Fwiw, bitcoin mining amounts to brute forcing SHA256 rather than ECC. Tendency these days for ECC (like in TLS) is to use Curve25519 rather than secp256k1. PQ (post quantum) is an entirely different topic and is in the direction of much more complicated schemes. RSA (or rather, integer factoring) has a long history of falling to better and better attacks, with a (now expired) 512 bit CA certificate recently having been factored on a single workstation. The first fielded deployment was at a nuclear lab and it used 336 bit keys! The big crypto nerds all seem to prefer ECC to RSA now. I tend to defer to them.
I would say, there are known sub-exponential algorithms for factoring, while nothing better than (exponential) brute force is known for ECC. So, slightly better algorithms that erode RSA further are incremental improvements, while anything sub-exponential at all for ECC would be a breakthrough. Of course as someone once said, predictions are hard to make, especially about the future.
Most of us don’t have control over the public keys we use. We connect to a web site with a browser, and the server supplies the public key.
If you want public keys for your own purposes, I guess nothing stops you from generating 4096 bit (or whatever) ECC keys. Of course the arithmetic will be slow.
If you’re really paranoid about potential math advances affecting ECC and/or RSA, then you may be best off avoiding public key schemes altogether. Just use secret keys, and maybe Merkle tree signatures.
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Fwiw, bitcoin mining amounts to brute forcing SHA256 rather than ECC. Tendency these days for ECC (like in TLS) is to use Curve25519 rather than secp256k1. PQ (post quantum) is an entirely different topic and is in the direction of much more complicated schemes. RSA (or rather, integer factoring) has a long history of falling to better and better attacks, with a (now expired) 512 bit CA certificate recently having been factored on a single workstation. The first fielded deployment was at a nuclear lab and it used 336 bit keys! The big crypto nerds all seem to prefer ECC to RSA now. I tend to defer to them.
Removed by mod
I would say, there are known sub-exponential algorithms for factoring, while nothing better than (exponential) brute force is known for ECC. So, slightly better algorithms that erode RSA further are incremental improvements, while anything sub-exponential at all for ECC would be a breakthrough. Of course as someone once said, predictions are hard to make, especially about the future.
Removed by mod
You could say the same things about AES keys being short.
Removed by mod
Most of us don’t have control over the public keys we use. We connect to a web site with a browser, and the server supplies the public key.
If you want public keys for your own purposes, I guess nothing stops you from generating 4096 bit (or whatever) ECC keys. Of course the arithmetic will be slow.
If you’re really paranoid about potential math advances affecting ECC and/or RSA, then you may be best off avoiding public key schemes altogether. Just use secret keys, and maybe Merkle tree signatures.
Removed by mod