I have some weird entries in my mail.log. What I'd like to ask is if postfix is avoiding correctly (according with the main.cf attached below) what seems to be relay attempts, presumably for spamming, or if I can enhance it's security somehow.

Feb  2 11:53:25 MYSERVER postfix/smtpd[9094]: connect from catv-80-99-46-143.catv.broadband.hu[80.99.46.143]
Feb  2 11:53:25 MYSERVER postfix/smtpd[9094]: warning: non-SMTP command from catv-80-99-46-143.catv.broadband.hu[80.99.46.143]: GET / HTTP/1.1
Feb  2 11:53:25 MYSERVER postfix/smtpd[9094]: disconnect from catv-80-99-46-143.catv.broadband.hu[80.99.46.143]
Feb  2 11:56:45 MYSERVER postfix/anvil[9097]: statistics: max connection rate 1/60s for (smtp:80.99.46.143) at Feb  2 11:53:25
Feb  2 11:56:45 MYSERVER postfix/anvil[9097]: statistics: max connection count 1 for (smtp:80.99.46.143) at Feb  2 11:53:25
Feb  2 11:56:45 MYSERVER postfix/anvil[9097]: statistics: max cache size 1 at Feb  2 11:53:25
Feb  2 12:09:19 MYSERVER postfix/smtpd[9302]: connect from vs148181.vserver.de[62.75.148.181]
Feb  2 12:09:19 MYSERVER postfix/smtpd[9302]: warning: non-SMTP command from vs148181.vserver.de[62.75.148.181]: GET / HTTP/1.1
Feb  2 12:09:19 MYSERVER postfix/smtpd[9302]: disconnect from vs148181.vserver.de[62.75.148.181]
Feb  2 12:12:39 MYSERVER postfix/anvil[9304]: statistics: max connection rate 1/60s for (smtp:62.75.148.181) at Feb  2 12:09:19
Feb  2 12:12:39 MYSERVER postfix/anvil[9304]: statistics: max connection count 1 for (smtp:62.75.148.181) at Feb  2 12:09:19
Feb  2 12:12:39 MYSERVER postfix/anvil[9304]: statistics: max cache size 1 at Feb  2 12:09:19
Feb  2 14:17:02 MYSERVER postfix/smtpd[10847]: connect from unknown[202.46.129.123]
Feb  2 14:17:02 MYSERVER postfix/smtpd[10847]: warning: non-SMTP command from unknown[202.46.129.123]: GET / HTTP/1.1
Feb  2 14:17:02 MYSERVER postfix/smtpd[10847]: disconnect from unknown[202.46.129.123]
Feb  2 14:20:22 MYSERVER postfix/anvil[10853]: statistics: max connection rate 1/60s for (smtp:202.46.129.123) at Feb  2 14:17:02
Feb  2 14:20:22 MYSERVER postfix/anvil[10853]: statistics: max connection count 1 for (smtp:202.46.129.123) at Feb  2 14:17:02
Feb  2 14:20:22 MYSERVER postfix/anvil[10853]: statistics: max cache size 1 at Feb  2 14:17:02
Feb  2 20:57:33 MYSERVER postfix/smtpd[18452]: warning: 95.110.224.230: hostname host230-224-110-95.serverdedicati.aruba.it verification failed: Name or service not known
Feb  2 20:57:33 MYSERVER postfix/smtpd[18452]: connect from unknown[95.110.224.230]
Feb  2 20:57:33 MYSERVER postfix/smtpd[18452]: lost connection after CONNECT from unknown[95.110.224.230]
Feb  2 20:57:33 MYSERVER postfix/smtpd[18452]: disconnect from unknown[95.110.224.230]
Feb  2 21:00:53 MYSERVER postfix/anvil[18455]: statistics: max connection rate 1/60s for (smtp:95.110.224.230) at Feb  2 20:57:33
Feb  2 21:00:53 MYSERVER postfix/anvil[18455]: statistics: max connection count 1 for (smtp:95.110.224.230) at Feb  2 20:57:33
Feb  2 21:00:53 MYSERVER postfix/anvil[18455]: statistics: max cache size 1 at Feb  2 20:57:33
Feb  2 21:13:44 MYSERVER pop3d: Connection, ip=[::ffff:219.94.190.222]
Feb  2 21:13:44 MYSERVER pop3d: LOGIN FAILED, user=admin, ip=[::ffff:219.94.190.222]
Feb  2 21:13:50 MYSERVER pop3d: LOGIN FAILED, user=test, ip=[::ffff:219.94.190.222]
Feb  2 21:13:56 MYSERVER pop3d: LOGIN FAILED, user=danny, ip=[::ffff:219.94.190.222]
Feb  2 21:14:01 MYSERVER pop3d: LOGIN FAILED, user=sharon, ip=[::ffff:219.94.190.222]
Feb  2 21:14:07 MYSERVER pop3d: LOGIN FAILED, user=aron, ip=[::ffff:219.94.190.222]
Feb  2 21:14:12 MYSERVER pop3d: LOGIN FAILED, user=alex, ip=[::ffff:219.94.190.222]
Feb  2 21:14:18 MYSERVER pop3d: LOGIN FAILED, user=brett, ip=[::ffff:219.94.190.222]
Feb  2 21:14:24 MYSERVER pop3d: LOGIN FAILED, user=mike, ip=[::ffff:219.94.190.222]
Feb  2 21:14:29 MYSERVER pop3d: LOGIN FAILED, user=alan, ip=[::ffff:219.94.190.222]
Feb  2 21:14:35 MYSERVER pop3d: LOGIN FAILED, user=info, ip=[::ffff:219.94.190.222]
Feb  2 21:14:41 MYSERVER pop3d: LOGIN FAILED, user=shop, ip=[::ffff:219.94.190.222]
Feb  3 06:49:29 MYSERVER postfix/smtpd[25834]: warning: 71.6.142.196: hostname db4142196.aspadmin.net verification failed: Name or service not known
Feb  3 06:49:29 MYSERVER postfix/smtpd[25834]: connect from unknown[71.6.142.196]
Feb  3 06:49:29 MYSERVER postfix/smtpd[25834]: lost connection after CONNECT from unknown[71.6.142.196]
Feb  3 06:49:29 MYSERVER postfix/smtpd[25834]: disconnect from unknown[71.6.142.196]
Feb  3 06:52:49 MYSERVER postfix/anvil[25837]: statistics: max connection rate 1/60s for (smtp:71.6.142.196) at Feb  3 06:49:29
Feb  3 06:52:49 MYSERVER postfix/anvil[25837]: statistics: max connection count 1 for (smtp:71.6.142.196) at Feb  3 06:49:29
Feb  3 06:52:49 MYSERVER postfix/anvil[25837]: statistics: max cache size 1 at Feb  3 06:49:29

