Problem in update manager during signature verification

Perhaps the mirror you are using is out of sync. Under the Administration -> Software Sources see what the value of the "Download From" drop down list is. Mine is Server for Canada and it works ok. I have also had success with Main Server.

If you are still having trouble open Administration -> Synaptec Package Manager and push Reload. See if that helps.

This is most likely a transient problem on the server. Your configuration should be fine.

i still facing a same problem after i change the download server to main server. i guess there is a problem in update distribution mechanism.

Ok, lets check your signatures.

Go to System -> Administration -> Software Sources -> Authentication

On my computer I have two signatures: 437D05B5 and FBB75451. What do you have?

A side note, is your clock set correctly?

I do have same signature on my laptop, also date and clock set correctly based on my timezone.
Is it something wrong or bad setting in my system..?

Please simple try to clean a bit your system... and then retry...

Open a Terminal from the menu Applications->Accessories->Terminal

Tip: right click with mouse on the terminal title caption and select the item "Always on Top" doing this you will force the terminal window to stay on top of the other windows and you will find very easy to copy single row from this web page into the terminal...
Something more about using the terminal https://help.ubuntu.com/community/UsingTheTerminal

Then type or better copy and paste a row a time then press enter:
(Tip: select the single row to copy then right click into the terminal and to quick paste click with middle button of mouse )

sudo dpkg --configure -a
sudo apt-get -f install
sudo apt-get --fix-missing install
sudo apt-get clean
sudo apt-get update
sudo apt-get upgrade
sudo apt-get dist-upgrade
sudo apt-get clean
sudo apt-get autoremove

then please reboot your system, type

sudo reboot

give your user password when requested, you don't see nothing when you type it, then press enter.

Hope this helps

Sorry for the late reply..
i've done you suggested, but it still won't fix my problem. I got these error messages now :

"W: GPG error: http://archive.ubuntu.com jaunty-security Release: The following signatures were invalid: BADSIG 40976EAF437D05B5 Ubuntu Archive Automatic Signing Key <email address hidden>
W: GPG error: http://ppa.launchpad.net jaunty Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 5227BEBD68436DDF
W: GPG error: http://ppa.launchpad.net jaunty Release: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 5A9BF3BB4E5E17B5"

Open a Terminal from the menu Applications → Accessories → Terminal and type or better copy and paste a row a time then press enter:
(if the system ask you a password give your user password, you will not see nothing when you type it, then press enter)

sudo apt-key adv --recv-keys --keyserver keyserver.ubuntu.com 40976EAF437D05B5
sudo apt-key adv --recv-keys --keyserver keyserver.ubuntu.com 5227BEBD68436DDF
sudo apt-key adv --recv-keys --keyserver keyserver.ubuntu.com 5A9BF3BB4E5E17B5

Then type: (when the system ask you a password give your user password, you will not see nothing when you type it, then press enter)

sudo apt-get update
sudo apt-get upgrade
sudo apt-get dist-upgrade

to update your system.

chi@DellChi:~$ sudo apt-key adv --recv-key --keyserver keyserver.ubuntu.com 40976EAF437D05B5
Executing: gpg --ignore-time-conflict --no-options --no-default-keyring --secret-keyring /etc/apt/secring.gpg --trustdb-name /etc/apt/trustdb.gpg --keyring /etc/apt/trusted.gpg --recv-key --keyserver keyserver.ubuntu.com 40976EAF437D05B5
gpg: requesting key 437D05B5 from hkp server keyserver.ubuntu.com
gpg: key 437D05B5: "Ubuntu Archive Automatic Signing Key <email address hidden>" not changed
gpg: Total number processed: 1
gpg: unchanged: 1
chi@DellChi:~$ sudo apt-key adv --recv-key --keyserver keyserver.ubuntu.com 5227BEBD68436DDF
Executing: gpg --ignore-time-conflict --no-options --no-default-keyring --secret-keyring /etc/apt/secring.gpg --trustdb-name /etc/apt/trustdb.gpg --keyring /etc/apt/trusted.gpg --recv-key --keyserver keyserver.ubuntu.com 5227BEBD68436DDF
gpg: requesting key 68436DDF from hkp server keyserver.ubuntu.com
gpg: key 68436DDF: "Launchpad PPA for qgis" not changed
gpg: Total number processed: 1
gpg: unchanged: 1
chi@DellChi:~$ sudo apt-key adv --recv-key --keyserver keyserver.ubuntu.com 5A9BF3BB4E5E17B5
Executing: gpg --ignore-time-conflict --no-options --no-default-keyring --secret-keyring /etc/apt/secring.gpg --trustdb-name /etc/apt/trustdb.gpg --keyring /etc/apt/trusted.gpg --recv-key --keyserver keyserver.ubuntu.com 5A9BF3BB4E5E17B5
gpg: requesting key 4E5E17B5 from hkp server keyserver.ubuntu.com
gpg: key 4E5E17B5: "Launchpad PPA for chromium-daily" not changed
gpg: Total number processed: 1
gpg: unchanged: 1

