Note: This post is 6 years old. Some information may no longer be correct or even relevant. Please, keep this in mind while reading.
Dropbear is a replacement for OpenSSH for environments with low memory and processor resources. With OpenSSH, you can use the well-known ssh-keyen command to create a private/public keypair for the client. In Dropbear, it is a bit different. Here are the commands on the client:
mkdir ~/.ssh
chmod 700 ~/.ssh/
dropbearkey -t rsa -f ~/.ssh/id_dropbearBoth private and public keys will be in ~/.ssh/id_dropbear, however in a binary format.
To output the public key to stdout in the usual SSH-compatible format, use:
dropbearkey -y -f ~/.ssh/id_dropbear