Why do we need two transactions for CommitCoin scheme I am studying BitCoin recently.

I noticed a method called CommitCoin for secure timestamping. It requires two transactions to send coins back with the same randomness so that others can compute the private key.

However, isn't it easier to just reveal the private key yourself? The whole point is to prove that at some time in the past, I knew something. If I send some coins to the address and send the coins back, and later reveal my private key and it matches the public key, shouldn't it be enough to prove that?

Thanks in advance.
We wrote this paper before Bitcoin supported OP_RETURN. Now you would just use OP_RETURN. 

In CommitCoin, you can reveal the private key off-blockchain. It might indeed be simpler. Our thinking is having it self-contained on the blockchain, without having to reference anything else or having to have a connection to the publisher was the simpler model.