# Elliptic curve over 16-bit binary field

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

add a comment

Elliptic curve over 16-bit binary field

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

add a comment

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]
```

Please start posting anonymously - your entry will be published after you log in or create a new account.

Asked: ** 2020-05-17 00:14:36 +0200 **

Seen: **58 times**

Last updated: **May 17 '20**

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.