Score:2

What is the quadratic character of the field over which elliptic curve is defined?

ng flag

I'm trying to understand the injective encoding of a message to an elliptic curve point (from this paper).

enter image description here

However, I'm not sure what do they mean by the quadratic character of the field. Do you know what does it mean and how to compute it? Is it somewhat similar to the Jacobi symbol?

Score:3
kr flag

For any finite field $\mathbb{F}_q$ of odd characteristic, there is a unique nontrivial morphism $\mathbb{F}_q^*\to\{-1,1\}$: it takes the value $1$ on squares and $-1$ on nonsquares (and it is usually extended to $0$ on $0$). This is the Legendre symbol when $q$ is prime, but it's called the quadratic character in general.

pintor avatar
ng flag
Thank you! Now it makes sense
kelalaka avatar
in flag
The downvoter, could you explain the reason? By the way, Mehdi is one of the authors of the paper!
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