Hiding the metadata of a one time pad message by encrypting the next key here is an idea that I feel has some big flaw I can't put my finger on.

The scenario is: Alice will go overseas for 5 days and will hopefully retrieve some information and send it back to Bob. She does not want to let anyone listening to know what day she got the information. She is taking with her a one time pad the size of the information, and a hardware random number generator.

The solution I thought of was:

Alice and Bob at home
Alice creates new key(key1) &gt; Bob (key1)

Alice travels to Elbonia
Alice creates new key (key2) XOR key1 &gt; Bob (key2)
Alice creates new key (key3) XOR key2 &gt; Bob (key3)
Alice creates msg + padding (msg) XOR key3 &gt; Bob (msg)
Alice creates new (rand) &gt; Bob (rand)
Alice creates new (rand) &gt; Bob (rand)
Alice travels home


Is this system any better or worse than just sending the encrypted message the day she receives the information, and pure random data on the other days?
Basically that's a one time pad variant where each day a cryptogram is sent, consisting of one between


on days before the actual message is sent, a new random pad replacing the previous random pad (of same size as the original), encrypted by XOR with the current random pad;
on a certain day, the message to be sent (padded to the pad size) encrypted by XOR with the current random pad;
random (of the pad size) on subsequent days.


That allows to send a single message. As is, the receiver has to know in advance or figure out on which day the message was sent, but the later is easy for practical messages.

That works; assuming all random bits generated are perfectly independent and unbiased, it insures the same unconditional security as the one pad, and meets the stated security objective of concealing on which day the information is sent. The quality of the generator is paramount: notice for example that a mere distinguishing attack allows to find on which day the actual message is sent.

Form a practical standpoint, the proposed system has a serious operational drawback compared to sending random on every day the message is not sent: if the cryptogram from any day before the actual message is sent gets lost (or is garbled), the message can not be deciphered (or is garbled).

I do not see any advantage, under the hypothesis that all random bits generated are perfectly independent and unbiased.