# Elliptic curve over 16-bit binary field

how can i generate and use elliptic curve over 16-bit binary field.

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Elliptic curve over 16-bit binary field

how can i generate and use elliptic curve over 16-bit binary field.

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0

To see how to create an elliptic curve, see:

```
sage: EllipticCurve?
```

To create a 16-bit binary field, you can do:

```
sage: K = GF(2^16)
sage: K
Finite Field in z16 of size 2^16
```

If you want to use the generator of the field:

```
sage: K.inject_variables()
Defining z16
```

Then, you can define the elleptic curve you want :

```
sage: E = EllipticCurve(K, [2, 3*z16^12,1,1,z16]) ; E
Elliptic Curve defined by y^2 + y = x^3 + z16^12*x^2 + x + z16 over Finite Field in z16 of size 2^16
```

This is of course an arbitrary example, you have to construct the curve that satisfies your needs.

To see quickly what you can do with the curve, you can use [TAB] completion:

```
sage: E.[TAB]
```

Asked: **
2020-05-16 17:14:36 -0500
**

Seen: **24 times**

Last updated: **May 16**

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