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Some Bitcoin wallet addresses can be found by google, but some others shows no result. For example, this wallet is visible on many Bitcoin websites and google has a lot of results 1ENFY4h7ntGZbqwcwpQtXVFJrPnfXRHQLe and we can see its transactions. But this other address 126kUxBmdLTk4M7w1uaQ2pjAhm9KbZ6dxp (a ransom-ware wallet!) has no result. How it is possible? How can people do this?
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The latter address does not show up in google because it has not been used for a transaction yet. Once someone sends money to it, it will show up.
It's possible that we'll be able to create systems in the future that don't have this problem, but don't hold your breath.
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Every (real) transaction made with Bitcoin is stored on the Blockchain. Forever. If you are able to send Bitcoins to another address without it showing up on the Blockchain, you are not sending (real) Bitcoins.
So for your question on how to create an anonymous wallet, (public key and private key i suppose) you can do so very easily by generating it on an offline machine (using bitaddress.org for example, how to use it is explained there), and only providing your public key to the services/people that would need to send Bitcoins to you.
This public key will remain anonymous as long as there aren't any obvious connections to it- making the exchange where you bought your Bitcoins and that has your credentials and ID send the Bitcoins directly to that public key for example.
And on how to 'hide' transactions on the Blockchain- it's impossible. You can send Bitcoins through various 'Mixers' (bitmixer.io - or the onion for that link, bitmixer2whesjgj.onion ) to 'hide' the actual destinations of your Bitcoins, or you can send Bitcoins through hundreds of wallets, in the hopes that anyone that might be tracing your digital steps get lost in the transactions.
But like i stated before, every transaction -ever- made on the Blockchain is saved by the many Full Nodes and will therefor never be hidden.
I hope this helped!
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126kUxBmdLTk4M7w1uaQ2pjAhm9KbZ6dxp has never been used in a transaction, as can be verified at
https://blockchain.info/address/126kUxBmdLTk4M7w1uaQ2pjAhm9KbZ6dxp
If 126kUxBmdLTk4M7w1uaQ2pjAhm9KbZ6dxp is also not showing up in normal search engine results, then this address has likely never been openly published anywhere online.
If 126kUxBmdLTk4M7w1uaQ2pjAhm9KbZ6dxp is known to you as a ransom-ware address, this most likely means that the person who made the ransom-ware recently generated this address and is asking you for payment to it, but has otherwise not published this address anywhere else.
Systems using mandatotry stealth addressing (such as cryptonotes) achieve this already, and are in production. – user36303 – 2016-08-19T20:38:15.703
@user36303 In some cases, yes, but in other cases, it's possible to correlate multiple transactions by the same person together. This reduces anonymity to psuedoanonymity. I would wait for more study before relying on those properties. – Nick ODell – 2016-08-19T22:41:05.520
You are right, but I should have mentioned I was talking about the point made in the post I was replying to, rather than some other tangentially related one :) – user36303 – 2016-08-20T09:17:05.193