe there are any assumptions that can simplify and allow efficiently to calculate Tr operation?
I used the Seroussi approach to decompress points but it seems like I need some basic knowledge.
Let $E$ be an elliptic curve defined over $F_q$, and let $\#E(F_q ) = q +1−t$. In this case, $t$ is called the trace of $E$. 

Also, $\#E(F_{q^n} ) = q^n + 1 − V_n$ for all $n ≥ 2$, where $\{V_n\}$ is the sequence defined recursively by $$V_0 = 2, V_1 = t,\text{ and }V_n = V_1V_{n−1}−qV_{n−2}$$ for $n ≥ 2$. In your question it's enough to compute $V_{431}$.

For more details, see Guide to Elliptic Curve Cryptography.