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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.)

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  • SHA256(entropy | index). 1st key = SHA256(entropy | 0x00000000), 2nd key = SHA256(entropy | 0x00000001),...
    – Coding Enthusiast
    Commented Jul 3, 2020 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
    Commented Jul 4, 2020 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
    Commented Jul 4, 2020 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
    Commented Jul 4, 2020 at 8:47

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