Hey there,
HKD stands for Hierarchical Key Derivation, e.g. BIP32 [1] or ChainKD [2].
Alternatively known as "blinded keys" per Tor's draft [3].
All these schemes generate a scalar to be mixed with the parent public key P
using an index or nonce i:
h(i) := Hash(P || i || stuff)
The first two schemes add a derivation factor (multiplied by the base point)
to the parent pubkey, while the Tor's approach is to multiply the parent pubkey
by the factor:
Child(i) := P + h(i)*G // BIP32, ChainKD
Child(i) := h(i)*P // Tor
Last time I asked Pieter Wuille (BIP32's author) a couple years ago about their
choice,
his reply (if I recall correctly) was that scalar multiplication for a base
point
is more efficient than for an arbitrary point.
I wonder if there's a difference in functionality if we add the factor (a-la
BIP32) or multiply (a-la Tor).
Maybe some weird ZK schemes benefit from blinding/derivation via multiplication
instead of addition?
[1] https://github.com/bitcoin/bips/blob/master/bip-0032.mediawiki
[2] https://chain.com/docs/protocol/specifications/chainkd
[3]
https://gitweb.torproject.org/torspec.git/tree/proposals/224-rend-spec-ng.txt#n1979
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