# Tagged Questions

**2**

votes

**1**answer

184 views

### Canonical lifts from $\mathbb F_q$ and CM-theory

One knows that (ordinary) Jacobians of hyperelliptic curves over a finite field $\mathbb F_q$ (mostly of genus 1 (elliptic curves) and 2) are extensively studied by cryptographers, as a platform for ...

**0**

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**1**answer

680 views

### Pairing on elliptic curve

Let $E(\mathbb{F_q})$ - elliptic curve.
$G_1 = E(\mathbb{F_q})[r]$. $|G_1| = r$.
$k$ is minimal such $r | q^k - 1$.
$\pi_q$ - $q$-power Frobenius endomorphism.
$G_2 = E(\mathbb{F_{q^k}})[r] \cap ...

**0**

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**3**answers

623 views

### Weil pairing, Kummer theory, help to decrypt what Wikipedia says

I do not quite understand the sentence in the Wikipedia article:
http://en.wikipedia.org/wiki/Weil_pairing
Section "Formulation" line 3:
"... for given points $P,Q \in E(K)[n]$, where $E(K)[n]=\{T ...

**4**

votes

**1**answer

452 views

### A silly question: is the number of points on a Jacobian (of a curve, over a finite field) known?

In a cryptography book I read that people does not known how to compute the number of points on a Jacobian of a hyperelliptic curve $C$ over a finite field $F_q$? Is this true? It seems easy to ...