I have Postfix 2.7.1-1 running on Ubuntu 10.10. This is my (modified por privacy) main.cf:

smtpd_banner = $myhostname ESMTP $mail_name (Ubuntu)
biff = no

append_dot_mydomain = no


readme_directory = no


smtpd_tls_cert_file = /etc/ssl/certs/smtpd.crt
smtpd_tls_key_file = /etc/ssl/private/smtpd.key


myhostname = mymailserver.org
alias_maps = hash:/etc/aliases
alias_database = hash:/etc/aliases
myorigin = /etc/mailname
mydestination = mymailserver.org, MYSERVER, localhost
relayhost = 
mynetworks = 127.0.0.0/8, 192.168.1.0/24
mailbox_size_limit = 0
recipient_delimiter = +
inet_interfaces = all
inet_protocols = all
home_mailbox = Maildir/

smtpd_recipient_restrictions = permit_sasl_authenticated,permit_mynetworks,reject_unauth_destination
mailbox_command = 
smtpd_sasl_local_domain = 
smtpd_sasl_auth_enable = yes
smtpd_sasl_security_options = noanonymous
broken_sasl_auth_clients = yes
smtpd_tls_security_level = may
smtpd_tls_auth_only = no
smtp_tls_note_starttls_offer = yes
smtpd_tls_CAfile = /etc/ssl/certs/cacert.pem
smtpd_tls_loglevel = 1
smtpd_tls_received_header = yes
smtpd_tls_session_cache_timeout = 3600s
tls_random_source = dev:/dev/urandom
smtp_tls_security_level = may