Many people are asking this exact question and after searching the internet for several days, I couldn’t find the answer. So a trip into the EOS Telegram room, and several people helped me. Thanks Fuzzy!
This infographic is based on the answers I received plus a fantastic EOS guide on Steemit that was written by 
This guide was the best out there as far as explaining how the EOS public key mapping works, and the deadline to do that is June 3, 2018.
There’s a lot of confusion surrounding the public key mapping of the EOS tokens, and rightly so. Most people don’t understand what is going on. After spending several full days unraveling this stuff, I think I know how to explain it in a clear way. This mostly applies to people using MyEtherWallet. EOS has setup their own method which is easy to use with Chrome and MetaMask. However, not everyone uses Chrome, so there is a need for people to figure out the steps associated with MyEtherWallet.
Here goes:
The EOS blockchain is not alive yet, but it will be after June 2018 (that’s the target date). These new EOS tokens will have specific functionalities, and these will only be live on the EOS blockchain in the future. In order to get these new EOS blockchain tokens that will exist in the future, you need to register your Ethereum wallet address with a public key to EOS. So all the EOS you own now will need to be in that same Ethereum wallet that you registered with EOS.
Think of it this way:
Your Ethereum wallet that holds your EOS tokens is like a house, with an address. You put your EOS tokens inside this house. But the future EOS blockchain has no idea where this house is. You must register your Ethereum wallet address with EOS so that you can get your new EOS tokens that reside on the future EOS blockchain.
When the snapshot of all EOS token ownership is taken in the future, your Ethereum wallet that holds EOS will be included in this snapshot as long as you registered it. When this snapshot is taken, you will be able to claim the real live EOS blockchain tokens. But only those who registered their tokens with EOS will be given these new EOS blockchain tokens.
So, a page has been set up in order to generate your public-private key pair for the future EOS blockchain. The person who created it states:
This will generate a private and public key pair for the EOS chain. The code is not mine. It is forked from the code the EOS team built. The difference is that this works in any browser without the web3 dependency. It will work in any browser and you don’t need any plugins. I’ve also removed everything else except the key generation bits.
Go here to generate your public-private key pair for EOS: https://nadejde.github.io/eos-token-sale/
Personally, If I were running EOS, I’d set up a technical helpline on the days before the snapshot, because I bet there will be a significant number of people who don’t understand what needs to happen and why. This stuff is pretty complicated because we are talking about future events, new technology that barely anyone understands and snapshots of a blockchain that doesn’t currently exist.
I’m looking forward to what EOS creates since creating smart contracts on Ethereum can be a costly endeavor that occurs accidentally. A friend of mine bought $35 worth of EOS through the crowdsale and ended up accidentally spending $12 in ETH gas fees in the process. The ETH gas fee was set automatically too high and my friend didn’t know she could manually adjust this amount.
Follow the official EOS blog on Steemit: https://steemit.com/@eosio
Hey, if you haven't submitted your video for my Steemfest2 Giveaway, do it today!
Cheers,
Stellabelle