[nybble41]

Using something like the Hierarchical Deterministic approach used for modern cryptocurrency wallets ("HD wallets") you can reuse a single master asymmetric key for any number of logins without linking those logins together.

In this scheme there is a single master private key which you protect in whatever way seems best and never share with anyone. From this master private key you can derive any number of subordinate private keys, each with its own public key. You share one of those public keys with each service, along with the derivation path, and authenticate using the corresponding private key. Only the unchanging master private key needs to be stored, so unlike a password manager there is no need to make new backups or sync a password database across multiple devices when you set up a new account. Best of all, without either the master private key or the corresponding master public key there is no (known) way to show that any two subordinate keys were derived from the same master key—they appear unrelated.