You are using the "encrypt with the private key" analogy. Don't do that, it will trigger only confusion.
What you want is a digital signature scheme. Such a scheme consists of three algorithms:
Key generation: this algorithm produces a new key pair, with a public key Kp and a private key Ks. The public key, as its name says, can be made public, i.e. revealed to the world at large, and this does not disclose the private key (though the private key is still mathematically linked to the public key).
Signature generation: given a message m, a signature s is produced, using the private key Ks.
Signature verification: given a message m, a signature value s and the public key Kp, the verification algorithm returns "true" or "false", depending on whether the signature matches the message for that public key, or not.
The signature is sound if what the signature generation algorithm produces is indeed declared valid by the signature verification algorithm. The signature is secure if it is not feasible, without knowing Ks, to produce a pair (m,s) that the verification algorithm will declare valid for public key Kp.
Unfortunately, when the first workable signature algorithm was described, the idea of the algorithm was said to be "asymmetric encryption in reverse": the signature was generated by "encrypting the message with the private key" (or, equivalently, by swapping private and public keys, i.e. making the private key public and vice-versa). This was unfortunate because:
- Not all signature algorithms can be seen as "reversed asymmetric encryption". This analogy works only for RSA.
- In fact, the analogy does not work for RSA either; it works only for the mathematical core of RSA, but not with the "full RSA" which also include things like padding, which are crucial for security but break the "reverse encryption" analogy.
The "encryption in reverse" description is a widespread way to "explain signatures" and, in doing so, mostly spreads confusion. Don't fall in that trap.
A signature algorithm seems to map well to what you are envisioning. The author would include his public key in the first message. Then each ulterior message would be signed with the corresponding private key, and everybody could verify that signature relatively to the public key in the first message.
However, note that authorship is the combination of two concepts:
- Responsibility: "Yes, I am willing to assert that I wrote these words and will be bound by them."
- Exclusivity: "All other people who claim having written these words are filthy liars."
A signature will ensure both only if people have a way to make sure that what they see as "first message" is indeed the true first message, i.e. contains the correct public key. Another person Y wanted to claim authorship of the same texts could publish his own "first message" with his own public key, and sign (with his own private key) whatever X publishes. The public at large would have a hard time finding out who wrote the text first. In order to establish true authorship (in that sense), timestamps may be used (in addition to signatures, not replacing them).