But technically it is possible, right? So what happens, when somebody smart enough will make some improvements of his own to the algorithm of adress generation in some services, like blockchain.info or others? He will gain access to your coins? Is this real?
No? Those addresses are randomly generated. It's possible to get the same address, but I don't think you can "make your own algorithm" to generate the private keys more easily.
Maybe if the service isn't pure RNG when generating those private keys.
I got, that they are randomly generated. What I mean is "random" in case of computer science - is a result of execution of some function, that returns "random" result after long line of mathematical operations. Address is not generated by blockchain, right? It just adds to next block of transactions after sending an amout of coins there, if I understand it correct. So, I`m asking what about if some third party will intervene in a process of generation of an adress (let`s say, some cool-*ss hacker) to generate exact the same adress the same moment (let`s say it`s happening on blockchain.info). Then you send your BTC to this adress, thinking that it`s safe. Will the bad guys get an access to your coins in this case? Sorry if I explaining it horribly, confused in technicalities.