ssh key login via public key - linux

Question

I am setting up ssh with public key access, I think I have correctly configured sshd_config and generate id_rsa.pub and authorized_keys.
ssh-kengen -t rsa
cd .ssh
cat id_rsa.pub >> authorized_keys
I also set the permission for these files
chmod 700 ~/.ssh
chmod 600 ~/.ssh/authorized_keys
When I try sudo ssh localhost, it works and no password is asked, but logged in as root.
But when I try ssh localhost, It is still asking for password.
logs generated during this are :-
OpenSSH_5.3p1, OpenSSL 1.0.1e-fips 11 Feb 2013
debug1: Reading configuration data /etc/ssh/ssh_config
debug1: Applying options for *
debug1: Connecting to localhost [127.0.0.1] port 22.
debug1: Connection established.
debug1: identity file /home/cwei/.ssh/identity type -1
debug1: identity file /home/cwei/.ssh/identity-cert type -1
debug1: identity file /home/cwei/.ssh/id_rsa type 1
debug1: identity file /home/cwei/.ssh/id_rsa-cert type -1
debug1: identity file /home/cwei/.ssh/id_dsa type -1
debug1: identity file /home/cwei/.ssh/id_dsa-cert type -1
debug1: identity file /home/cwei/.ssh/id_ecdsa type -1
debug1: identity file /home/cwei/.ssh/id_ecdsa-cert type -1
debug1: Remote protocol version 2.0, remote software version OpenSSH_5.3
debug1: match: OpenSSH_5.3 pat OpenSSH*
debug1: Enabling compatibility mode for protocol 2.0
debug1: Local version string SSH-2.0-OpenSSH_5.3
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: SSH2_MSG_KEX_DH_GEX_REQUEST(1024<1024<8192) sent
debug1: expecting SSH2_MSG_KEX_DH_GEX_GROUP
debug1: SSH2_MSG_KEX_DH_GEX_INIT sent
debug1: expecting SSH2_MSG_KEX_DH_GEX_REPLY
debug1: Host 'localhost' is known and matches the RSA host key.
debug1: Found key in /home/cwei/.ssh/known_hosts:1
debug1: ssh_rsa_verify: signature correct
debug1: SSH2_MSG_NEWKEYS sent
debug1: expecting SSH2_MSG_NEWKEYS
debug1: SSH2_MSG_NEWKEYS received
debug1: SSH2_MSG_SERVICE_REQUEST sent
debug1: SSH2_MSG_SERVICE_ACCEPT received
debug1: Authentications that can continue: publickey,gssapi-keyex,gssapi-
with-mic,password
debug1: Next authentication method: gssapi-keyex
debug1: No valid Key exchange context
debug1: Next authentication method: gssapi-with-mic
debug1: Unspecified GSS failure. Minor code may provide more information
Credentials cache file '/tmp/krb5cc_604' not found
debug1: Unspecified GSS failure. Minor code may provide more information
Credentials cache file '/tmp/krb5cc_604' not found
debug1: Unspecified GSS failure. Minor code may provide more information
debug1: Unspecified GSS failure. Minor code may provide more information
Credentials cache file '/tmp/krb5cc_604' not found
debug1: Next authentication method: publickey
debug1: Trying private key: /home/cwei/.ssh/identity
debug1: Offering public key: /home/cwei/.ssh/id_rsa
debug1: Authentications that can continue: publickey,gssapi-keyex,gssapi-with-mic,password
debug1: Trying private key: /home/cwei/.ssh/id_dsa
debug1: Trying private key: /home/cwei/.ssh/id_ecdsa
debug1: Next authentication method: password
cwei#localhost's password:

Answer 1

Ssh public key access is user based. The configuration may be done for the root user. It needs to be done for the local user by configuring local users local .ssh directory.