As there isn't a provided backport of OpenSSL 1.x for Debian 6.0, if you're unable to upgrade to a newer Debian release the best option is to create your own backport. As has been suggested, installing from source is not recommended.

If you start with the source package for Debian 8.0 (jessie) it should be reasonably straightforward. This post on Stack Overflow has a nice summary of what's required to build from source and there's a guide to creating your own backport.

This should be fairly safe as your own OpenSSL package will have a new major number - just make sure you follow the suggestions in that aforementioned Debian guide or you will have problems when you upgrade.

As there isn't a provided backport of OpenSSL 1.x for Debian 6.0, if you're unable to upgrade to a newer Debian release the best option is to create your own backport. As has been suggested, installing from source is not recommended.

If you start with the source package for Debian 8.0 (jessie) it should be reasonably straightforward. This post on Stack Overflow has a nice summary of what's required to build from source and there's a guide to creating your own backport.

This should be fairly safe as your own OpenSSL package will have a new major number - just make sure you follow the suggestions in that aforementioned Debian guide or you will have problems when you upgrade.