I’ve read about BIP32 key derivation functions, and also:
Any Elliptic Curve could work in the BIP32 scheme. The only property
of a Curve that BIP32 relies on is that a * G + b *G = (a + b mod N) *
G, which is true for any Elliptic Curve.
(from Is BIP 32 Technology Cryptographic Curve Agnostic?.)
Are there simpler forms of weak-child-only key derivations? (I’m guessing that the HMAC, splitting and concatenation is unneeded for a simpler/weaker scheme. Such a scheme would just have a large number of weak children and no layers/tree.)
Is a simpler scheme possible? (I’m asking about cryptography generally, not whether it’s a good idea for Bitcoin.)