Challenge: an Asymmetric Key System That Does Everything

I’m curious if anyone has thought about this before:

We have asymmetric cryptography, but the main systems all have trade-offs:

RSA: You can encrypt/decrypt and sign/verify, but you cannot derive hierarchical public/private keys—every key pair must be generated independently.

ECDSA (elliptic curves): You can sign/verify, and you can derive hierarchical deterministic keys (HD wallets!), but you cannot do encryption/decryption natively.

So here’s the challenge:

Can anyone design an asymmetric key system that can do all five things:

1. Encrypt

2. Decrypt

3. Sign

4. Verify

5. Hierarchical key derivation (master → child public/private keys)

Right now, no single system can do this perfectly. Either you get encryption or hierarchical keys, but not both.

If we could create such a system, it would unify digital identity, secure messaging, and deterministic key management in a single cryptosystem.

I’d love to see ideas, proposals, or even wild theoretical approaches. Has anyone tried combining elliptic-curve deterministic keys with encryption in a clean way?

Oiko