Quote from: cypherdoc on February 21, 2012, 04:22:21 AM

so how do u get priv/pub keypairs out of the root key/Bitcoin address?

I picked a sub-optimal construction, and wished I had talked to gmaxwell and sipa before I commmitted myself to it, because I like theirs better. However, there's nothing wrong with what I did, it's just that it can be a little slow, and theirs has some nice properties (like random access). I will be adding support for their method in Armory and deprecating mine (eventually). Until then, here is both algorithms:

Let the root address be considered keyIndex=0, C be the chaincode, and O be the order of the elliptic curve group:

Mine:
M = doubleSHA256(PublicKey(i)) XOR C
PrivKey(i+1) = (PrivKey(i) * M) mod O

gmaxwell and sipa use HMAC construction; || represents concatenation
PrivKey(n) = SHA256( C || SHA256(C || PubKey(0) || n) )