If the ECDSA is broken (address crypto), new coin time.
Not necessary.
Develop a new address type based on an alternate public key system.
Bitcoin addresses have versioning prefix these new addresses would have an alternate prefix.
Get miner support for verification of new address type.
Release new client which will verify transactions involving new address type but not allow their creation.
Once sufficient % of miners and nodes are on the new client release a new version which allows creation of new address type.
Users download new client and transfer their balance from old (deprecated) ECDSA based addresses to new addresses.
Now this assumes there is sufficient time but the history of cryptographic breaks has been slow with the time from theoretical flaw to real world exploit measures in multiples years (often decade or more).
When was the last time that there was a multi-billion dollar "prize fund" broken into small pieces and made available to anyone who had
A) an internet connection
and
B) understanding of the exploit
with no need for entry, confirmation, or waiting around for prize distribution at all?
Not to be combative with you at all.
I just think that's pretty hilarious. Someone, knowing they would never get it all to exchanges before the whole blockchain was written off, might share their tools just for shits and giggles. Whether they did or not, The entire market cap of BTC would probably vaporize faster than you can say "C++ For Dummies" because absolutely not a single soul would relinquish a penny of fiat for it after that.
Not "moved to bank accounts" or "safe in exchange accounts" or anything. Just freaking vaporized. If this is a few years down the road, it could be the first "fully distributed" economic event on a par with a whole first world economy crashing.
I've had some amusing thoughts about the amount of money that is probably brute-forcing ECDSA into rainbow tables right now. I'm tempted to start. But an announced flaw in the crypto would start a rush we may not even be able to envision.
I've never really thought that through in context before. It's always all chatter about securing the blockchain, heh.
I can't shake the picture of a bunch of rednecks sitting in a fishing boat with beers and laptops trying to sort out cryptography and programming "reeeeeeeaaaaaal quick".