What will be the consequences of discovering the fast factorization algorithm?

Question

SSH

As far as I know, modern data exchange (confirmation of banking transactions, ssh, digital signature, banal e-mail) is based on cryptography based on the inability to quickly factorize large numbers, such as rsa (correct me if I'm wrong).
If an algorithm is found in the coming years (months / days) that allows decomposing numbers of any length quickly (in a time comparable to multiplication, for example, only 10 times slower), then what will be the consequences? What harm will this bring to the economy? Or maybe no one will notice this at all, and everyone will immediately switch to another cryptography (how quickly this transition can happen)?

Answer 1

All systems based on algorithms like RSA will be compromised. Secure communication over HTTPS, software and hardware update signing, SSH authorization keys.
Manufacturers will try to roll out software updates as soon as possible that close the resulting holes in the update and authorization algorithms (using, for example, elliptic curve algorithms), but not all will update, and some devices will be completely impossible to update.
If such an algorithm is indeed found and made publicly available, there will be a complete mess in the IT world for the next 5 years.