Has anyone cracked 4096 bit RSA public key encryption, the same one available to use in GPG?
Has anyone cracked 2048 bit RSA encryption for that matter?
As far as I am aware, the largest RSA that was factored is 795 bits, in November 2019. The CPU time spent on finding these factors amounted to approximately 900 core-years on a 2.1 Ghz Intel Xeon Gold 6130 CPU.
However, we are talking about eliptic curves here, so the situation is a bit different. I am merely responding to the OP's title.
128 to 256 bit symmetric encryption will not be broken in a very long time, so that's not an issue.
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Unfortunately, you confuse the path of the monkey - this is hacking the system with brute force attack and the path of an intelligent person, the path of cryptanalysis is the mathematical solution to the problem of factorization and hacking RSA.
Quantum computing - just as everyone sees it as a monkey path, as a brute force attack.
But you can go through analysis, even with a quantum computer.
4096-bit RSA keys are easier than 96-bit keys in AES.
Keys in AES less than 128 bits are not used anywhere.
Why so? Because it breaks.
In symmetric systems, the method of comparing plaintext with a ciphercode is a difficult task, you need to have a lot of text, you need to think a lot to calculate the key.
In asymmetric systems, a cryptanalyst always has any amount of plaintext, encrypted text, and the public key is known. The cryptanalyst himself will write any amount of material for analysis - after all, the public key is not hidden. See the difference?
Do not think that someday you will know the mathematical methods of hacking. Why would they tell us about this?
These are big secrets.
Cryptanalysis is a weapon, opening a cipher is a victory.
That was the whole story.
This is a tool that can get a lot of valuable prizes if it remains a secret!
Cryptanalysts live secretly, lead a double life, and are guarded very well.
Why?
Why don't any serious organization use asymmetric cryptography? Because it is a household system, today it is forbidden to use it in important issues. And only symmetric systems are allowed.
No one will make themselves difficult in life just like that.
Do you agree?
It means that they know something, but they are silent.
Who knows - he is always silent. But we can observe and draw conclusions.
Post-quantum cryptography is actively sought after. But they can’t find it yet!
There were cases when the post-quantum system was actively offered, everyone clapped their hands, and then cryptanalysts worked - and the system was withdrawn from the competition.
This is far from an isolated case! This is the path of cryptanalysis.
By the way, the path of a monkey (brute force attack) in post-quantum cryptography is generally not possible even after hundreds of years, even by all super-quantum computers combined. The keys are different in different systems, but keys with a length of 38.64, 256 thousand bits (and not just a bit) are not uncommon there. There are even megabytes - and this is not the limit.
So no one sees the danger of brute-force attack as a danger. Neither today nor tomorrow.
Therefore your example: "As far as I am aware, the largest RSA that was factored is 795 bits, in November 2019." - nothing more than a distracting maneuver from the problem.
Why did they chase new asymmetric systems, if you can simply increase the key length in the same RSA?
A system in which there are principles of factorization or discrete logarithm in the fields of numbers of any magnitude are not considered at all !!! Generally.
Everything, RSA time is over. This is the rudiment that smart people fear.
Why? What was so bad about our asymmetric household systems today?
That’s why, for which there is only one answer - any modern asymmetric system is an ear on clay feet!