how can I retrieve an authentication key for my system

All you need is your login password, assuming your user is in the 'sudo' group. There is no file needed to install updates.

Can you give the output of:

sudo apt-get update; lsb_release -a

Thanks

Open a terminal and (CTRL+ALT+T) give us the output of

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lsb_release -a; id
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 I see this

~$ lsb_release -a; id
No LSB modules are available.
Distributor ID: Ubuntu
Description: Ubuntu 12.04.1 LTS
Release: 12.04
Codename: precise
uid=1000(warren) gid=1000(warren) groups=1000(warren),4(adm),24(cdrom),27(sudo),30(dip),46(plugdev),109(lpadmin),124(sambashare),125(wireshark)

If this shows your a member of the 'sudo' group you should be able to update using the commands given in the post above.
If it does but you don't know the password you can reset it using the links below

There are a few methods (mostly similar) take a look at these

http://www.psychocats.net/ubuntu/resetpassword

https://help.ubuntu.com/12.04/ubuntu-help/user-forgottenpassword.html

http://askubuntu.com/questions/24006/how-do-i-reset-a-lost-administrative-password

http://naveenubuntu.blogspot.co.uk/2012/05/recover-login-password-of-ubuntu-1204.html

If it doesn't you need to be added to the 'sudo' group. Let us know the output of the above commands and we will tell you how to do this