# Is there a simpler form of BIP32-like key derivation?

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.

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.)

• `SHA256(entropy | index)`. 1st key = `SHA256(entropy | 0x00000000)`, 2nd key = `SHA256(entropy | 0x00000001)`,... – Coding Enthusiast Jul 3 '20 at 16:10
• @CodingEnthusiast Could you expand that into an answer, please? I can't understand how these keys relate to the parent keys, as they do not depend on them at all. In particular I want to derive child public keys from just a parent public key, knowing that the owner of the parent private key can derive the associated child private keys. – fadedbee Jul 4 '20 at 6:10
• It is a very very weak way of deriving child private keys from an initial entropy. If deriving pubkey in a weak way is desired then a similar scheme to BIP-32 for non-hardened children could be used to compute `SHA256(parentPubKey | index)` where child private key is the `parent+child % N` – Coding Enthusiast Jul 4 '20 at 8:35
• Is `parentPrivKey+index % N` the private key for `parentPubKey | index`? (I cannot see how the unreversable SHA256 can help here at all, but that may well be my lack of knowledge.) – fadedbee Jul 4 '20 at 8:47