Today, hot smartphone wallets save your private keys in the secure element at rest, but pull it out to sign in the normal environment where malware can get access to it.

This is necessary because these secure chips can't do secp256k1 natively.

So I know private keys can't be kept locked in your phone's secure element today, but your phone CAN do challenge response with other cryptographic algos.

I'm just thinking out loud, but with taproot, can't we create addresses that use another algo that is not secp256k1 to embed a challenge into the spending conditions for your address that the smartphone CAN protect and sign with securely?

This way we have funds in a wallet that is a bit better than hot. It is in a secure element which is used to secure other things like your password manager and other things.

Possibly then we can also create modified XPUBs using your private key's public key and this other pubic key that relates to the secret used by your phone.

Overall, I'm thinking a new type of wallet that has 2 keys: your bitcoin key, and an adaptor key. You need both to spend funds, the algorithms are all standard public ones, we get the assurance that secp256k1 provides that it isn't secured by a potentially compromised NIST algo, but also the convenience that it is partially secured by a NIST algo that popular smartphones can secure.

Is this possible or a dumb idea?