How to determine a package checksum
From Joomla! Documentation
A checksum is a string of characters created by applying a mathematical algorithm to the contents of a file. It allows you to determine whether two files are identical because changing even a single bit in a file will cause the checksum to change. Although it is possible for two different files to have the same checksum it is statistically unlikely for an error introduced during a file copy to leave the checksum unchanged. Furthermore, it is extraordinarily difficult to deliberately change a file without also changing the checksum.
Although there are several different kinds of checksum available, the Joomla! project publishes the popular MD5 checksum for all full distribution and patch files. The MD5 checksum string is always exactly 32 characters long.
Unix-style systems (such as Linux)[edit]
From the command line use the md5sum program. For example, here we determine the MD5 checksum for a Joomla! patch file.
md5sum Joomla_1.0.11_to_1.0.12-Stable-Patch_Package.tar.bz2 67534a24ca89b76f5ae197ed171bd75e Joomla_1.0.11_to_1.0.12-Stable-Patch_Package.tar.bz2
Type man md5sum at the command line for full details on the md5sum program.
Apple Mac OS X[edit]
<anybody know?>
Microsoft Windows[edit]
Download the free File Checksum Integrity Verifier from Microsoft here http://support.microsoft.com/kb/841290
All neccessary information and help is included in the article.