Default Trac ticket permissions are TICKET_VIEW for 'anonymous' sessions (everyone) and editing for 'authenticated' users, yes.
You'll want to remove TICKET_VIEW, so only authenticated users will see (and modify) tickets. To accomplish that, any user with PERMISSION_REVOKE (inherited by TRAC_ADMIN and PERMISSION_ADMIN as well) is allowed to navigate to the permission web admin page, can check and submit the 'remove' action. Alternatively you could use the trac-admin command:
trac-admin <path_to_trac_env> permission remove anonymous TICKET_VIEW
where you need to replace the path with you real one, like /var/www/trac_env/myTrac
.