According to the gemara (bottom of Gittin 11a), you need to be "אפיצן" to documents in order for them to be considered valid, in order to be a "שטר שאינו יכול לזייף," a document that cannot be proven false.
Rashi there writes that this means that they would smear the document with gall-nut juice, so that if someone would erase anything it would be clear that they had done so. Tosfos there ask how documents in their time could possibly be valid, since they didn't do that; they answer that the documents of their time were covered in lime, which accomplishes the same thing.
So we've established (from the gemara) that documents need to be "שטר שאינו יכול לזייף," a document that cannot be proven false, preferably through the אפיצן process, smearing them with gall-nuts. Tosfos teaches us that any method of accomplishing אינו יכול לזייף is valid, and doesn't necessarily need "אפיצן."
What about notarization? If I were to notarize my documents, would they be halachically valid according to the rules set out in this gemara?
What if the notary keeps a copy of the document that he notarized?1
I might argue that these documents would be valid, because it is very difficult to prove a notarized document false, especially if the notary keeps a copy; however, all that can be proven from the gemara and Tosfos are that processes done directly to the document itself work to prove the truth of a document -- notarization (and keeping a copy) is not a process that is done to the actual paper of the document.
1 13. In some cases, retaining a copy of the document in the register or protocol ~ Wikipedia