RSA Algorithm
leimao.github.io
leimao.github.io
The very definition of modern public-key crypto is that it doesn't use RSA :)
> Cracking the RSA encryption system using brute force is not practically feasible.
Cracking the RSA encryption system as implemented by someone reading a lecture like this is straightforward. Heck, "padding" doesn't even appear in it, most university slides at least mention "oh by the way, this thing's pretty useless without padding".
In my opinion this article falls squarely in the "talking about RSA considered harmful" category: showing textbook RSA, then saying it [RSA] is secure, without mentioning how hard it actually is to achieve that.
Reminds me of when I was at University. One of my professors had implemented RSA as one of his lecture examples in their advanced C class. I forget why, I was too busy reading the implementation.
The net result was that a brute-force attack was possible, simply because the keys were generated from an insecure RNG and seeding system: https://github.com/cipherboy/coms327-RSA_Crack
There are two secure ways to use RSA: as a signature scheme with appropriate padding (PSS), or as a Key Encapsulation Mode (KEM) which inherently doesn't require padding.
The general rule is that if an article on RSA includes anything about "encrypting a message" it's naive and outdated, and should be ignored. RSA encryption is slow and error-prone. RSA signatures are slow to generate (though fast to verify) and error-prone. RSA-KEM is at least not any more error-prone than the rest of cryptography, it's just slow.
> The ordinary algorithm to do integer factorization takes sub-exponential time according to the Wikipedia. This is the fundamental reason which makes the RSA cryptosystem so reliable.
I'd say it is akin to a proprietary technology which never got released to the general public, and then some FOSS technology comes along which does arguably the same, yet is FOSS and gets widely adopted.
Want the credit? Should've released it to the public then. That's a side effect of working for secret services; you don't get much, if any, personal credit. Nor even credit as a secret service. E.g. because the ops remain secret.
Does increasing the size of the key get around this problem, if not is there any solution to this?
Essentially something that both quantum and classical computers cannot crack/brute force.
I would look into lattice-based crypto. It is one of the strongest candidates under review by NIST for post-quantum public/private key mechanisms.