If you own a significant amount of Ethereum you must understand that moving your coins on one chain (ETC or ETH) can have unintended consequences on the other.
This topic has been covered over the last few days by more technical folks, dubbed the "replay attack". Here follows a layman's version for your average non-techie whale.
Calling this a "replay" brings up memories of putting songs on replay on a CD or mp3 player (or cassette for some of us ;). I assure you that it is much more disturbing and worse than having to listen to Celine Dion "My Heart will go one" on constant replay.
Here's the deal. I will try to make this as simple as possible.
DO NOT SEND ANY ETC OR ETH UNTIL YOU ARE 100% SURE YOU HAVE SPLIT THEM TO SEPERATE PRIVATE KEYS.
A simple scenario:
You have created a transaction to either send some ETH or ETC. You broadcast this to the relevant network. Your transaction goes through.
Everything is great right?
Well not necessarily.
Someone can grab the raw signed transaction from the blockchain it was committed to and broadcast it on the other.
If you were just sending ETC to your own address it isn't a threat, you need to do this anyway to separate the funds to different keys.
However, let say that you borrowed 100,000 ETC from someone to short (say they were careful and only sent you ETC). You had them send the 100,000 ETC to an address that contained 100,000 ETH as well. A few days later you return their ETC.
That same transaction can be copied from the ETC blockchain by ANYONE to have your 100,000 ETH sent to the same address you returned the ETC to.
BEFORE ANYONE ELSE CAN DO THAT YOU MUST MAKE A TRANSACTION ON THE OTHER CHAIN TO MOVE THOSE COINS TO AN ADDRESS THAT HAS ANOTHER PRIVATE KEY!
Perhaps if you miss this it might not be an issue if it is someone you know.
But now consider this scenario...
You find yourself owning a ton of ETC that you don't care about. You get a tempting offer from someone in IRC to buy your ETC stash, and you have not segregated (moved) your ETH to another address yet.
You sell your ETC, but at the same time the buyer can take the raw signed tx and broadcast it on the other network and take all of your ETH.
Since you are the one that only has access to your private keys there is no way to prove that you did not intend to also send this person your ETH. Even if you could identify the individual, this is akin to handing out signed blank checks.
YOU MUST ENSURE THAT YOUR ETH AND ETC BALANCES ARE ATTACHED TO DIFFERENT PRIVATE KEYS. THE ONLY WAY TO DO THIS IS TO MOVE BOTH YOURSELF AND VERIFY BEFORE SENDING TO AN ADDRESS YOU DO NOT CONTROL.
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If you have concerns talk to a professional.
Some more technical reading on the subject:
https://gist.github.com/taoeffect/c910ebb16d9f6d248e9f1f3c6e10b1b8
https://github.com/ethereumclassic/README/issues/3
https://medium.com/@timonrapp/how-to-deal-with-the-ethereum-replay-attack-3fd44074a6d8#.ttsgvkrtc
http://vessenes.com/do-not-mess-with-eth-classic-it-will-f-you-up/
Thanks to @roelandp for making steemtools.com and @blueorgy for steemimg.com which was used to host the whale and pirate graphic.