Im trying to set access from ServerA(SunOS) to ServerB(Some custom Linux with Keyboard Interactive login) with SSH Keys. As a proof of concept I was able to do it between 2 virtual machines. Now in my real life scenario it isnt working.

I created the keys in ServerA, copied them to ServerB, chmod'd .ssh folders to 700 on both ServerA,B.

Here is the log of what I get.

    debug1: SSH2_MSG_KEXINIT sent
    debug1: SSH2_MSG_KEXINIT received
    debug1: kex: server->client aes128-ctr hmac-md5 none
    debug1: kex: client->server aes128-ctr hmac-md5 none
    debug1: Peer sent proposed langtags, ctos:
    debug1: Peer sent proposed langtags, stoc:
    debug1: We proposed langtags, ctos: en-US
    debug1: We proposed langtags, stoc: en-US
    debug1: SSH2_MSG_KEX_DH_GEX_REQUEST sent
    debug1: expecting SSH2_MSG_KEX_DH_GEX_GROUP
    debug1: dh_gen_key: priv key bits set: 125/256
    debug1: bits set: 1039/2048
    debug1: SSH2_MSG_KEX_DH_GEX_INIT sent
    debug1: expecting SSH2_MSG_KEX_DH_GEX_REPLY
    debug1: Host 'XXX.XXX.XXX.XXX' is known and matches the RSA host key.
    debug1: Found key in /XXX/.ssh/known_hosts:1
    debug1: bits set: 1061/2048
    debug1: ssh_rsa_verify: signature correct
    debug1: newkeys: mode 1
    debug1: set_newkeys: setting new keys for 'out' mode
    debug1: SSH2_MSG_NEWKEYS sent
    debug1: expecting SSH2_MSG_NEWKEYS
    debug1: newkeys: mode 0
    debug1: set_newkeys: setting new keys for 'in' mode
    debug1: SSH2_MSG_NEWKEYS received
    debug1: done: ssh_kex2.
    debug1: send SSH2_MSG_SERVICE_REQUEST
    debug1: got SSH2_MSG_SERVICE_ACCEPT
    debug1: Authentications that can continue: publickey,keyboard-interactive
    debug1: Next authentication method: publickey
    debug1: Trying private key: /XXXX/.ssh/identity
    debug1: Trying public key: /xxx/.ssh/id_rsa
    debug1: Authentications that can continue: publickey,keyboard-interactive
    debug1: Trying private key: /xxx/.ssh/id_dsa
    debug1: Next authentication method: keyboard-interactive
    Password:
    Password:

ServerB has pretty limited actions since its a custom propietary linux.

What could be happening?

EDIT WITH ANSWER:

Problem was that I didnt have those settings enabled in the sshd_config (Refer to accepted answer) AND that while pasting the key from ServerA to ServerB it would interpret the key as 3 separate lines.

What I did was, in case you cant use ssh-copy-id like I couldnt. Paste the first line of your key in your "ServerB" authorized_keys file WITHOUT the last 2 characters, then type yourself the missing characters from line 1 and the first one from line 2, this will prevent adding a "new line" between the first and second line of the key. Repeat with the 3d line.