Dead-Man's Switch Cryptography?

Question

I was looking at Time Capsule cryptography? and came up wth this idea.

Question:

Is there a way to store a secret such that the creator must update it or the secret will be decrypted and anyone can access it?

Example:

I use this algorithm to encrypt the message, $enc(M)$, now if I don't update, $update(enc(M))$, then $M$ will be publicly known with high probability after some given time $t$

One idea was to use the Time Capsule cryptography to encrypt a (URL, key) pair that points to my data, and the update function would be me moving the data to another URL. I feel that this is kind of cheating though, since I could just as easily write a script to give public access to the computer if I don't log in (for example) for a fixed period of time.

So, for this problem let's say that we don't have access to a server and $enc(M)$ must be publicly known and contain the message $M$. i.e. this should become a Time Capsule crypto algorithm if I never perform an update.

I have a feeling this may be impossible, if so could you give a high level proof of why?

Answer 1

The scheme you propose is not possible as far as I know. This is because $enc(M)$ has to be known for the dead-man's switch to operate (in a time capsule like way, as you described), but there is no way in taking away the time capsule from someone non-cooperative (Eve), to substitute it with $update(enc(M))$.

Another possible scheme can be thought of, if you have a group of trusted parties. One can then use a threshold scheme in order to hide the key $k$ to your encrypted message $enc_k(M)$.
Whenever you don't update those trusted parties, after $t$ time, they can connect to each other, and if they reach the threshold of the scheme, release the key $k$.
This protocol requires a couple of external trusted parties. Although they can be computers, both computer and human can get compromised before the dead-man's switch fires.