Secure timestamping and confidential auditing
The modern protocol uses cryptographic hash functions instead of anagrams. Any set of bits (digital content, a network event, whatever) is passed through the hash function, turning into into a unique random-looking string of bits. Those bits are then published to multiple timestamp servers on the Internet. The timestamp servers create a chain of hashes. Using the chain of published hashes, it is easy to later prove that (1) the hash was published before one event and after another event, thus proving the time of publication, and (2) that the hash uniquely corresponds to a particular content.
Note that the content of the file does not need to be published until proof is needed. Thus, for example, one could digitally timestamp a secret digital inventor's notebook in order to prove later that the invention existed at that time. (Might be quite useful under the American first-to-invent system).
Indeed, using multiparty secure computation or the related protocols called zero-knowledge proofs, one can even make a later proof without publishing the content. For example, if Bob received a secret encrypted e-mail message from Alice, Alice and Bob could prove to the world that Alice sent a message at 18:42:39 and Bob received it at 18:43:05 without revealing the actual contents of the message. In a confidential audit of Alice's books based on securely timestamped transactions between Alice and Bob and Alice and Charles, performed using secure multiparty computation, Alice can prove to the auditor that her books balance based on real transactions with Bob and Charles, without revealing in unencrypted form to the auditor either the transactions or the books. Such is the magical reality of cryptography!
Here are some links to papers and other references on secure timestamping.