I was looking all over the Internet list of ALL existing symmetric and asymmetric ciphers.
I know that there's, for example, AES, DES, Blowfish, DSA. But how about more? Where to find such list?
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You can, of course, not get a list of all existing ciphers. You could maybe get a list of all documented ciphers, if you would have a lifetime looking for them.
Unfortunately for you, just like operating systems, most ciphers lead a hidden life. Most people know Microsoft Windows, iOS and Android. Possibly they have heard of something called Linux or Apple OS. Heck, maybe they even have heard of Windows Phone 8. But there are thousands of operating systems out there, on anything like a smart card to a mainframe. It's the same thing for ciphers.
So have fun looking on the internet and try and make a list yourself. You could try some software like Bouncy Castle that tries to implement most algorithms found in the wild to start your search. Or try wikipedia, scientific papers etc. etc.