Unfortunately i still got a same error messages..
chi@DellChi:~$ sudo apt-get update
...
...
Reading package lists... Done
W: GPG error: http://archive.ubuntu.com jaunty-security Release: The following signatures were invalid: BADSIG 40976EAF437D05B5 Ubuntu Archive Automatic Signing Key <email address hidden>
W: GPG error: http://ppa.launchpad.net jaunty Release: The following signatures were invalid: BADSIG 5A9BF3BB4E5E17B5 Launchpad PPA for chromium-daily
W: You may want to run apt-get update to correct these problems

chi@DellChi:~$ sudo apt-get upgrade
Reading package lists... Done
Building dependency tree
Reading state information... Done
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.

chi@DellChi:~$ sudo apt-get dist-upgrade
Reading package lists... Done
Building dependency tree
Reading state information... Done
Calculating upgrade... Done
0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded.

Can you post the contents of /etc/apt.d ?

In particular what do you have in /etc/apt.d/sources.list and /etc/apt.d/sources.list.d/?

unfortunately i have no /etc/apt.d/sources.list.d/ in my system, while my /etc/apt.d/sources.list is :

# deb cdrom:[Ubuntu 9.04 _Jaunty Jackalope_ - Release i386 (20090420.1)]/ jaunty main restricted
deb-src http://archive.ubuntu.com/ubuntu/ jaunty main restricted #Added by software-properties
# See http://help.ubuntu.com/community/UpgradeNotes for how to upgrade to
# newer versions of the distribution.

deb http://archive.ubuntu.com/ubuntu/ jaunty main restricted
deb-src http://archive.ubuntu.com/ubuntu/ jaunty multiverse universe #Added by software-properties

## Major bug fix updates produced after the final release of the
## distribution.
deb http://archive.ubuntu.com/ubuntu/ jaunty-updates main restricted
deb-src http://archive.ubuntu.com/ubuntu/ jaunty-updates restricted main multiverse universe #Added by software-properties

## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu
## team. Also, please note that software in universe WILL NOT receive any
## review or updates from the Ubuntu security team.
deb http://archive.ubuntu.com/ubuntu/ jaunty universe
deb http://archive.ubuntu.com/ubuntu/ jaunty-updates universe

## N.B. software from this repository is ENTIRELY UNSUPPORTED by the Ubuntu
## team, and may not be under a free licence. Please satisfy yourself as to
## your rights to use the software. Also, please note that software in
## multiverse WILL NOT receive any review or updates from the Ubuntu
## security team.
deb http://archive.ubuntu.com/ubuntu/ jaunty multiverse
deb http://archive.ubuntu.com/ubuntu/ jaunty-updates multiverse

## Uncomment the following two lines to add software from the 'backports'
## repository.
## N.B. software from this repository may not have been tested as
## extensively as that contained in the main release, although it includes
## newer versions of some applications which may provide useful features.
## Also, please note that software in backports WILL NOT receive any review
## or updates from the Ubuntu security team.
# deb http://id.archive.ubuntu.com/ubuntu/ jaunty-backports main restricted universe multiverse
# deb-src http://id.archive.ubuntu.com/ubuntu/ jaunty-backports main restricted universe multiverse

## Uncomment the following two lines to add software from Canonical's
## 'partner' repository.
## This software is not part of Ubuntu, but is offered by Canonical and the
## respective vendors as a service to Ubuntu users.
deb http://archive.canonical.com/ubuntu jaunty partner
deb-src http://archive.canonical.com/ubuntu jaunty partner

deb http://archive.ubuntu.com/ubuntu/ jaunty-security main restricted
deb-src http://archive.ubuntu.com/ubuntu/ jaunty-security restricted main multiverse universe #Added by software-properties
deb http://archive.ubuntu.com/ubuntu/ jaunty-security universe
deb http://archive.ubuntu.com/ubuntu/ jaunty-security multiverse
deb http://ppa.launchpad.net/qgis/ubuntu jaunty main
deb-src http://ppa.launchpad.net/qgis/ubuntu jaunty main
deb http://ppa.launchpad.net/chromium-daily/ppa/ubuntu jaunty main
deb-src http://ppa.launchpad.net/chromium-daily/ppa/ubuntu jaunty main

Open a Terminal from the menu Applications → Accessories → Terminal and type or better copy and paste a row a time then press enter:
(if the system ask you a password give your user password, you will not see nothing when you type it, then press enter)

sudo apt-key adv --recv-keys --keyserver keyserver.ubuntu.com 40976EAF437D05B5

Then type: (when the system ask you a password give your user password, you will not see nothing when you type it, then press enter)

sudo apt-get update
sudo apt-get upgrade
sudo apt-get dist-upgrade

to update your system.