Private Key Authentication
DroidEdit supports private key authentication since version 1.5. This is still fairly new code and there is still no support for passphrase supported private keys. A lot of things have changed under the hood so be patient if things break and please use this post to share your experience with SFTP in this new version.
To use private key authentication copy your private key file (e.g. id_rsa) to the sdcard and then use the SFTP preferences screen to set the path to the private key file.