1
vote
2answers
381 views

Equations of elliptic curves

First part of question I have asked on mathoverflow already: http://math.stackexchange.com/questions/467088/explict-form-of-the-equation-of-elliptic-curve 1) Let $E(\mathbb{F}_{q^2})$ is elliptic ...
0
votes
1answer
599 views

Elliptic curve over finite field: scalar multiplication

I'm implementing arithmetics for elliptic curves over secp256r1 as a homework assignment. For scalar multiplication, the assignment specifically specifies that $k$ is "any hexidecimal encoded ...
0
votes
0answers
132 views

elementary question on ECDLP

If $\mathbb{F}_q$ is a finite field and the elliptic curve E is defined over finite field $\mathbb{F}_p$ such that ECDLP is hard in E($\mathbb{F}_p$), where $q, p$ are prime and $q \ll p$. Let T $\in ...
3
votes
3answers
566 views

how to generate the n-torsion group

Hello, I was curious about the following sentence: "then the $n$-torsion on $E(\overline{K})$ has known structure, as a Cartesian product of two cyclic groups of order $n$" (found at ...
2
votes
2answers
474 views

Elliptic curves over proper variety over $\mathbf{F}_q$ isotrivial

Why is every elliptic curve over a proper (edit: smooth and geometrically connected) base over $\mathbf{F}_q$ isotrivial, i.e. is constant after base changing with $\bar{\mathbf{F}}_q$? If the moduli ...