Quote from: coastermonger on October 08, 2013, 11:02:43 PM

Importantly, this network enforces your rules as to when this 2nd extra key can be decrypted.

How's the key encrypted/decrypted? With some piece of information (password/another key/etc.). How do you hide that information? Hint: it's turtles all the way down.
Seriously, enforcement isn't magical. Unless I'm missing something really obvious, your approach isn't going to fly.

Your idea can work, but it's not safe/distributed in the same way that bitcoin is:

Approach 1:
1. Use Shamir's Secret Sharing to split the key into n pieces of which n/2+1 are required to recreate the original key. Send each key to a different peer.
2. When you want to spend your money, you need to contact n/2+1 peers, and request their part of the key. Once you have enough parts, you can recreate it and sign your transaction.

Problems with this approach:
1. If n/2+1 peers collude together, they can get the full key back (and maybe get a cut of your stolen funds by giving it to the guy that stole your money).
2. You can't tell if the people you're sending your parts of the key are actually independent, or they're all run by one attacker (Sybil attack).
3. If enough peers go away, you have lost the ability to spend your funds, ever. And you can't get around that by asking the peers to share their part of the key with others, because that breaks the security.
4. The set of rules under which to allow spending is openly known. So a smart thief will know what conditions to satisfy in order to spend your funds.

So you end up with Approach 2:

1. Use trusted peers that have some reputation to lose, and that you're reasonnably confident will remain online semi-permanently.
2. Give each peer a different full key. Store a copy on paper, to guard against loss.
3. Store money in a "m of n" address, ideally where m is high.

It's safer but not peer-to-peer. In fact it's one of jedunnigan's suggestions.